Kelly Criterion Calculator With Risk of Ruin

This Kelly criterion calculator gives the stake that grows a bankroll fastest for any win chance and decimal odds, and then shows what that stake risks. For quarter, half, full and double Kelly it works out the exact risk of ruin, the chance of finishing ahead and the typical bankroll after the number of bets you choose.

Risk of ruin, chance of finishing ahead and typical result for different stake sizes
Stake size	Bet	Risk of ruin	Finish ahead	Median bankroll	Expected result
Quarter Kelly	25.00	0.0036%	91.1%	1,500	+500
Half Kelly	50.00	1.14%	91.0%	2,000	+1,000
Full Kelly	100.00	11.93%	84.8%	3,000	+2,000
Double Kelly	200.00	35.22%	64.0%	4,200	+4,000

The Kelly criterion formula

With a win chance p, a loss chance q = 1 − p, and decimal odds d, the net odds are b = d − 1 and the Kelly stake, as a share of your bankroll, is:

f* = (b × p − q) ÷ b

A bet that wins 55% of the time at even money, decimal odds 2.00, gives 10%. If the result is zero or negative, the bet has no edge and the Kelly answer is to stake nothing, however the bet is sized.

Why most people bet half Kelly

Full Kelly maximises long-run growth, but only if your win chance is exactly right, and the ride is rough. In the example, full Kelly grows the bankroll about 0.50% per bet on average, while half Kelly still grows it 0.38% with half the stake. Double Kelly grows it not at all: overbetting by a factor of two turns an edge into a slow loss.

Risk of ruin shows the same thing more bluntly. From a bankroll of 1,000 over 200 flat bets, the chance of dropping below one stake is:

Quarter Kelly (25 a bet): 0.0036%.
Half Kelly (50 a bet): 1.1%.
Full Kelly (100 a bet): 11.9%.
Double Kelly (200 a bet): 35.2%.

Because an estimated edge is usually too optimistic, a fraction of Kelly is the practical choice for anyone who is not certain of their numbers.

Using it as a risk of ruin calculator

When a bet has no edge, the table switches to stakes of 1%, 2%, 5% and 10% of your bankroll, which makes it a plain bankroll calculator. The risk of ruin column is exact: it counts every sequence of wins and losses rather than sampling some of them. On a 1.90× coin flip, which loses 5% of each stake on average, betting 50 at a time from 1,000 ends in ruin within 200 bets 36.5% of the time, and betting 100 does 72.4% of the time.

No stake size turns a negative edge positive. If you want to see what a doubling system does instead of flat stakes, try the martingale simulator.

Frequently asked questions

What does the Kelly criterion calculate?

The share of your bankroll to stake on a bet so that the bankroll grows as fast as possible over many bets, given your win chance and the odds.

What does a negative Kelly percentage mean?

The bet has no edge: at those odds and that win chance you lose money on average. The Kelly criterion then says to bet nothing.

Should I use full Kelly or half Kelly?

Half Kelly keeps most of the growth with much less risk of ruin, and it protects you if your win chance is overestimated. Most bettors who use Kelly use a fraction of it.

How is risk of ruin calculated here?

Exactly. For a fixed stake, the bankroll after any number of bets depends only on how many were won, so the calculator tracks the probability of every win count bet by bet and adds up the paths that fall below one stake.

Does the Kelly criterion work for casino games?

Only as a warning. Casino games have a house edge, so Kelly always recommends staking nothing; the table still shows how quickly different stake sizes use up a bankroll.