I was considering an interesting situation. Imagine you are playing poker against someone who is always raising in a tournament game (both start with a stack of chips, and win when they have the other persons chips). We are talking pot limit omaha. This means that people get dealt 4 cards, and they are supposed to make a best match with 5 cards on the board. Person with the highest cards according to poker (pair, two pair, straight etc), wins.
What makes this question particularly interesting is that blinds (the amount you have to pay to stay in the game) increase over time (so the maximum pot size automatically increases over time). Every 10 rounds, the big blind increases in size (first +10, later +20, then +40 etc)
Contrary to texas holdem, omaha has a lot more spread since people are dealt 4 cards instead of 2.
Basically, this means you can not just sit and wait for getting the best possible cards, especially since it cannot be too clear at the start (a lot can happen: e.g. in texas holdem the best starting cards AA has something like 78% chance to win, while in omaha the best starting cards would only have like 65% chance to win).
I am trying to find a way to find the optimal strategy when you know someone would always raise.
You start with a big blind of 10. You know that in the subsequent turns, the pot size would triple for each turn (disregarding the fact that you can raise as well). Since the opponent will never fold, this means that it will be quite expensive to see the cards after all the rounds.
A certain way to play would be to only call when you believe you have higher than 50% of a chance to win, but this is certainly not optimal.
What would be the way to solve this problem analytically? I was trying to consider some simulation study where I try to be more picky initialially.
In fact, I came up with 3 criteria:
-How deep is your stack (how many times can you call the opponent and lose a round before you lose the whole game) --> You can be more picky when you have "more to lose". Then again, desperate times could call for desperate measures (why slowly bleed to death?). Does this even have an influence at all? -What is the chance to win given your current cards, and given the current board, compared to "random" cards (yields a probability to win on each turn in a round) -->You could for example quit halfway in a round when your probability to win dropped dramatically -What is the ratio of your stack divided by the size of the stack of the opponent? -->Also some kind of measure that can either be used to be "picky" or "desperate" or neither.
I am pretty sure the problem can be solved with these 3 criteria (together with the increasing-over-time blind), I just do not know how I can come up with a design that would test this adequately. Perhaps some people even know if some of these criteria do not apply?