Powerball lottery - Boosting jackpots to boost sales

The January 2016 jackpot reached $1.5B because the carried-over jackpot increased faster than ever before in the streak of 19 drawings without winner. To show this, the table below compares the $1.5B jackpot to the $564M jackpot of February 2015, which concluded a streak of 20 drawings without winner.

Streak	Jackpot amount ($M)
	Jan'16	Feb'15
15	255	208
16	300	230
17	334	261
18	529	289
19	948	317
20	1,500	395
21	-	564

Streak	Tickets sold (M)
	Jan'16	Feb'15
15	26	24
16	41	28
17	54	29
18	176	37
19	440	48
20	635	73
21	-	190

The February 2015 jackpot reached half a billion dollars after 20 consecutive drawings without winner. The January 2016 jackpot reached three times that amount in one drawing less. In fact, it is surprising that the January 2016 jackpot could triple from $529M to $1.5B in two drawings. What happened?

Funding Powerball's jackpot

To understand how jackpots build up, we have to understand some of the inner workings of the Powerball lottery. The 2015 Powerball group rules published by the Multi-State Lottery Association (MUSL) managing Powerball are sometimes ambiguous, so this section may not be perfectly accurate. To keep it simple, the Power Play option is ignored.

Although MUSL runs Powerball, each state lottery is in charge of advertising, selling tickets, and giving non-jackpot prizes to their respective winners. Each state lottery keeps half of ticket sales, which probably directly goes into the state's budget. The other half funds MUSL's four accounts: the prize pool, jackpot pool, bootstrap pool, and reserve.

The prize pool (aka Powerball Set Prize Pool) is filled weekly by each state lottery to pay the small prizes. Ignoring Power Play, it should receive at least $4 / 38.32 + ... + $1M / 11.7M = 32 cents per ticket to be able to pay out the prizes. In-between two drawings, its balance is close to zero.

The jackpot pool (aka Grand Prize Pool) holds the jackpot money. When the other pools (usually the bootstrap pool) need to be topped-up, up to 5% of sales is transferred from it to them. By the time the jackpot reaches $110M annuity/$70M cash, ticket sales have filled all other pools, and the jackpot pool receives the full 68 cents per ticket.

The bootstrap pool (aka Set-Aside Account) backs up the jackpot pool when the jackpot is won at the beginning of a streak. For example, every streak starts with a jackpot of $40M annuity/$25M cash. These drawings usually sell 10 million tickets, ie $20M in sales. The state takes $10M, small prize winners $3.2M (32 cents per ticket), and so there is only $6.8M left to pay the $25M jackpot. The extra $18.2M comes from this pool. Fortunately, 10M tickets have only 4% chance to win the jackpot, so the bootstrap pool is rarely emptied. It is filled by "taxing" the jackpot pool 5% of sales, ie 10 cents per ticket, until it has reached its $20M cap.

The reserve (aka PRA and SPRA) exists so that MUSL does not get bad press for not paying winners their full prize. This could happen because of a system error, miscalculation, or because all other pools are depleted. When the reserve itself is depleted, prizes stop being fixed (eg $1M or $7) and become parimutuel to prevent breaking the bank. Until the reserve reaches its $40M cap, filling it takes precedence over the other pools.

January 2016 vs February 2015

To illustrate how these pools work, we can use the streak of 20 drawings leading to the jackpot of $1.5B annuity / $930M cash as an example. The streak starts on November 7, when 374k 2-dollar tickets and 101k 3-dollar tickets won small prizes. Ticket sales (estimated) are 24.87 * (374k * $2 + 101k * $3) = $26M. The state takes $13M, and small-prize winners $4M. Let's imagine that the reserve is full. The jackpot had reached $90M cash on November 4, so the bootstrap pool should be full, but to illustrate its workings, let's assume it is empty. Since the jackpot is not won, the bootstrap pool receives 5% of sales = $1.3M. The jackpot pool receives the remaining $7.7M. This process goes on until December 19, when the bootstrap pool reaches its $20M cap. All these numbers are listed in the first table below.

On closure day, January 13, when the $930M cash jackpot is won, the ten-week streak has raised a total of $3.4B. Around $623M has been paid to small-prize winners, $930M shared between the jackpot's three winners, and $1.7B kept by the states. As for the February 2015 jackpot, the states only received $679M in roughly the same amount of time (ten weeks and a half). Judging from these two jackpots only, the 2015 tweaks seem to have tripled Powerball's profits.

Pool amounts (in $M) leading to the $1.5B annuity jackpot

date	jackpot (cash)	ticket sales	prize pool	jackpot pool	bootstrap "tax"	bootstrap pool
11/7	25	26	4.2	7.6	1.3	1.3
11/11	32	22	3.0	15	1.1	2.4
11/14	38	28	4.1	23	1.4	3.8
11/18	44	24	7.7	26	1.2	5.0
11/21	50	27	6.4	32	1.3	6.3
11/25	57	28	3.1	41	1.4	7.7
11/28	63	28	4.8	49	1.4	9.1
12/2	69	32	3.7	59	1.6	10.7
12/5	80	38	8.2	68	1.9	12.6
12/9	91	33	5.5	78	1.7	14.3
12/12	103	38	7.4	88	1.9	16.2
12/16	113	39	6.2	99	2.0	18.2
12/19	127	51	9.6	113	1.8	20
12/23	143	58	9.9	132	full	20
12/26	161	54	6.3	153	full	20
12/30	189	84	14	181	full	20
1/2	210	118	21	219	full	20
1/6	333	375	66	341	full	20
1/9	597	963	159	663	full	20
1/13	930	1,374	274	1,077	full	20
closure	930	3,440	623	0	NA	20

