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Dice payout calculator: win chance to multiplier

This dice payout calculator converts between win chance, payout multiplier and the roll under or roll over target. Pick a house edge, edit any one of the four fields and the others follow. The table below lists the win chance and targets for common multipliers from 1.01x to 9,900x.

Convert

House edge

Win chance

Payout multiplier

Roll under target

Win when the roll is below this

Roll over target

Win when the roll is above this

Edit any field and the other three update. Rolls run from 0.00 to 100.00.

Payout2xProfit per 1 staked on a win: 1.0000

Win chance49.5%Lose chance 50.5%

Targets< 49.50 or > 50.50Roll under or roll over, same odds

Return to player99%Expected loss 1% of each bet

Common payouts at 1% house edge

Rows marked not available need a win chance outside 0.01% to 99.99%. Targets are rounded to two decimals, the precision of a roll.
Payout	Win chance	Roll under	Roll over
1.01x	98.0198%	98.02	1.98
1.1x	90%	90.00	10.00
1.5x	66%	66.00	34.00
2x	49.5%	49.50	50.50
3x	33%	33.00	67.00
5x	19.8%	19.80	80.20
10x	9.9%	9.90	90.10
50x	1.98%	1.98	98.02
100x	0.99%	0.99	99.01
1,000x	0.099%	0.10	99.90
9,900x	0.01%	0.01	99.99

Dice payout formulas

payout = (100 − house edge) / win chance

win chance = (100 − house edge) / payout

roll under: win if roll < win chance

roll over: win if roll > 100 − win chance

Win chance and house edge are in percent. The payout is the total returned on a win, stake included, so a 2x payout on a bet of 1 returns 2 and the profit is 1. The same rules are used by the DiceSim simulator and the main crypto dice calculator.

Worked examples

49.5% at 1% house edge: (100 − 1) / 49.5 = 2x.
2x at 2% house edge: (100 − 2) / 2 = 49% win chance.
10x at 1% house edge: (100 − 1) / 10 = 9.9%. Bet roll under 9.90 or roll over 90.10.

Same multiplier, different house edge

The win chance needed for a payout goes down as the house edge goes up. These values are computed with the formula above.

Payout	0% edge	0.5% edge	1% edge	2% edge
2x	50%	49.75%	49.5%	49%
10x	10%	9.95%	9.9%	9.8%
100x	1%	0.995%	0.99%	0.98%

How the edge turns into an expected loss over many bets is on the house edge calculator page, and dice house edge explained covers where the edge comes from. For streak odds and payouts at a single win chance, see dice odds by win chance.

FAQ

Dice payout questions

How do I convert win chance to a payout multiplier?

Divide the return to player by the win chance: payout = (100 − house edge) / win chance. At 1% house edge, 49.5% pays 2x and 9.9% pays 10x.

How do I find the win chance for a multiplier?

Turn the formula around: win chance = (100 − house edge) / payout. A 2x payout at 2% house edge needs a 49% win chance.

What is the difference between roll over and roll under?

Only the target. Roll under wins when the roll is below the win chance. Roll over wins when the roll is above 100 minus the win chance. Both cover the same number of outcomes, so the odds and the payout are identical.

Why does roll over use 100 minus the win chance?

Rolls go from 0.00 to 100.00 in steps of 0.01, which is 10,001 outcomes. Roll under 49.50 wins on 0.00 to 49.49, which is 4,950 outcomes. Roll over 50.50 wins on 50.51 to 100.00, also 4,950 outcomes. The two targets give the same odds.

How does the house edge change the payout?

It scales every payout down by the same factor. At 50% win chance a fair game pays 2x; at 1% house edge it pays 1.98x. The win chance stays the same and the profit on each win is smaller.