You and Kelly face the same bets. The same outcomes. All you control is how much you risk.
You have a 45% chance to 2.6× your bet.
Otherwise, you lose what you risk.
50 rounds. No real money.
Last round stack: units
Your current stack: 10000 units
The deal
You have a chance to your bet.
And a chance to lose what you risk.
50 rounds complete
You ━ Kelly ┄
Same odds. Same outcomes. Different stakes. A single game is influenced by luck; the decisions are where the lesson begins.
A longer game: 100 rounds 200 rounds
Compare your stakes with Kelly’s, round by round. The outcomes were identical for both players.
| Round # | Expected value | Win probability | Multiplier | Your stack | You risked | Kelly stack | Kelly risked | Round won |
|---|
01 / Find the fraction
A binary outcome: win the stated payout, or lose your stake. Change the assumptions to see the trade-off.
Full Kelly fraction
20%
A positive edge under these assumptions.
| Approach | Fraction | Stake | After a loss |
|---|---|---|---|
| Full Kelly | 20% | 2,000 | 8,000 |
| Half Kelly | 10% | 1,000 | 9,000 |
| Quarter Kelly | 5% | 500 | 9,500 |
Full Kelly maximizes expected log growth in this model. Smaller fractions reduce exposure; they do not remove risk.
Calculator values are not personal investment recommendations. Real probabilities, losses and correlations are rarely known this precisely.
02 / Behind the decision
For a win probability p and total payout d, the full Kelly fraction is:
f* = (p × d − 1) / (d − 1)
We constrain it to 0–100%: no borrowing or negative bets. At 60% and a 2× payout, full Kelly is 20%. A 100-unit winning stake returns 200 units in total.
Kelly maximizes expected logarithmic growth for repeated bets under the model’s assumptions. It does not maximize the probability of finishing first in a short contest.
Half and quarter Kelly reduce the stake. In the model, that trades some expected growth for less exposure to losses.
The game supplies known probabilities, independent outcomes and exact payouts. Markets do not. Estimation error, correlated positions, transaction costs and changing conditions can make a mathematically optimal stake too large in practice.
This binary-bet model is not a portfolio allocator. A positive edge does not guarantee a profit.
Offers follow the original Gaussian expected-return generator with 5–94% win probabilities and payouts rounded down to one decimal. Outcomes are generated before you choose a stake and reused for every strategy. Benchmarks recalculate their fractions from their own remaining capital each round. Stakes and balances are rounded to whole units each round, as in the original game. Game progress resets when this page is reloaded.
Read J. L. Kelly Jr., A New Interpretation of Information Rate (1956) and Busseti, Ryu & Boyd, Risk-Constrained Kelly Gambling.
Adapted from Beat Kelly, created by Burak Yenigun and Demircan Celebi. The original credited Data36’s betting game as its inspiration.