Pool amounts (in $M) leading to the $564M annuity jackpot

date	jackpot (cash)	ticket sales	prize pool	jackpot pool	bootstrap "tax"	bootstrap pool
12/3	26	22	2.2	7.7	1.1	1.1
12/6	33	26	4.4	15	1.3	2.4
12/10	39	25	4.1	22	1.2	3.6
12/13	46	27	4.8	29	1.3	5.0
12/17	52	25	4.4	36	1.2	6.2
12/20	59	32	10.2	40	1.6	7.8
12/24	65	35	9.2	47	1.8	9.6
12/27	72	32	10.3	51	1.6	11.1
12/31	78	38	8.4	59	1.9	13.1
1/3	85	35	4.6	70	1.7	14.8
1/7	95	35	5.0	81	1.8	16.6
1/10	105	41	10.2	90	2.1	18.6
1/14	114	38	7.0	100	1.4	20
1/17	126	48	16	108	full	20
1/21	135	52	12	122	full	20
1/24	150	62	18	135	full	20
1/28	170	60	11	154	full	20
1/31	188	74	15	176	full	20
2/4	206	100	18	209	full	20
2/7	257	151	30	255	full	20
2/11	381	401	74	381	full	20
closure	381	1,358	278	0	NA	20

The Powerball tweaks have only been implemented for three months now. With little data to rely on, it is not guaranteed that profits will stay triple what they were before. Profits may have soared this time because of the buzz surrounding the record-breaking jackpot. The next billion-dollar jackpot may see mediocre sales because people got tired of Powerball or found other games to play. Will the next billion-dollar jackpot generate a billion dollars in profits? Will players adapt to the new odds? We will probably find out within a year.

Powerball lottery - Rules and patterns of play

On January 13 2016, the Powerball lottery made the news by reaching a jackpot of $1.5B, the largest in US history. Lotteries are interesting because they are a gambling game used by governments to raise funds without raising taxes. Let's have a closer look at the rules, odds, and profits made by lotteries, using Powerball as an example since it's one of the lotteries with highest sales.

Basics

The official simplified rules stipulate that five white balls are drawn among 69, and one red ball among 26. The jackpot is won by matching all five white balls in any order and the red Powerball. The jackpot starts at $40M, and increases every drawing by at least $10M until won. Combined with the minuscule odds of being won, this mechanic makes it possible for the jackpot to become huge. The match-5 prize, worth $1 million, is won by matching five white balls in any order. Consolation prizes, worth $4 to $50k, are won by matching at least three white balls or at least the red Powerball. Tickets cost $2. Players can buy as many tickets as they want.

Drawings happen twice a week, on Wednesdays and Saturdays. The boxplot below plots the median number of tickets sold per drawing. Data consists of drawings with jackpots below $200M, from April 13 2013 (right after California joined the Powerball group) to January 20 2016. Drawings sell an average of 14.0 million tickets on Wednesdays, versus 15.4 millions on Saturdays (p=.0001).

Jackpots predict sales

Ticket sales are very predictable from the jackpot amount. This is shown in the graph below. For jackpots under $300M, the number of tickets sold increases quadratically with the jackpot. Above $300M, we do not have enough data to build a model, but the trend seems logarithmic, probably because ticket sales grow much faster than the jackpot.

Optional features

Power Play is an optional feature that launched in 2001. As of 2015, it multiplies the value of non-jackpot winnings by 2 to 10 by paying an extra $1 per ticket. A wheel determines the multiplier for each drawing (24/43 chance for 2x down to 1/43 for 10x). Interestingly, Power Play used to have a 1x multiplier, but it was removed within a year. Why have a bonus that is sometimes not a bonus?

Random picks: Players can choose their 6 numbers themselves, or have the computer pick them randomly. About 70% to 80% of purchases are computer picks.

Annuity vs cash

Jackpot winners can choose to receive their share of the jackpot immediately through a 30-year annuity, or immediately in cash. When winners choose the cash, they immediately receive the advertised cash amount, which is usually 60-70% the annuity amount. That is why the lottery organizers advertise the jackpot's annuity, and not its cash.

When winners choose the annuity, they immediately receive 1/30th of the cash amount. The organizers invest the rest into government bonds or securities. Every year for 29 years, they sell 1/29th of the bonds and give the proceeds to the winner, with a 5%-interest per year. Choosing the annuity prevents people from blowing through all their money quickly. Yet only one jackpot winner out of 72 chose the 30-year annuity from 2011 to 2015.

Hearthstone - luck-based mechanics

I covered Hearthstone in a previous post, but there is more to say. Hearthstone is a collectible card game (CCG) for Windows, iOS, and Android, by Blizzard. Its gameplay is very similar to Magic: The Gathering, and its theme is World of Warcraft. It is free to play, but players can purchase coins, which are spent to acquire card packs or unlock certain cards. Hearthstone launched in March 2014.

Influx of new players

Hearthstone has seen 30M players and generated $250M as of May 2015. Hearthstone had 25M registered players in January 2015. That means 15% of the player base (5M players) have been playing for less than 6 months. This is very good: a constant influx of new players keeps a game alive.

Luck-based mechanics

Many mechanics in Hearthstone are based on luck. Very few mechanics help manage that luck.

Mechanics involving luck in Hearthstone

Mechanic	Description	Solution
Topdeck	Drawing by luck the right card at the right time	Filtering cards like Tracking
Starting hand	3-4 cards out of a deck of 30	One Mulligan (redrawing unwanted cards)
Card effects	E.g. deal 2 damage to a random enemy, or get a random beast.	Anticipating all possible outcomes
Card packs	After 2 months, most cards from packs are already owned and redundant.	One card per pack is guaranteed to be rare or above. Convert redundant cards into crafting dust. Collect golden cards.
Match-making	Random opponent decks that may be very (in)effective against yours	Tavern Brawls with pre-made decks. Best-of-3 in championships.
	At rank 15-20, opponent skill varies greatly.	Provide incentives against bottom-feeding.

When playing for skill, all luck aspects can be annoying. In my experience, topdecking and random card effects have been the most frustrating: a strategy works, it's about to win against an opponent, but the opponent draws the right card, or receives by chance the one perfect card to counter the strategy. Some decks such as Oil Rogue even rely on making a combo of 4 particular cards in the same turn. If these cards are in the starting hand, these combos fire after a couple turns, and the loser feels like the game was over before it even started. Unlike in Dominion, strategy in Hearthstone is too heavily mitigated by chance.

Diablo's randomness: competition vs variety

In Diablo 3, randomness is everywhere: in item rolls, maps, monster types, critical hit chance, and more. This randomness bothers competitive players. Greater Rifts (GR) are the platform where competition takes place. GR are random in several ways: their maps are generated randomly, their monsters picked randomly, and the monster density also happens to be random. Therefore, ranking high on the leaderboards is mostly a matter of luck, not skill.

