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.
Comments
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.