Crypto dice calculator: Martingale risk of ruin & streak odds
Enter your win chance, bankroll and bet progression to see the longest losing streak you can survive, how often it happens, the risk of ruin over any number of rolls and a best/median/worst bankroll projection. Works for Stake, Bitsler and any provably fair dice site.
- All seven formulas are shown below
- Instant, with no API call or sign-up
- Current risk of ruin: 49.7%
Input parameters
over 10,000 rolls
how is this computed?Bankroll projection · 100,000 rolls
95% confidence band around the expected house-edge drift
- best (97.5th pct)
- median
- worst (2.5th pct)
Every number on this page is computed in your browser from the formulas explained below; nothing is sent to a server. The address bar updates as you type, so you can bookmark or share any configuration.
The math behind the numbers
How the dice calculator works
Seven short formulas turn your inputs into every output above. The worked values use the configuration currently in the calculator (win chance 49.5%, house edge 1%, balance 0.01000000 btc, base bet 0.00000100 btc, +100% per loss).
- 01
Payout multiplier
M = (100 − HouseEdge) ÷ WinChanceA fair game would pay100 ÷ WinChance. The casino shaves the house edge off the numerator, so a 49.5% bet pays 2.00× at 1% edge instead of 2.02×. That gap is the whole house advantage. The rest is variance.M = (100 − 1) ÷ 49.5 = 2.00×
- 02
Single-loss probability
q = 1 − WinChance ÷ 100The chance that one roll loses. Rolls are independent, so the chance of several losses in a row is justqmultiplied by itself.q = 1 − 49.5 ÷ 100 = 0.5050
- 03
N consecutive losses
PL(N) = qNThe probability that a specific run ofNrolls is all losses. Small per streak, but you are exposed to a fresh streak starting on almost every roll, which is why formula 4 matters more than this one.PL(13) = 0.505013 = 0.014% (1 in 7.2K)
- 04
Expected rolls until an N-loss streak
ES(N) = (1 − qN) ÷ ((1 − q) · qN)The standard waiting-time result for a run ofNidentical outcomes in a Bernoulli sequence. It is the average number of rolls you get to play before the fatal streak shows up, and it is what the Expected rolls to hit and Bankroll runway cards report.ES(13) ≈ 14,539 rolls
- 05
Bankroll needed for N losses
Breq(N) = BaseBet · (rN − 1) ÷ (r − 1), r = 1 + LossIncrease ÷ 100The sum of a geometric progression of bets. Withr = 2(doubling) it is simplyBaseBet · (2^N − 1); with no increase (r = 1) it collapses toBaseBet · N. The calculator evaluates it atN = N_max.r = 2.00 · Breq(13) = 0.00819100 btc
- 06
Max survivable streak
Nmax = floor( ln(1 + Balance · (r − 1) ÷ BaseBet) ÷ ln r )Formula 5 solved forN: how many steps of the progression fit inside the balance. Because the relationship is logarithmic, adding more money buys surprisingly few extra losses, while lowering the base bet or the loss multiplier helps a lot more.Nmax = 13 losses (the 14th loss busts the bankroll)
- 07
Risk of ruin over T rolls
RoR(T) ≈ 1 − e−T ÷ ES(Nmax)A fatal streak shows up on average once everyE_Srolls, so the chance of at least one within T rolls is one minus e to the power of−T ÷ E_S. When T equals E_S that is already about 63%. The gauge colours it green below 1%, yellow from 1% to 10% and red above 10%.RoR(10,000) ≈ 49.7% → red band
Expected P/L and the projection chart
Expected profit is the house-edge drag on turnover:
Compare with a real simulation−HouseEdge ÷ 100 · avgWager · T, where the average wager accounts for how often the progression sits at each step. The chart draws that drift as the median line and a 95% band (±1.96 standard deviations of the per-roll outcome) as best and worst case, clamped at zero. Real runs can and do leave the band; the simulator shows what that looks like.
FAQ
Crypto dice calculator questions
What does the crypto dice calculator actually compute?
Given a win chance, house edge, bankroll, base bet and a bet progression (how much the stake grows after a loss or a win), it computes the payout multiplier, the longest losing streak your bankroll can absorb, how likely that streak is, how many rolls you can expect before it happens, the total turnover involved, your expected loss from the house edge, a risk-of-ruin figure for a chosen number of rolls and a best/median/worst bankroll projection.
What is the Martingale max survivable streak?
It is the largest number N of consecutive losses you can pay for before the next bet in the progression exceeds your remaining balance. With bet doubling (100% increase on loss) each loss costs base × 2^k, so N grows only logarithmically with the bankroll: ten times more money buys you roughly three more losses.
How is risk of ruin calculated?
First the calculator finds the fatal streak length N_max, then the probability q^N_max that any given streak of N_max rolls is all losses, then how many rolls you expect to wait for such a streak, and finally how many of those waiting periods fit in your horizon. Risk of ruin is the chance that at least one fatal streak arrives within your horizon: one minus e to the power of minus (horizon divided by that waiting time). It is an approximation that treats fatal streaks as independent random arrivals.
Why does the expected profit always come out negative?
Because every dice game pays out slightly less than true odds. The payout multiplier is (100 − house edge) ÷ win chance, so on average you lose house edge percent of every unit wagered regardless of the pattern of your bets. A progression changes how the losses are distributed over time, not their expected size.
Which house edge should I use?
Use the edge of the casino you are planning to play at. Stake dice uses 1%, Bitsler 2%, and several smaller sites run 0.5% or lower. The presets cover those; the custom field accepts anything from 0% to 10%.
What is the difference between betting under and over?
Nothing in the odds. Betting under wins when the roll is below your win chance; betting over wins when the roll is above 100 minus your win chance. Both give exactly the same probability and payout; the toggle only changes the target roll shown and the setting passed to the simulator.
Does the calculator work in satoshis?
Yes. Pick sats as the unit and amounts are converted to and from BTC (1 BTC = 100,000,000 sats). All formulas are scale-free, so results are identical whichever unit you choose; only the labels change.
Can I test these exact settings in a real simulation?
Yes. The Open in simulator button carries the win chance, balance, base bet and progression into the Lua IDE pre-filled with a matching Martingale script, where you can run up to ten million provably-fair rolls in your browser and compare the realised drawdown with the theoretical figures here.