Blizzard probably launched the first season as a sort of test drive. They figured players would still find some exploits during season 1. I think Blizzard learned many lessons from season 1. I thought one of them was that they should level out, or even remove, the sources of randomness in GR. For example, I really expected that they would remove pylons from GR. Others expected the same. But Blizzard has decided to keep pylons inside GR for season 2. I was bewildered: why keep a luck-based mechanic in a competitive setting? I can now see at least two reasons.

One reason is that Diablo 3 is not about player skill, but about grinding. I think looting a full set of decently-rolled gear takes around 50 hours. Then the game is all about looting better-rolled gear and acquiring decently-rolled ultra-rare gear such as Tasker and Theo or Wand of Woh (both below 0.2% chance from Kadala). Crafting a good Hellfire Amulet, another end-game yet crucial piece of equipment, can take months. The hardcore players who compete on the leaderboards have acquired all this gear. While they may object to the contrary, they love grinding, or they would never have obtained such great gear. Thus re-rolling GR for slow and benign Risen Deads instead of fast and dangerous Winged Assassins may be less boring to them than it is to me.

Another reason for keeping randomness in a competitive setting is variety. The developers admit that they use randomness in Diablo III to increase the replayability, Greater Rifts included. Pylons can be a hell of a lot of fun to encounter in game, and that’s one of the big reasons we added them to Greater Rifts. The great majority of players do not compete seriously for the leaderboards, so they actually really enjoy the occasional Conduit Pylon in GR. Moreover, even competitive players may become bored if the GR were completely standardized: they would always know where to go, which monsters to avoid, and so on.

In short, Blizzard is probably right to keep pylons inside GR, but they should definitely look at 1) leveling out monster density across GR, and 2) leaderboards that measure player skill by their ability to deal with randomness.

Diablo 3 - item sets

Modern item games like Diablo 3 (D3) use a mechanic called sets: when used together, certain items unlock particular bonuses. For example in D3, Litany of the Undaunted increases attack speed, The Wailing Host increases crit chance, and used together they give 15% extra gold from monsters. Item sets is an old mechanic - the Diablo 2 expansion already had some in 2001.

Sets in D3 are a great mechanic for at least two reasons. First, sets let developers encourage the use of certain skills. Since the bonuses from set items nearly always provide more damage than regular non-set items, players use them. For example, the Marauder set for Demon Hunters requires the use of sentries, a skill that would not be used otherwise because its AI for picking a target is unpredictable. Second, set items are a great mechanic also because they give players a goal. When I dropped my first set item and saw the set bonuses, I immediately wanted other items in the set.

Sudden increase in power

End-game starts after reaching level 70. Reaching level 70 by yourself takes roughly 15 hours. Difficulty from then on can be measured by the Greater Rift (GR) level your character can reach. Set bonuses are so powerful that they make your character jump multiple GR levels at once. For example, going from 5 set items to 6 can double your character's effective damage or toughness, and make you reach 5 or 6 GR levels higher. This explains why the Ring of Royal Grandeur, which reduces the number of items needed for set bonuses by 1, pretty much a wild-card for all your sets, is such a game-changer. These sudden increases in power sometimes surprise players, but I think each bump makes them suddenly feel very powerful. Interestingly, back in 2013, sets used to be as good as non-set legendary items.

Vague descriptions or hidden mechanics?

The descriptions of D3 set bonuses are often vague, and require the player to check the forums and Youtube videos for details. Here are two examples.

Marauder set

This is a Demon Hunter set. The 2-piece bonus is straightforward: it gives 500 dexterity (on top of the approximately 500 dexterity already contributed by each set piece).

The 4-piece bonus makes the Companion skill call all possible companions (instead of only one). Do passive effects from the Companion skill (e.g. the boar increases life regeneration) apply as well? And do all active effects trigger when I use the skill? The answers are not written in the description, but people figure it out quickly by trying.

The 6-piece bonus reads: Sentries cast your equipped Hatred spenders. After trying it out, I realized that sentries have a different rate of fire for each spender: Cluster Arrow (massive area damage) seems to happen only every 5 shots, whereas Elemental Arrow (small multi-target damage) the rest of the time. Looking at high-level Demon Hunters, most wear Tasker and Theo, which increases the attack speed of your pets by 40-50%. Are sentries pets? (Yes!) And how can I make my sentries use Cluster Arrow more often? (You can't!) Theorycrafters figured it all out by analyzing game frames one by one and sharing their findings. But is the average player supposed to read the forum to improve their character?

Zunimassa set

This is a Witch Doctor set. The 2-piece bonus gives 250 intelligence and grants 30 Mana per Kill. Is it only when my character performs the killing blow on a monster? Does it also work when it's one of my pets? Does it also work when it's another player?

The 4-piece bonus reads: Your Fetish Army (FA) lasts until they die. This is straightforward, and it made me think about the passive skill Fetish Sycophants (FS). FS seems to combo well with FA: When you hit enemies with your spells, you have up to a 10% chance to summon a dagger-wielding Fetish to fight by your side for 60 seconds. There are several problems with this apparent FA-FS synergy.

First, why the up to? What makes the rate be less than 10%? That is where theorycraft comes to the rescue. The community found out that one can have at most 15 active FS at the same time. So the rate of FS trigger is 10% until 15, at which point it becomes 0%. The description of FS should also mention this cap of 15.

A second problem is the easy confusion between the two types of fetishes. 1) Witch Doctors can have many pets: a Gargantuan, zombie dogs, FA fetishes, FS fetishes, and mimics. FA and FS are both fetishes, so intuitively, they must benefit from the same bonuses. 2) Why excluding FS from the 4-piece bonus when the effect from the Carnevil helm applies to both FA and FS? 3) The distinction between FA and FS is not for game balance: in practice, it's very easy to maintain 15 FS active all the time by speeding through monsters.

Why so vague?

I can see several reasons:

• Practicality: the developers want to be able to modify the bonus (through hotfix or patch) without modifying the description.
• Brevity: a precise description may require too much space in the item tooltip.
• Practice: figuring it out by trial is more visceral than by just reading the description.
• Theorycraft: explaining everything spoils the fun of theorycrafters.

