Martingale on Dice: the Arithmetic Instead of a Fake Log
This page reported that “we scripted and ran exactly 100,000 consecutive provably fair dice rolls” with a classic Martingale at 1.98× payout. No such run was scripted and the log that followed was written rather than recorded. The good news is that Martingale does not need a simulation: every number in it can be derived on paper, and the derivation is below.
The setup, and the one number that decides everything
Take the usual crypto dice configuration: payout 1.98× at a 49.5% win chance. The expected return per unit staked is 0.495 × 1.98 = 0.9801, so the house keeps 1.99% of everything that passes through the game. Martingale does not touch that number. Doubling after a loss changes when you win and how much you stake, never the average return per stake.
What doubling actually buys and costs
A run of n losses happens with probability 0.505n, and surviving it from a base bet of one unit requires 2n − 1 units already staked, with the next bet at 2n:
| Losses in a row | Probability | Units already lost | Next bet |
|---|---|---|---|
| 5 | 3.3% | 31 | 32 |
| 8 | 0.43% | 255 | 256 |
| 10 | 0.11% | 1,023 | 1,024 |
| 13 | 0.014% | 8,191 | 8,192 |
| 17 | 0.0009% | 131,071 | 131,072 |
Read the third line carefully. A ten-loss streak is rare per attempt — about one in 920 — but across a thousand sequences it appears with probability 66%. When it does, recovering one unit of profit requires risking 1,024. That is the trade Martingale makes: many small wins in exchange for one loss that ends the session, and a table maximum that stops the doubling long before your bankroll does.
The verdict the old log was standing in for
Over any number of rolls, expected loss equals total turnover × 1.99%. A doubling script raises turnover fast, so it raises the expected loss fast. It changes the shape of the outcome distribution and nothing else — the same conclusion the invented 100,000-roll table claimed, now derived instead of asserted. The cost of turnover itself is in the 99% RTP piece, the impossible version of the same dream in the “$200 into $9,400” story, and why no bet pattern can influence a roll in the provably fair explainer. Terms used here are defined in the glossary.
Does Martingale ever work?
It produces frequent small wins, which feels like working, and one rare loss that cancels them. The average result is still turnover × house edge.
What bankroll does it need?
To survive ten losses in a row from a $1 base you need $1,023 and a table that accepts a $1,024 bet. Both limits usually arrive before the streak ends.
Is a longer streak more likely after several losses?
No. Each roll is independent, so the chance of losing the next one is the same as it was at the start.
