A candy-shop janken machine: put a medal in, beat the calico cat at rock, paper, scissors, and the ring of lamps decides how many medals you win.
みけじゃんけん
CALICO JANKEN
Finding your medals…
Medals are for playing the games on this site only. They are not money: they cannot be bought, cashed out or exchanged for anything.
Keys: M a medal in · 1 2 3 rock, scissors, paper · D double up · T take
Your medals are the same at every machine of the Medal Center, and are reset only there. Go to the Medal Center
Everything on this machine is drawn fairly, and so every chance below is exact. The cat’s hand is rock, scissors or paper a third each, drawn when you press yours, so no hand of yours is better or worse than another. The roulette stops on any of its 30 lamps as likely as any other.
| Outcome | Per throw | Per medal |
|---|---|---|
| Win | 1/333.33% | 1/250% |
| Draw (thrown again) | 1/333.33% | — |
| Loss | 1/333.33% | 1/250% |
A draw is thrown again, so a medal always ends in a win or a loss: a win with chance 1/3 + 1/3 × 1/3 + … = 1/2. A medal takes 1.5 throws on average.
Each of the 30 lamps is as likely as any other. A win gives the medals on the lamp the light stops on.
| Medals | Lamps | Chance when it spins | Chance per medal | Comes back per medal |
|---|---|---|---|---|
| 1 | 20 | 2/366.67% | 1/333.33% | 0.333 |
| 2 | 5 | 1/616.67% | 1/128.33% | 0.167 |
| 3 | 3 | 1/1010.00% | 1/205.00% | 0.150 |
| 5 | 1 | 1/303.33% | 1/601.67% | 0.083 |
| 10 | 1 | 1/303.33% | 1/601.67% | 0.167 |
| Total | 30 | 100% | 50% | 0.900 |
A double-up wins half the time (draws are thrown again) and doubles the medals on it, so on average it gives back exactly what it takes. Doubling up never changes the 90%; it only makes the wins rarer and bigger. Up to 4 in a row.
| Double-ups after every win | Biggest win | Back per 100 | Spread per medal (σ) |
|---|---|---|---|
| 0 | 10 | 90 | 1.55 |
| 1 | 20 | 90 | 2.36 |
| 2 | 40 | 90 | 3.46 |
| 3 | 80 | 90 | 4.98 |
| 4 | 160 | 90 | 7.10 |
The Medal Pusher gives back about 90 medals of every 100 when it is played the best way. This machine gives back exactly 90, however it is played.
How much a real candy-shop janken machine gives back has never been published that we could find. Its hand is often said to be set by the machine, and here it is not: it is drawn fairly, and the figure above is exact.
Plays many sessions at once, each with the same number of medals, and shows how they ended.
Expected: -10.0 medals per session, exactly.