Uselessness, sub-optimality, and combinatorics

Some sets are clearly underpowered compared to others. The Witch Doctor Invoker set and the Demon Hunter Shadow set are only useful when your character gets hit. Sadly, in D3, the best defense is offense: the goal is to kill monsters quickly enough that they don't kill you. Therefore these sets end up never being used (except the 2-piece Shadow set in hardcore mode, maybe?).

The Natalya set is not useless, but rather suboptimal. Both the 2-piece and 3-piece bonuses increase damage slightly and enhance mobility (more discipline means more Vaulting). The 4-piece bonus reduces the cooldown of Rain of Vengeance by 2 seconds for each enemy you kill. RoV has a base cooldown of 30 seconds, and does 1000% area damage for 5 seconds, so the set seems very interesting. In practice however, it is difficult to keep monsters grouped in an area for 5 seconds. So while some players use the 2- and 3-piece bonus, nobody cares about the 4-piece bonus. I wonder if the set would be more used if the cooldown was reduced by 2 seconds for every enemy hit (instead of killed).

ArcheAge boasts 120 classes, but it's only because players can pick 3 skill trees among 10, ie C(10,3) = 120 different combinations of skill trees. I don't think that all combinations are efficient, but ArcheAge achieves such diversity simply by leveraging combinatorics on 10 coherent sets of skills. In D3, a player using a Demon Hunter can pick 6 active skills among 24, so that's a total of C(24,6) = 134k different builds. Add to this that each active skill has 4-5 runes, and that there are also another 4 passive skills (5 if we count the Hellfire Amulet) to pick among 18. That's billions of combinations! Yet the only sustainable Demon Hunter builds actually played are minor variations around the same 6 skills. That is because the Marauder set forces players to pick these skills. Moreover, I really liked combining multiple 3- and 4-piece sets together, but the 6-piece Marauder took all the spots. I wish D3 had 1) more 4-piece sets and fewer 6-piece sets, and 2) combinations between sets, not just between sets and legendary items (e.g. Marauder and Tasker and Theo)

Diablo 3 - the item game

In item games, the main goal of players is to continuously upgrade their gear. Diablo 3 (D3) is the perfect example: kill monsters in order to drop better gear in order to kill monsters faster. Bungie just released Destiny, an item-game FPS budgeted with half a billion dollars. Yet Destiny could learn from Diablo 3. So here are some thoughts about the item game in D3.

Prevent farming ...

In D3, like in D2, the drops are completely random: with a few exceptions, nearly any item can drop from any monster or wreckable object (e.g. jars). The odds are just higher for harder monsters, and way lower for wreckable objects. The exact drop rates are secret (except the 10% legendary drop rate from Kadala). This secrecy has led to various rumors and tinfoil hat theories about how loot can be influenced.

D3 has, or used to have, farming spots such as the Decaying Crypt, but they were mostly for XP, not for drops. In D3, farming boss monsters actually brings fewer drops than farming normal or elite monsters. This contrasts with Diablo 2, where players were grinding bosses like Baal or Diablo for XP and loot. So in a way, the grind in D3 is less boring than in D2.

... Yet allow farming

As of October 2014, there are 2 exceptions to what I just wrote: 1) bounty rewards like RoRG or Helltrapper, and 2) Hellfire Amulet.

The RoRG was introduced in February 2014. It is a mandatory item to reach the game's highest difficulty levels. Players have to camp Act-1 bounties to get one with good rolls. To farm as quickly as possible, players join co-op games to split farm: instead of spending 15-20 minutes completing the 5 bounties together, they each complete a bounty in 5 minutes. I am surprised that the developers did not see it coming: split farming is very clearly not how we want players to play the game. Yet nearly a year later, they still have not changed the bounty system.

The Hellfire Amulet is not as mandatory compared to the RoRG. But its bonus is so useful that all of the top players have it. Farming it is somewhat more fun than farming for RoRG, since it is a quest in itself: a) hunt for the 4 Keywardens on the game's largest maps to obtain 4 keys, b) combine the 4 different keys into a portal, c) kill 2 super bosses at once, a somewhat more difficult task than the Keywarden hunt, and d) combine 4 super bosses' loots to obtain a Hellfire Amulet.

The Reaper of Souls expansion

From launch in May 2012 until the retirement of the Auction House (AH) in February 2014, players were mostly buying their gear from the AH, and sometimes grind-crafting it. They nearly never dropped it themselves. Legendary weapons had 7-8 affixes. After the AH retired, Loot 2.0 arrived, and the expansion Reaper of Souls (RoS) shortly after that. Legendary weapons now have 4 primary and 2 secondary affixes. Secondary affixes do not matter much (e.g. more XP when killing a monster), so RoS drastically reduced the item entropy.

The expansion also reminded me of Blizzard's somewhat elegant solution to a common MMO problem. Most MMOs in the early 2000s had the same problem: players who have been playing for a year have too much of a head start compared to players who have been playing for 3 months. New players are hopeless, especially in PvP situations. World of Warcraft solved this problem with what I call expansion gating: WoW vanilla capped the character level at 60 and item level at 92. Until the first expansion came out to increase these two caps, players were gated there. The advantage of expansion gating is that it gives the same chance to old and new players. The main drawback (if any) is mudflation. Diablo 3 is no different: level-70 items have twice more DPS than level-60 items. Thus when the expansion launched, players threw away all the gear they had acquired before.

Few links to other end-game activities

Item games have a great loop, but it is not enough in itself. D3 launched in May 2012. The Auction House (AH) launched in May 2012 too, so players could play two games in one: the action RPG and the auction game. Note that you did not need to play the aRPG to play the auction game, but you did need to buy gear off the AH to play the aRPG well. Had it been the opposite, I think the game would have been much better.

In July 2012, the developers realized that the item hunt is just not enough for a long-term sustainable end-game. Since launch, the game also allowed players to hunt for achievements and start new characters (in softcore or hardcore). In August 2012, the developers added the leveling up grind through 100 Paragon levels. Every Paragon level increased the chance to drop an item and the amount of gold dropped by 3%. In February 2014, Paragon levels became infinite, and the 3% bonus was removed. Clans and communities were also added in February 2014. Since August 2014, players can compete on the greater rift leaderboards, and start new seasonal characters (in softcore or hardcore). Interestingly, the item game is completely independent of all other end-game activities (except the AH and the original 100 Paragon levels increasing magic find and gold find). In other words, the item game of Reaper of Souls could be directly copied into another game without having to also copy the other activities.

