Betting Board Game
Three columns of bets on coins, dice and cards, each with a quoted price, and a bankroll to stake on them. Work out the fair odds, find the mispriced lines and size them before the clock runs out.
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How to play
Each round is a bookmaker’s board. Some of the prices on it are wrong. Find the ones that are wrong in your favour, size them, and move on before the clock runs out.
- 1Read the boardThree columns of bets on coins, dice and cards, and a bet or two on the board as a whole, each with the price the house is quoting. Every probability is exact and can be counted. Easy deals a coin, a die and a card; hard adds sums, products, two-card draws and conditional bets (“given at least one 6”).
- 2Price each lineTurn the probability into fair odds: (1 − p) to p. A 1 in 6 event is fair at 5:1. Quoted above fair the bet earns, quoted below fair it loses, and a few lines sit at fair on purpose. Easy prices are wrong by at least 15%; hard by as little as 5%.
- 3Stake the edgeA $1,000 bankroll carried from board to board, staked with chips of $5 to $100 in any amounts you like. The size that grows it fastest on one line is the edge divided by the payout, as a share of the bankroll. Over-bet a real edge and the bankroll shrinks in expectation.
- 4Beat the clockEvery board is on a timer. Pick a chip, click a line to add it, Shift-click to take it off. Enter places the bets, S passes on the board. Then the coins, dice and cards are drawn, the board is settled for real, and the next one is dealt.
The board quotes “two dice sum to 7” at 7:1: stake $1, and if it lands you win $7 and keep the $1. Is it worth a bet, and how much?
| Probability | 6 of the 36 rolls sum to 7 | p = 1/6 |
| Fair odds | (1 − p) to p = 5/6 to 1/6 | 5:1 |
| Edge per $1 | win $7 × 1/6, lose $1 × 5/6 | +$0.33 |
| Stake | edge ÷ payout = 0.33 ÷ 7 = 4.8% | $48 of $1,000 |
Quoted 7:1 against a fair 5:1, so the line pays more than it should and is worth backing. Each $1 on it is worth 33 cents on average. The stake is the Kelly size: big enough to grow the bankroll fastest, small enough that the five losses in six do not sink it.
Choose how the prices are written in the settings. It changes the spelling, never the maths, so scores compare across formats. Mixed writes each line in its own format and is the closest to a real screen.
| Event | p | Ratio | Decimal | American |
|---|---|---|---|---|
| Two dice sum to 7 | 1/6 | 5:1 | 6.00 | +500 |
| One die shows 5 or 6 | 1/3 | 2:1 | 3.00 | +200 |
| A coin lands heads | 1/2 | 1:1 | 2.00 | +100 |
| One die does not show a 1 | 5/6 | 0.2:1 | 1.20 | −500 |
Ratio is profit to stake. Decimal is the total return per $1, so fair is 1 divided by p. American is the profit on $100 when positive and the stake it takes to win $100 when negative, so a price flips sign at evens.
Your score: how much the bankroll grows in expectation under your stakes, compounded over every board, in dollars on the starting bankroll. It rewards a real edge and punishes a stake so big that one loss would set the bankroll back further than the edge is worth. A pass scores nothing.
After every board the coins are tossed, the dice rolled and the cards drawn, and the bankroll moves by what your stakes won or lost. That is what you carry to the next board. Over eight boards it swings far more than the edge does, which is why the score is the growth and not the final figure.
The review grades every line on every board: the exact probability, the fair odds, the quoted odds, the edge, what the draw did, and your stake against the Kelly size. Timeouts and passes stake nothing and score nothing.
Know the small tables cold: two-dice sums (1, 2, 3, 4, 5, 6, 5, 4, 3, 2, 1 out of 36), coin counts (1, 3, 3, 1 out of 8 and 1, 4, 6, 4, 1 out of 16), a deck (4 of each rank, 13 of each suit, 12 face cards). Rule out the prices below fair first, then size the rest by edge over payout, not by how big the payout looks: a long shot at 20:1 against a fair 35:1 is the worst line on the board, and a 10% edge at evens takes a bigger stake than a 30% edge at 9:1.