Bankroll Calculator: Risk of Ruin and What Staking Plans Change

What the simulation shows

Enter a price, a win rate and a stake, and the calculator plays out that sequence of bets several thousand times. What comes back is not a forecast but a distribution: where the bankroll usually ends, how wide the spread is, and how often it runs out before the bets do.

The default case is the one worth understanding first. Two hundred bets of twenty dollars at −110, winning exactly half the time, starting from a thousand. Half the time is a perfectly ordinary result on a spread, and it is what a coin flip produces. The median ending bankroll is about $818.

That number is not a simulation artefact. Two hundred bets at twenty dollars is four thousand dollars of turnover, and a market holding 4.55% keeps $182 of it. The arithmetic and the simulation agree exactly, which is the point: the loss is not bad luck, it is the price, and it arrives whether the run feels good or bad.

Staking plans, and what they do not do

Three plans are available and the comparison between them is the most useful thing on the page. Flat staking bets the same amount every time. Percentage staking bets a share of the current bankroll, so stakes shrink after losses. Doubling after a loss chases each losing run with a larger bet.

Run all three at the same price and win rate and the averages land in the same place. That is not a coincidence or a limitation of the model; it is arithmetic. Expected value per bet is fixed by the price and the win rate, and a staking plan only decides how much money rides on each one. It can change the shape of the distribution and it cannot change its centre.

The shapes do differ, and in ways worth seeing. Percentage staking cannot reach zero, because each bet is a fraction of what remains, so the risk of ruin falls and the middle of the distribution tightens. Doubling after a loss produces a slightly better median and a dramatically worse tail: most sequences recover their small losses, and the ones that do not lose everything, because a long enough losing run exceeds any bankroll. Watch the worst-5% figure while switching plans and the trade is obvious.

None of that makes any plan better than another in expectation. It makes them different in variance, which is a real thing to care about and a different thing from winning.

Risk of ruin is the number that binds

Expected value tells you what a price is worth. Risk of ruin tells you whether you will still be there to collect it. It rises with stake size, with the number of bets, and with the margin, and it is the reason stake sizing matters even when the expected value is fixed.

Raise the stake from twenty dollars to a hundred at the same price and the expected loss merely multiplies by five, while the risk of ruin climbs far faster than that. The distribution widens enough that the bottom of it reaches zero, and once a bankroll reaches zero the remaining bets never happen. That asymmetry is the whole argument for small stakes relative to the bankroll, and it does not require any view about edges.

This is also why Kelly staking is deliberately absent. Kelly answers how fast a bankroll can grow given a real, measured advantage. Applied to an advantage someone believes they have, it produces confident stake sizes and a fast route to zero. Risk of ruin answers the question that applies whether or not the advantage is real, which makes it the more honest tool for the situation most people are actually in.

Change the win rate to 52.38% and the picture changes completely: the expected loss goes to zero because that is exactly the break-even rate for −110. Anything above it and the distribution drifts upward. That single field is the difference between a hobby and an edge, and the simulation will happily model a win rate nobody has, which is worth remembering every time the output looks encouraging.