A simulator that allows you to test the 'Kelly standard' to see how much your optimal stake is

One of the well-known ideas in the financial and gambling industries is the ' Kelly Criterion ', which calculates how much risk you can take in maximizing expected returns. You can experience what this really means with the simulator created by engineer Paul Butler.

The Kelly criterion: How to size bets

Making the simulator is very simple, and the player starts with $ 25 (about 2900 yen) in cash. Enter the amount with the slider and bet on either 'the front that appears with a probability of 60%' or 'the back that appears with a probability of 40%'. If the person who chooses it comes out, the bet amount will be doubled, but if it does not come out, the bet amount will be forfeited. It ends when you have zero or if you exceed $ 250 (about 29,000 yen), which is 10 times the initial funds.

If you just want to maximize the amount you can get, the amount you bet is 'all your money'. For example, if you bet $ 25 on your first bet, you'll get $ 50.

If you can keep hitting, your money will reach $ 400 with just five bets.

However, betting all your money also means that the game is over once you remove it.

You can't be game over to get the maximum return, so you have to think about how to maximize the return, assuming you make multiple bets.

It is said that there is an unsolved part in the original paper of Mr. John Kerry of Bell Institute who devised the 'Kelly standard', but Mr. Butler simply thinks that a certain percentage of the possession money is set for each bet. Limited to betting strategies. In the case of the game shown this time, there is an option of '60% chance of winning', so if you keep choosing this, the median return when you bet 10 times will be the maximum of 20 of your possession each time. It is said that it is 30.58 dollars (about 3500 yen) when betting%. This is also shown by Wolfram Research, the developer of the computer algebra system Mathematica.

What percentage of your money should you invest when you challenge a winning bet? --GIGAZINE

Therefore, the simulator embedded at the bottom of the page can be set to bet the specified% of the amount of money you have each time. You can see what happens if you keep selecting the 'table' with a probability of winning 60% by continuing to click 'Bet Heads (60%)'.

The probability of winning is only 60%, so in some cases your money may decrease considerably, but you should reach your goal someday.