Game Theory Analysis
CRASH
Crash
The concept is simple: a multiplier climbs from 1x upward, and you cash out before it crashes. Wait too long and you lose everything. It's provably random, but when you pull out is entirely your call. Every round is a test of greed versus discipline.
Crash quick sim
Pick an attempted cashout multiplier and house edge. Results are per 1 unit wagered.
EV -0.001
House Edge
0.10%
STD
0.999999
P(win)
49.95%
Win Multiplier
2.00x
OVERVIEW
Crash is a multiplier game where the round starts at 1.00x and rises until a random crash event ends it.
SETUP
- Choose your bet amount.
- Choose your auto cashout target
C(for example,2.00x).
ROUND FLOW
- The multiplier increases continuously from
1.00xupward. - If the round crashes before reaching your target, the bet loses.
- If the multiplier reaches your target before crash, the round cashes out and you win.
PAYOUT LOGIC
Your target controls hit rate and payout tradeoff:
- Lower target -> higher hit rate -> lower win size.
- Higher target -> lower hit rate -> higher win size.
GAME MATH
Crash can be modeled using a fixed auto cashout target.
PARAMETERS
| Symbol | Meaning |
|---|---|
C | auto cashout target multiplier (> 1) |
EDGE | 0.001 for Duel, 0.01 for Stake |
PROBABILITY OF WINNING AT TARGET C
NET RESULT PER ROUND
If the round reaches target C, net win is (C - 1) * bet_size.
If the round crashes before C, net result is -bet_size.
EXPECTED VALUE
Substituting the probability formula gives:
This means the player's expected return per round is:
PROVIDER COMPARISON
| Provider | Base RTP | Base House Edge | Effective House Edge @ 100% Rakeback |
|---|---|---|---|
| Duel | 99.9% | 0.10% | 0.00% |
| Stake | 99.0% | 1.00% | 1.00% (if rakeback is 0%) |
RAKEBACK ADJUSTMENT
If rakeback returns a fraction r of house edge, effective edge is:
With Duel's 100% rakeback (r = 1), modeled effective edge is 0%.
You can test any auto cashout from 1.01x to 1,000,000x in the simulator below.
VOLATILITY / STD
Each auto-cashout target creates a binary outcome (hit target or lose bet):
At 2.00x with Duel edge 0.10%:
At 10.00x with Duel edge 0.10%:
At 50.00x with Duel edge 0.10%:
Higher auto-cashout targets increase SD quickly.
TEST STRATEGIES
You can test strategies here in the strategy tool.
WARNING
Strategies are methods of shaping your risk and payout profile, not ways to beat the house.
They can be used to:
- Smooth variance and generate more frequent, smaller wins.
- Increase variance to chase larger, less frequent payouts.
This means each wager has a negative expected value, or neutral when playing zero-edge, and changing bet sizes or betting patterns won't change that.
MARTINGALE STRATEGY
Increase bet size after losses (typically doubling) to recover all previous losses plus a fixed profit. This works extremely well until it doesn't and all of your bankroll is gone.
Bet size sequence: b, 2b, 4b, 8b, ...
Stop when a win occurs, then reset to base bet.
Martingale — Distribution Effect
- Very high win frequency.
- Many small profits.
- Rare but extreme losses (one big loss can drain your bankroll).
PAROLI (INVERSE MARTINGALE)
Bet sequence after wins: b, 2b, 4b, ...
Reset to base bet after a loss.
Paroli — Distribution Effect
- Lower win frequency.
- Many small losses.
- Occasional large wins.
First Casino
Live Economics
House edge: 0.100%
House Edge after Rakeback: 0.000%
STD: 1.00
Max Possible Win: 1.00x
Second Casino
Live Economics
House edge: 1.000%
House Edge after Rakeback: 1.000%
STD: 1.00
Max Possible Win: 1.00x
Shared Session