Quote:
Originally Posted by fagfgff
Suppose you play NLHM heads up and are using a Nash equilibrium strategy.
1. Is everytime you have the same hand is in the same situation do you do the same action? Or do you consider the history (previous hand played) aswell?
2. Does this strategy differ from how you would play in a zoom heads up game with infinitely many opponents? Ie you only play 1 hand against each opponent.
3. Is there a pure Nash strategy which does not loose against a mixed Nash strategy?
4. Suppose you know the (crappy) strategy of your opponent completely, we call it S1, and you compute the optimal play against it, call it P1, if your opponent is given P1 and computes the optimal strategy in repsonse, S2, etc. Consider the sequence P1,P2,P3..., does this sequence converge to Nash equilibrium? Or does it oscillate?
I will have a go at the answers...
1. You have the same options each time, but should have a RANGE which behaves with some randomness. So sometimes you bet out and sometimes you check/call the exact same hand. GTO never remembers a previous hand for this reason, but humans may choose to do so.
2. GTO strat would work perfectly in Zoom, but other exploit methods may work also. From question 1, it follows that GTO works in zoom.
3. "Mixed" is undefined, but if you mean a mixture of methods, or an approximation of Nash with added exploit strategy, then pure Nash would not lose money to this, heads up, and would likely not lose money multiways unless both opponents are colluding specifically against you. However, pure Nash may not be the most profitable strat at a given poker table.
4. Yes, all logical exploit strategies arrive at Nash when level infinity is reached. It oscillates but each revolution is closer to Nash.
Sent from my iPhone using Tapatalk