Kelly Criterion

The Wheel of Money

Are you clever enough to reach $1,000?

Adjust your bet amount and spin the wheel! If you land on green, you'll double your bet. If you land on grey, you lose your bet.

Bet Amount
2X Your Bet (60.0%)
Lose Bet (40.0%)
Spin the Wheel

Probability Theory

Is there an optimal strategy?

A game like this has many applications. You have a fixed amount of money to start with, and you want to make bets (investments) that maximize your profit in the long run without going broke first.

It turns out, the best approach is to bet the same percentage (given fixed probability of winning) of your current bankroll each time.

Using the Kelly Criterion we can calculate this exact percentage. "This bet sizing leads almost surely to higher wealth compared to any other strategy in the long run." - Wikipedia

Adjust the Winning Multiple and the Probability of Winning to calculate the optimal bet percentage.


Kelly Criterion

Probability of Winning
Winning Multiple

  • If you win, you 2× your bet
  • If you lose, you lose your bet
  • You have a 60% chance of winning
See it for yourself


It's easier to see the process if we simulate the betting and you can view the outcomes.

Probability of Winning
Winning Multiple
Starting Bankroll
Optimal Bet
Simulate 500 Bets

2X Your Bet (60.0%)
Lose Bet (40.0%)

Balance ($)
Bet %
Bet Amount ($)


While you can't apply the Kelly Criterion directly to your investment strategy (since rarely are the Winning Multiple and Probability exactly known) it's a useful concept to be familiar with. It can give you a starting point when considering the risk of your potential bets.


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