03 February 2016

Shop Heroes - Opaque UI

Shop Heroes is an item-shop game released on mobile and Kongregate in mid 2014 by CloudCade. The gameplay consists of crafting equipment for heroes, who then go on quests to find materials, which are used to craft more equipment. Players can gather in Towns to share the costs incurred by leveling up buildings, which unlock more heroes and quests.

CloudCade advertise striving for useability and superior gameplay. I understand that when they launched Shop Heroes, they were still a small studio. But their UI needs more work: it has too many screens, too many taps to start an action, too much information, and fragmentation/duplicate information. Sometimes, information is not just missing or duplicated. It's purposefully hidden, misleading, or manipulative.

Manipulating emotions

An example of UI manipulating emotions is the Roulette, which gives players one random award among 12. The UI shows each award equally likely to happen - 1 in 12, or 8% each. Yet the actual chance of keys, gems, and blueprint fragments is less than 1%. Why raise players' hopes so high if it never delivers? So they get 10 seconds of fiero after 10 months of frustration? It's as if a slot machine displayed the jackpot symbol with the same chance as others, but was actually rigged to nearly never stop on it. The gambling industry actually forbids such machines. One could argue that the Roulette is a minor mechanic in Shop Heroes, and that players may understand that it's rigged. A sincere UI would make the area of a reward on the wheel proportional to its likelihood.

Hidding information

An example of UI purposefully hidding important information can be found in the screen where players build their quest teams. Players send heroes on quests dozens of times per day. When heroes are strong enough to tackle the quest, a green smiley is displayed above their head. When they are not strong enough, the smiley turns to yellow or red, showing that they are more likely to be injured. Injured heroes are unusable for several hours, so players strive for green smileys. But each of the 8 equipment slots of each hero has a 1-10% chance to break during a quest. Therefore players equip their heroes with just enough equipment to reach green smileys, so as to minimize the costs incurred by broken equipment.

Yet players noticed discrepancies in the odds of injury. They asked on the forum whether increasing power above green smiley reduces the chance of injury. The community manager did not answer clearly at first, saying it's fun for those playing to figure out, and that it's impossible to create a tutorial for every single detail in the game. Players replied that 1) they are not asking for a tutorial but for explicit numbers to be displayed, 2) core mechanics should not be hidden, and 3) discovering 1%-likelihood mechanics is annoying and time-consuming. The community manager eventually cleared the matter, but why was this important information not explicitly provided inside the game? The in-game UI should, and can, do a better job at displaying the chance of injury, however small it is. One way would be to display the green smiley only when the chance is exactly 0%. Another way would be to display the percentage number, rounded up (0.123% would be 1%). Providing feedback through numbers is the only way that hardcore players can theorycraft and reverse-engineer the most intricate mechanics.

27 January 2016

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.

StreakJackpot amount ($M)
Jan'16Feb'15
15255208
16300230
17334261
18529289
19948317
201,500395
21-564
StreakTickets sold (M)
Jan'16Feb'15
152624
164128
175429
1817637
1944048
2063573
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
11/725264.27.61.31.3
11/1132223.0151.12.4
11/1438284.1231.43.8
11/1844247.7261.25.0
11/2150276.4321.36.3
11/2557283.1411.47.7
11/2863284.8491.49.1
12/269323.7591.610.7
12/580388.2681.912.6
12/991335.5781.714.3
12/12103387.4881.916.2
12/16113396.2992.018.2
12/19127519.61131.820
12/23143589.9132full20
12/26161546.3153full20
12/301898414181full20
1/221011821219full20
1/633337566341full20
1/9597963159663full20
1/139301,3742741,077full20
closure9303,4406230NA20
Pool amounts (in $M) leading to the $564M annuity jackpot
date jackpot
(cash)
ticket
sales
prize
pool
jackpot
pool
bootstrap
"tax"
bootstrap
pool
12/326222.27.71.11.1
12/633264.4151.32.4
12/1039254.1221.23.6
12/1346274.8291.35.0
12/1752254.4361.26.2
12/20593210.2401.67.8
12/2465359.2471.89.6
12/27723210.3511.611.1
12/3178388.4591.913.1
1/385354.6701.714.8
1/795355.0811.816.6
1/101054110.2902.118.6
1/14114387.01001.420
1/171264816108full20
1/211355212122full20
1/241506218135full20
1/281706011154full20
1/311887415176full20
2/420610018209full20
2/725715130255full20
2/1138140174381full20
closure3811,3582780NA20

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.