Theory problem update
It’s been a few days since I first posted my puzzle. If you missed it, you can find it here. Aside from the comments there, there is also some discussion about it going on over at Poker VT which you can see here (no account needed). People have also talked to me in private about the problem.
In my history of asking this problem, there are some common solutions that people come up with:
Bet $1 because you have less risk of busting.
When I did bonuses like this years ago, betting $1 is exactly the method I used precisely for the reason that I was risk-averse and had a limited bankroll. Such reasoning doesn’t apply to this situation, though, where we don’t care about variance, only EV.
Bet whatever you want because it doesn’t matter.
Some people reason that it doesn’t matter what bet we place, since a $100 bet has the same expectation as a series of 100 $1 bets. This is true, however despite the truth of this statement it’s not a valid reason as a solution to the problem.
Some people come up with the martingaling strategy, doubling bets every time you lose and such. Many people believe this is not only the best strategy, but one in which you can’t lose. This, also, is not right. Plenty of good information on the subject is available here.
A note about martingaling, and here’s a hint about the correct solution: martingaling has no worse EV than betting $1 repeatedly. Would it be possible for me to convince you that martingaling has a higher EV than betting $1 at a time?
The solution will be posted in a couple of days.