Imagine being handed $25 and told you can place even-money bets on a coin that lands heads 60% of the time. You get about 300 flips in 30 minutes, with a chance to walk away with as much as $250. Sounds like a promising opportunity—yet in an actual study with these exact rules, 28% of participants lost everything, and on average people walked away with just $91. Only one in five players hit the $250 cap, while others made puzzling choices like betting it all at once or even backing tails. 1 With these surprising outcomes in mind, how would you have played it differently? The $250 cap has been removed so you can feel free to maximize your winnings.
Did you win? Did you go bust? Do you think you chose a good strategy? Why not take a look at how you would do if you played through this scenario 100 times? We’ve added the $250 cap back in.
Multi-Run Betting Simulator (Capped at $250)
So what is the optimal fraction of your bank roll to bet? To calculate this, we use the Kelly criterion.2
The Kelly criterion provides a mathematically proven way to determine the optimal fraction of your bankroll to wager each time, so you can maximize your overall winnings in the simulations (and in real life). It does this by focusing on long-term growth rather than a single big win, balancing your gains against the risk of ruin. Put simply, if you know your chance of winning and the payout odds, the Kelly formula tells you exactly what percentage of your bankroll you should bet to see the fastest compound growth over many plays. For example, if a coin has a 60% chance to pay even money, the Kelly bet would be 20% of your bankroll every time. Over many bets, using Kelly leads to significantly higher final outcomes than betting arbitrary fractions or going all-in.
Kelly Bet Calculator
- Haghani V, Dewey R. Rational Decision-Making Under Uncertainty: Observed Betting Patterns on a Biased Coin. arXiv [q-finGN]. Published online 2017. http://arxiv.org/abs/1701.01427 ↩︎
- https://en.wikipedia.org/wiki/Kelly_criterion ↩︎
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