Ken Lobb FDG 2014 keynote

Ken Lobb designed Golden Eye and Killer Instinct in the 90s. Here are notes from a keynote he gave at the FDG 2014 conference.

Having an extensive knowledge of games is mandatory for game designers, because they provide a common vocabulary to talk about games.

In the late 80s, teams rolled their own tools. Nowadays, AAA teams still have the not created here problem and waste a lot of time reinventing the wheel. That's why indies using Unity or Unreal can save on costs and take a bite at AAA.

The most important tool in game development is the game build, because it is how the game improves, little by little. Next comes the schedule, ie what to do next. Finally comes the spec and docs, because they change all the time. Microsoft has the process mastered. In fact, Microsoft is too good at planning: they always ship what they speced, and not exactly what they should create. The industry in general, and Microsoft in particular, sign games that cost way too much money.

Difficulty: games have shifted from lose vs win, to win vs big win vs epic win. now in call of duty, high kd ratio is winning. dying is not too bad. before in golden eye, die means restart whole 10min level. now, focus on positive reinforcement rather than punishment.

Major game design issues:

• Tutorials are hard to build right. Should players be reminded of mechanics they may already know, or should they instead be taught from scratch? The Zelda series have great tutorial design: they simply give the player the tool, and teach by giving more and more difficult challenges that require using that tool. Achievements can also encourage a particular behavior.
• Cheating is OK. 90% of Xbox players are also on a second device when they play. Players use Youtube, watch Twitch, and look for cheats and FAQs all the time. Procedurally-generated or randomized content can curb this practice down, but a real solution may involve the game itself showing tips or videos from the players who passed an obstacle to those who are stuck.
• Making a game noticed on app stores/platforms is difficult. Advertising and charts do not target particular players. Word of mouth is more effective, but how does it start? Maybe app stores could recommend games to hardcore players, which would trickle them down to their friends? [This may have an answer: according to Wooga, it takes $250k to reach the first spot on the App Store]

Diablo 3 - Randomized content

A lot of game content in Diablo 3 is determined randomly. Arguably, more randomness means more diverse content and therefore players less likely to become bored by repetition. But randomness also has drawbacks.

Maps

Maps are generated somewhat procedurally. Some elements like the map borders remain constant, but events and dungeon entrances are picked randomly among a pool and placed randomly in predetermined places.

Maps like The Den of the Fallen sometimes have loops, which is annoying: players kill monsters on their way, but when they realize they have been looping around, they go back on their way without any monsters to kill. It is a waste of time. A solution could involve using heuristics to prevent loops.

A Greater Rift (GR) is a dungeon in which players race against time. The higher the level of a GR, the tougher its monsters. GR is a competitive activity: leaderboards show the teams who achieved the highest GR levels. Problem: the GR map is picked randomly; sometimes it is a maze, sometimes it is linear, and sometimes it has loops. The randomness does not make for a fair competition. One solution would be to remove maze maps from the selection. Another solution would involve keeping the map and monsters constant, and make one leaderboard per map. It would be pretty much like a racing game.

Elite affixes

Elite monsters can have up to 5 affixes. Affixes have 3 categories: crowd-control such as Vortex, defensive such as Extra health, or offensive such as Desecrator. These affixes are picked randomly, with a couple heuristics making sure that an elite can have at most one crowd-control affix and at most one defensive affix. Some affixes such as Invulnerable Minions were so annoying that they were removed from the game altogether.

Still, some combinations remain more deadly than others. For example, elites combining Molten (they burn where they walk on), Fast, and Horde (create 8-10 Molten and Fast minions) are the bane of melee characters.

Gear

In the original Diablo 3 (also known as D3v for Diablo 3 vanilla), loots were completely random. For example, a Wizard could drop a mace only Barbarians can use. Enters the Auction House (AH for short): the Wizard sells the mace on the AH and, with the money received for it, buys a better wand from the AH. Trading through the AH worked well from launch in May 2012 until August 2012 when the designers realized that the AH can short circuit the natural pace of item drops, making the game feel less rewarding for some players. Indeed, players could obtain second-best gear in only a couple days, play for a week, get bored for not progressing, and leave the game. Conclusion: completely-random loot with an AH for trading does not work.

Loot 2.0 landed in the game just before the Reaper of Souls expansion. Loot 2.0 has 3 parts: 1) little to no exchange between players (to prevent gold farming), and no AH, 2) loot is targeted to the player, ie Wizards only drop Wizard gear, and 3) the Mystic lets the player reroll an attribute on any piece of gear. Six months after the release of the expansion, this has been holding fine.

Improving the end-game of social strategy games

Improving the end-game of social strategy games

I removed Clash of Clans (CoC) from my iPad on August 20, 2014. The game had just reached two years old, and I had been playing it since February 2013. I played very actively (2-3 hours per day on average) until December 2013, then considerably slowed down (1 hour per week).

No new content

I think I slowed down, and eventually stopped playing mostly because no significantly new content was introduced. New content mattered a lot to me because I had reached Town Hall 10, the very end of the game, for many months. So far, the game has received four updates in 2014.

Month	Description
January	Introduced Hero abilities, which are not really a new gameplay feature, but rather a design fix to encourage players to use and upgrade their heroes. Great, and perhaps even necessary, but no impact on battle strategy or base design.
April	Introduced Clan Wars, a feature asked by players since the game came out. My clan was very excited, but we stopped Clan Wars after a couple weeks. We realized that the match-making algorithm alternated pairing our clan against once a much stronger clan, once a moderately weaker clan. Clan Wars require a lot of time and in-game resources, so we kept asking for enemy clans, but only attacked when we were sure to win. After a few weeks, we realized the Clan Wars rewards were not worth the frustration, so we stopped match-making.
May	Mostly usability tweaks.
July	Improved Hero abilities. Once again, this was more a design fix to encourage the use and upgrading of Heroes than a new feature.

Moreover, in these four updates, the Hog Rider received three nerfs, but my base still got trampled by mass-hog armies. (Yes, anti-hog base designs exist, but these designs are very vulnerable to air attacks). The Valkyrie was buffed twice, but it still was not enough to make her useful for her cost. To sum up the last 8 months, no new mechanic, be it a unit or a tower, was introduced, and I did not find the balance tweaks adequate.

