How the odds work
Every game here is a game of chance with a built-in edge, like the real thing. The difference is that we print the edge in full, worked out exactly.
Where the randomness comes from
Each draw, drum stop, card and tile is picked in your browser by its built-in secure random number generator, the same one it uses to make encryption keys. We use rejection sampling, so no number is ever slightly more likely than another. The server is not involved and nothing adapts to you.
What return means
Return is the average number of coins a game gives back for every 100 coins played, over a very long run. A return of 93% means that, on average, 100 coins played come back as 93. Short sessions swing a long way either side, which is the fun and also the trap.
The four games at a glance
| Game | Stake | Return | How it was worked out |
|---|---|---|---|
| Tombola | 20 coins a card | 94.79% | exact (hypergeometric) |
| Limoni | 1, 2 or 5 coins a line, five lines | 93.13% | exact (all 8,000 drum stops counted) |
| Alta o Bassa | 10, 25 or 50 coins | from 92.62% (one guess, exact) | exact per guess, ladders by 5,000,000-round simulation |
| Piastrella | 50 coins a tile | 93.00% | exact (fixed table of 100,000 tiles) |
Tombola
You choose 5 numbers from 90, and 18 balls are drawn without replacement. The chance of exactly k matches is C(5,k) × C(85,18−k) ÷ C(90,18), the hypergeometric formula. Multiplying each chance by its prize and dividing by the 20-coin stake gives 94.79%.
Limoni
Each drum has a strip of 20 painted stops, so there are 20 × 20 × 20 = 8,000 equally likely ways for the drums to land. We counted every line on every one of them: 37,250 line-units returned for 40,000 staked, which is exactly 93.125%.
Alta o Bassa
Each guess is priced from the cards still in the deck: the multiplier is the fair odds of your side among the cards that are not a tie, times 0.95, rounded down to three decimals. A tie hands your ladder back unchanged. So every guess is worth at most 95% of fair on its decided part, and the game page prints the exact figures.
Piastrella
The tile's prize is drawn first from a fixed table of 100,000 equally likely outcomes, then a grid is painted to show it. The table returns 4,650,000 coins for 100,000 tiles at 50 coins, which is exactly 93.00%.
Things that are not true
- A game is never hot or cold, and nothing is due after a dry spell.
- Your nickname, your balance and the time of day make no difference to any result.
- Near misses are not arranged. A losing tile simply shows motifs placed at random with none appearing three times.