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I made a 'game' to help me son get some intuition for bet sizing: https://tools.encona.com/investor

Good game, but the fact that there is a target that you have to achieve in a fixed number of rounds changes the math.

For instance, if all I care about is satisfying your win conditions, and I am above $20,000, then I should just pass till the end. Similarly, if I have been unlucky (even with Kelly bets) for the first 14 rounds, I should go all in on the 15th round.

You are right! It's stupid to have a target.

The target wasn't there in the original version... I'm embarrassed to say I asked Claude to do a bunch of general 'make this better' on a few of the items on that site, and didn't check the output closely :(

Fixed number of rounds with a target should use DP for solution, not KC.

What is DP?

Dynamic programming. Although if you don't know the distribution of how the bets will look beforehand, there's no real optimal strategy. Think you see first bet has 99% chance of giving you x2. Do you bet everything and take it? It could either be the worst bet of the 20 bets, in which case you just took 1% chance to lose everything unnecessarily, or it could have been the single bet that would be winning money, in which case betting it all would be the only strategy that could win.

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