Lessons for social strategy games

Troop synergies

The game was released with 10 basic units that make sense when used together. For example, the Giants are slow and target defenses so that the Healer can follow them without being hit. These synergies are expected: the team had time to iterate and polish before launch. But introducing new troops after launch is tricky: the new troops must 1) have an interesting gameplay element, 2) complement existing troops, and 3) keep existing troops useful.

The Minion is a perfect example: it is cheap and flying. This makes it a great complement for farming with Barbarians and Archers (called the BAM strategy). It is also great for high-level PvP when paired with Balloons (Balloonion strategy). And since it costs dark elixir and has low HP, it can't be used by itself.

The pricey Golem is another great example: it synergizes well with Wizards and Pekkas (GoWiWi strategy), which are necessary troops in high-level PvP. The Golem's production stats are perfect: 45 minutes to make, and a cost of 2.5 hours-worth of dark elixir, which is the same as Pekka. The Golem was clearly designed to be trained in parallel of Pekka. Plus Supercell must have made a lot of money from players gemming it!

On the other hand, the moderately expensive wall-jumping Hog Rider does not complement any other troop. Neither does the Valkyrie. Interesting ideas, but no synergy! Supercell keeps trying to fix them, so they may have realized that. Or maybe Supercell abandoned them completely, and has been working on more troops, such as the Spider, Centaur, or Yeti, which have not been released yet, but were leaked in July 2014.

More things to do in the end game

As the Town Hall levels go by, so does the average duration of building upgrades. For example, upgrades take 3-10 hours at TH3, 1-3 days at TH6, and 7-14 days at TH10. By TH10, the player should have 5 Builders, so the average time between two building upgrades is still 2-3 days. During these 2-3 days, players come back to the game only because their troops are ready for battle, not because they have something to do with their base. But by TH10, players have spent months being progressively conditioned to come back for their troops and not their base. So they still come back, but more and more reluctantly, since the rewards are less and less frequent. At some point, they unlearn the habit of coming back to play: what's the point when nothing seems to be happening? They eventually stop playing.

Possible solutions involve shortening upgrade times or providing more builders, but both may seem like Supercell would lose money. The game should at least give players things to do with their buildings (beyond collecting resources twice a day). The Bomb very short upgrade times have been a step in that direction. A crafting system like in Monster Legacy, or Angry Birds Epic, but applied to strengthening buildings, or increasing towers' rate of fire, may increase the game's lifespan even more.

List of tower defense games

I had started to compile a list of tower defense games a couple years ago, but never managed to finish it. The goals were to 1) list the basic gameplay elements that define the tower defense genre, 2) spot original gameplay elements that have made the genre progress, and 3) track the history of the genre, much like what has been done for shmups.

Name and URL	Release date	Image
Players	Platform
Bosses	Path
Comments
Backyard Monsters	early 2011
single player + Facebook friends	Flash on Facebook
Champion units never die	Free path
Receive and donate monsters from/to your Facebook friends. Send your troops against the base of another player to steal their resources. Half-cloned by Clash of Clans in 2012. By Casual Collective (now Kixeye).
Bubble Tank Defense	2009
Single player	Flash
Has bosses	Free path
Mega towers are a combination of 4 adjacent normal towers. Tower upgrade is a tree: all towers start as basic towers, then they become zone, slow, specialize against ghost, etc.
Canyon Defense	2007
Single player	Flash
no	Fixed path
Unlock towers by completing missions such as building 15 towers or acquiring $1000. Developed by Russian studio Iriysoft.
CreepSmash	2008
2 to 4 players	Java
no	Fixed path
6 tower types, each with 4 upgrade levels. Player can specify AI for each tower (eg. target creeps with fewest HP). Receive income every 15 seconds. Increase income by 10% of the price of the creeps you send to your left neighbor. Receive creeps from your right neighbor. Green creeps regen life, white are immune to slow, blue are fast, red have lots of HP. Winning strategy: sell towers to send more creeps to increase your income faster than other players. Attack-defense gameplay. 4-player games, quickly turn into 2v2. Developed by a group of German students. The community is mostly German. open source.
Cursed Treasure	May 2010
single player	Flash
Has bosses	fixed path
3 families of towers: Demon (fire AoE or burn DoT), Orc (poison DoT or strong single-target attack), and Undead (freeze, fear, or slow). Towers gain XP and level up by attacking creeps. Tower effects change when they level up. Creeps are assassins (hide temporarily), crusaders (block damage), monks (heal other creeps), and other medieval characters. Each level completed grants the player XP used to level up to acquire and level up passive skills such as more gold at the start of the level, more gold per creep, reduced tower costs, or increased tower range or damage. Player can use 3 active skills: cut tree to place tower, temporarily double the fire rate of all towers, and splash meteor damage in an area. Developed by Russian studio Iriysoft.
DemonRift TD	Sep 2011
Single player	Flash
2 Bosses	Fixed Path
4 types of towers (swordsman, archer attacks long-range but not short-range, knight can chase fast enemies, and golem can stun and block up to 5 enemies). Command points are generated over time and when killing enemies, and are used to buy or upgrade units. Upgrades only add more creatures to a tower.
Desktop TD	release?
Single player	Flash
Has bosses	Free Path
Creeps go from top to bottom or from left to right. Mazing/juggling matters a lot. By Casual Collective (now Kixeye). Spawn, flying, and many other kinds of creeps.
Dungeon Defenders	2011
single-player	Unreal Engine
No bosses	Fixed Path
3D. Originally a showcase of the Unreal Engine. Source code available.
Flash Element TD	Feb 2007
Single-player	Flash
Has boss?	Fixed path
Start the first level with the 3 basic towers. Kill enemies to earn a bit of money to upgrade towers. At the end of each wave, earn 10% of your current money (+5% per skill point spent in a certain research skill). Earn Wood every 8-10 waves to unlock towers (earth, fire, water, and combo of the 3), skills, or increase your life. Also known as 3d tower defense.
Garden TD	release?
Single player	Flash
Has bosses	Fixed Path
Spitting cactus are overpowered, gnomes are useless.
Hold the holy pig	release?
Single player	Flash
Has bosses	Fixed Path
Towers are elemental: water slows down, earth is zone damage, fire attacks fast, plant poisons, wind only attacks flying creeps.
Mini tower defense	release?
Single player	Flash
No boss	Fixed path
Creeps are tanks, towers are lasers. Winning a level gives points that can be spent to increase tower powers.
Orcs must die	Oct 2011
Single player	XBLA and Windows
No Bosses	Path?
The game happens in 3d like a normal FPS. Creeps are Orcs. The player controls an FPS avatar with deadly skills and places traps and archers in that 3d-FPS view.
Plants versus Zombies	May 2009
Single player	Flash
One final boss	No path
Zombies come from the right towards your house on the left. 5-6 lines, zombies never change line (except when you use garlic). Every 5 levels, there's a mini game. Plants are cards acquired when winning levels. No shortcuts, just clicks. The money is sun, it falls from the sky and players have to click on it to collect it. Click fest at higher levels. Five worlds: backyard by day and by night, pool by day and by night, roof by day. Lots of Easter Eggs. Very easy to understand and play through.
Rat Poker	1998
Single player	Windows 95 and 98
No boss	Fixed path
Tower defense where creeps keep looping until you order them in series like Poker hands. The player has to organize rats in series resembling Poker series (three of a kind, six of a kind, rainbow series, etc.). Rats are walking and can be grabbed and released at specific locations.
Turett Tyranny	release?
Single player	Flash
No boss	Fixed path
Creeps HP keep increasing wave after wave. Kill creep to get money. Unlock, place, and upgrade towers with money. Towers have a size (e.g. 1x1 or 3x3) and can only be placed where they fit. Walls constrain towers' line of sight. There is friendly fire between towers, but you can pay to protect them from friendly fire.
Vector TD	release?
Single player	Flash
No boss	Fixed path
Usual basic TD. Graphics resemble CreepSmash. Steep learning curve.
Viking TD	Release?
Single player	Flash
No boss	Fixed Path
Creeps are boats of Vikings, towers are catapults and others. Towers are unlocked progressively in pseudo-quests such as "build 5 catapults to unlock the tree of wisdom" or "kill 3 Big Boats at once with a spell to get the Stone Head". By Russian studio Iriysoft.
VR defender Y3K	April 2007
Single Player	Flash
No boss	Fixed path
6 kinds of towers, such as normal, slow, and flame thrower. Tower appearances reflects its upgrade level. It's hard to figure out which strategy to use as ennemies just only keep having more HP wave after wave, cf also player feedback. Graphics resemble CreepSmash.
Wicked Defense	2007
Single Player	PC
Has bosses	Fixed path
Some creeps can buff other creeps. Spells can slow down or damage monsters. Weird graphics. 3D.

