Game Probability Calculator

Calculate exact win probabilities, multipliers, and expected value for Crash, Mines, and Dice. Understand the math behind every bet before you play.

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Inputs

Target Multiplier cashout target

House Edge 1.00%

Bet Amount

Results

Win Probability

49.5000%

EV per Bet-$0.10

Effective House Edge1.0000%

Multiplier2.00x

P/L per 100 Bets-$10.00

Crash Probability Table

Multiplier	Win Prob.	Std Dev / $1
1.5x	66.0000%	±0.71
2x	49.5000%	±1.00
3x	33.0000%	±1.41
5x	19.8000%	±1.99
10x	9.9000%	±2.99
20x	4.9500%	±4.34
50x	1.9800%	±6.97
100x	0.9900%	±9.90

EV per bet is the same at every target: the win probability falls exactly as fast as the payout rises, so each row costs 1.0% of the stake on average. What the cashout target controls is the swing, shown as the standard deviation of profit per $1 staked.

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The Math Behind Crypto Casino Games

Crypto casino games like Crash, Mines, and Dice are built on provably fair algorithms. This means the outcome of each round is determined by a combination of server and client seeds that can be independently verified after the fact. While provably fair guarantees that the casino is not manipulating individual results, it does not eliminate the house edge. The mathematical advantage is built into the payout structure, not the randomness.

How House Edge Works

In a perfectly fair game, a 2x multiplier would hit exactly 50% of the time. But the casino takes a small cut, typically 1%, so a 2x actually hits 49.5% of the time. This seemingly tiny difference compounds over hundreds of bets into a predictable drain on your bankroll. The house edge is the percentage of every dollar wagered that the casino expects to keep over the long run.

Mines and Combinatorial Math

Mines uses combinatorial math. The probability of safely revealing k tiles from a 25-tile grid with m mines is the number of ways to pick k safe tiles divided by the total ways to pick k tiles from all 25. Each additional tile you reveal dramatically decreases your probability of survival but increases the payout multiplier proportionally.

The Mathematical Certainty

No betting strategy, Martingale, Fibonacci, D'Alembert, or otherwise, can overcome a negative expected value. Every bet in these games has negative EV by design. Strategies can change the variance (how volatile your balance is), but they cannot change the expected value. Over a sufficiently large number of bets, your results will converge to the house edge. This is a mathematical certainty governed by the Law of Large Numbers. The only winning move in a -EV game is to play for entertainment with money you can afford to lose.

Crash Formula

P(win) = (1 - houseEdge) / targetMultiplierExample: At 2x with 1% edge → P(win) = 0.99 / 2 = 49.50%

Mines Formula

P(win) = C(25 - mines, reveals) / C(25, reveals)Multiplier = (1 - houseEdge) / P(win)C(n, k) = n! / (k! × (n - k)!)

Dice Formula

P(Over x) = (100 - x) / 100P(Under x) = x / 100Multiplier = (1 - houseEdge) / P(win)

Playing on Stake?All Stake Originals use exactly 1% house edge. See how rakeback offsets your expected loss.

Stake Rakeback Calculator

Mines Pattern Gen →Dragon Tower Pattern →Keno Pattern Gen →Hilo Pattern Gen →Flip Pattern Gen →

Take Your Edge Further

GAMB·8 gives you automated bot strategies, real-time analytics, poker HUD, and sports intelligence: all the tools to find and exploit +EV opportunities.