And a list of games I have not broken down yet.

Name	Comments
W3 mod
Colony Defense	The terrain is a sphere, which gives a Populous-like view of the planet.
Sol Survivor	3D, fancy graphics, multiplayer co-op
Garden Defense
Defense Grid	Matrix atmosphere, 3D, fancy-ish graphics, fixed path.
Fieldrunners	Resembles Desktop TD, old-school war atmosphere, kawaii 2D god-view graphics.
TriDefense	for iPhone
Besiegement	for iPhone
The Horde	1994, contender for first TD game around; Its FAQ says that The Horde currently deletes all other non-horde saved games in NVRAM when you save a game
Harvest: Massive Encounter	Creeps are aliens, towers are human. planet exploration atmosphere.
Protector	Towers are medieval characters.
Immortal Defence
Pixel Junk Monsters
Lock's Quest	DS game
Guns' n' Glory	For iOS. UI is intuitive, but moving units around looks clumsy. Video.
TowerMadness	iPad game, free placement, towers can be upgraded, creeps are aliens, lives are sheeps that you have to protect. 2 players can play at the same time on the same ipad, but there are no interactions between players (no co-op, no PVP).
Starship defense	DSi game, slow, fixed path, rubbing/touching creeps with stilet inflicts damage. towers can be positioned on slots on the wall or on the roof. Video.
Castle-Combat	Clone of Rampart, old game from 1990, possible origin of the TD genre.
Kajaani	in space
Lockdown TD	"lifting" system that lets you move towers temporarily and reposition them between waves
Pokemon TD	So successful it has a sequel.
Ninja vs Pirates
Starland	Multiplayer

And a list of lists of TD games, mostly Flash:

• Newsground
• playthisthing.com
• playTD.com
• tdgames.net
• andkon.com
• TD.cz
• tdgames.ca

Mobile crap - upgrades

This series of articles is a rant about mobile game design. It may extend to console and PC gaming, but I only talk about what I experienced through most games featured on the iPad app store in the past year or so.

The upgrade mechanic is found in more and more iOS games. In Clash of Clans or Birzzle, the player spends coins to upgrade something. In Mother of Myths and Star Wars: Assault Team, the player must use a specific category of loot (e.g. spells for spells in MoM). In Plundernauts, the player must follow recipes using specific items previously looted in battle (e.g. 3 Poltergas for a Poltergas Tank). In Mutants, the player can breed two mutants of type A and B together to make a stronger mutant of type A and B. Finally, in Birzzle, owning more birds increases the play time, and the sum of the bird levels provides a score bonus. The only purpose of this mechanic is to make players buy birds with real money - not to make the game more interesting.

This kind of upgrades is not new, and not exclusive to mobile games: UO had crafting in 2000, Ragnarok Online gear could be upgraded up to ten times with materials in 2003, Diablo 3 has it nowadays with gems and enchanting, and some games in the Final Fantasy series must have had something close to it as well. It seems that iOS developers have just realized that they could use this decade-old mechanic everywhere they need players to grind - and therefore pay real money to skip the grind.

Mobile crap - daily login

This series of articles is a rant about mobile game design. It may extend to console and PC gaming, but I only talk about what I experienced through most games featured on the iPad app store in the past year or so.

Designers could invent new mechanics to improve the core gameplay, and thereby improve retention metrics in the long run. But they cheat: they invent new mechanics to immediately improve retention metrics, thereby ignoring or forgetting to improve the core gameplay.

Mobile games try to maximize various metrics: their number of daily and monthly active users (DAU and MAU), the average session length, and so on. To do so, they introduce game mechanics that encourage players to come back every day or play longer. In games like Clash of Clans or Farmville, the come-back mechanic is the core game loop, so it is not a problem. Waiting and coming back is what these games are about. But in traditional fighting, racing, or match-three games, the only reason why players would come back or play longer is because they like the fighting, racing, or match-three mechanics, not because they like waiting.

More and more games have been adding come-back mechanics on top of their core gameplay. In 2004, World of Warcraft started granting a rest XP bonus to players who do not login for a long time. Blizzard designers originally implemented the rest mechanic to prevent hardcore players to level up too quickly. Beta-testers hated it, so Blizzard made it a reward for casual players instead of a punishment for hardcore players. Nothing changed mathematically, but players prefer mechanics if they are framed as a reward.

More recently in mobile games, Plundernauts has been giving out a welcome-back reward for logging in. They also give out bounties which must be completed within 24 hours - an incentive to play at least a few battles during the day, most likely in one session. 24-hour bounties are great for metrics such as the average session length, but they do not make the game more fun in the long run.

Puzzle and Dragons gives two login bonuses: 1) a consecutive login bonus, with rewards increasing every consecutive day, and reset the day the player does not login, and 2) a cumulative login bonus, increasing every day the player logs in, and never reset. Also, there are 5 exclamation marks for 7 lines of text in the login bonus message. By abusing the exclamation mark they over-emphasize my login, and it looks very amateur.

And finally, mobile games such as Birzzle or Mother of Myths show a daily login calendar when the player logs in. Some calendars focus on the week (4x7 cells), others on the month (5x6 cells). The calendar resembles an Advent Calendar, except 1) nothing happens at the end, and 2) the calendar mechanic is not properly tied to the core gameplay (receive more and more gold, or increasingly better gifts). The only point of the calendar is to keep people logging in for the rewards, not to have more fun playing the game.

A lot of mobile games have mediocre and dull core gameplay. These games are often sugarcoated in happy-shiny graphics and habit-forming mechanics. None of those improve their core gameplay. These games remain shallow.

Mobile crap - clones

This series of articles is a rant about mobile game design. It may extend to console and PC gaming, but I only talk about what I experienced through most games featured on the iPad app store in the past year or so.

Ideally, designers should keep a working recipe and incorporate new mechanics into it, or at least aim for a fresh take on an old recipe. These days, entire genres should be avoided entirely: designs involving a match-three mechanic have nearly all been done, one way or another. I covered Clash of Clans clones before, Raph Koster and others came up with a small family tree of shmups, and somebody probably covered the lineage of match-three games. I won't talk much about cloning in itself - everybody knows it is omnipresent in the game industry. So I focus on the imperfect features that cloners should upgrade or replace, but actually keep by laziness.

UI-wise, some developers are really lazy: instead of trying to improve an existing one, they just copy-paste it blindly. For example, Dungeon Keeper's UI HUD is a near-exact copy of Clash of Clans. Yet CoC had, and still has, several UI issues raised on the CoC forums by the players. For example, the default battle zoom-in forced players to always zoom-out before starting a fight. The team behind CoC fixed it, but the Dungeon Keeper team could have thought about it too. Another CoC example is the spells that remain selected when players try to deploy troops, thereby wasting a spell. One solution would be to deselect the spell after it has been cast, but this issue has not been fixed yet, and it's easy to spot with playtesters. A last example of UI laziness can be found in Plundernauts. Plundernauts adapted the item game made famous by WoW and Diablo to spaceship battles. They changed nothing to the UI when displaying equipment stats. In short, if you are cloning a mechanic, at least try to question and improve the interface.

Finally, the name. I understand that developers target a particular audience. Sometimes, this audience needs to know that the game is a puzzle game. So they make the name of their game rhyme with puzzle: Birzzle, Chuzzle, and so on. It's nice, but it looks like even the names are clones!

The loops of Diablo 3

In Vanilla D3 (D3 for short), players could buy or sell gear for in-game gold or real money at the auction house (AH). Players reported feeling frustrated: they drop legendary gear (yay!), but when they check the AH, they realize their legendary gear is actually average. So they buy amazing gear from the AH for cheap, roll over monsters they used to have so much trouble with, and become bored with the game quickly. Damion Schubert, a designer on SWTOR, echoed that the core loop of D2 was much stickier than D3's. So did players during a Reddit Q&A session with D3 designers. Personally, I started a year after the game launched, bought all my gear from the AH for little gold, never dropped any better gear, rarely managed to sell gear on the AH, and left after a month.

Blizzard removed the AH for the D3 expansion, Reaper of Souls (ROS), released in March 2014. The game feels better. Is it because the core game loop is back to what it was in D2?

Two core loops

At its core, Diablo (D2, D3, and ROS) has actually two intertwined core loops: the usual XP loop and the item-game loop. XP loop: kill monsters to accumulate XP to increase level to improve stats and skills to do more damage to kill harder monsters. Item-game loop: kill monsters to drop gear to improve stats and skills to do more damage to kill harder monsters.

To mix these two loops together, the Diablo designers decided that damage was dealt by skills, but increased by stats (e.g. each point of DEX increases damage by 1%) and gear (e.g. increase the damage of fire skills by 10%), especially weapons (which is why 40% of all drops are weapons or off-hand gear).

In D3, characters unlock skills every level until they reach 70. After level 70, characters gain Paragon levels. Each Paragon level gives 1 point to increase a stat. The real goal of Paragon levels is not better stats, but rather frustration control. The item-game loop triggers randomly and irregularly: a player could go for hours without dropping a better gear. The XP loop, on the other hand, is reliable and constantly increasing. In other words, the item-game is a roulette, while the XP loop a grind. While not super fun by themselves, combined they make the game more fun. Interestingly, Paragon levels were an afterthought, and only shipped 3 months after launch.

ROS and removing the AH

The XP loop did not change between Vanilla D3 and ROS, but the item loop did. In D3, the primary way to convert gold into items and vice-versa was the AH. But the AH went out of hand: powerful items were available for cheap, and a hyper-inflation boosted by a gold dupe bug made the economy collapse. In ROS, the AH was decommissioned and replaced by a beefed-up crafting system (crafting was insignificant in Vanilla D3).

As of patch 2.0.5, though, the gear available from crafting is mostly defensive or utility. The best gear is offensive, and dropped from monsters in high difficulty or found randomly in bounty rewards. Except for enchanting, crafting is pointless.