If such a player is approximating a game-theoretic-optimal (GTO) strategy, then they are essentially putting their opponent in a situation where it doesn't matter what they do. In other words, whatever information you believe you could glean from their play will not help you alter their expectation (i.e., reduce their expectation while increasing yours).
Judging from what you wrote in the question, I think you are misunderstanding a few concepts here.
First, math is math. Math doesn't care if you play poker, running, feeding your dog or doing something else. Math's laws are universal. This means that the math will have the same precision both in the heat of the battle and after the session is over and you ...
It sounds like we're looking for game states.
The game is Texas Hold 'Em
We round bets to multiples of the big blind for calculating state
We don't distinguish between raising and re-re-re-re-raising because we only care about "betting / checking outcomes."
For the sake of example, we'll assume $0.50 / $1.00 blinds with a $100 buy-in.
Kahnemans theory is slightly more nuanced. You are actually supporting his evidence with your example as he found that people are more risk averse when they are winning and conversely they are more risk seeking when they are losing.
So in your example, when a player is losing they may be likely to take actions that in retrospect are more risky/uncertain ...
Your question is very general. Game Theory, which employs Nash equilibrium, is a set of methods to model situations where players are in conflict.
If your input is the entire game, the problem becomes unsolvable. First of all I am not sure if it exists a Nash solution, but even if it does, it would be nearly impossible to calculate, given all these ...
The solution is actually known. I can solve it in 2-3 days using a server I rent for that exact purpose (studying poker) and some specialized software.
To the answer from Ying Li:
You misunderstand Nash Equilibrium in poker. If you played a perfect GTO strategy, you essentially would be unbeatable. There is no way your strategy would be beat by drunk ...
It's not optimal. For NL hold'em, consider when each player has a stack size several thousand times the big blind. If you're limited to push-fold, then here's my strategy:
In the big blind, I only call with aces, and fold with everything else.
On the button, I min-raise with everything. I then call with aces, and fold anything else.
You can only push with ...
Hand rankings are based on the probability to make a given hand when drawing five cards: the lower the probability, the stronger the hand.
When you add more suits to a deck:
The value of flush increases (i.e. its probability decreases)
The value of pairs, three of a kind etc decreases
The value of straight very sightly increase
When you add more ranks to ...
Nash Equilibrium is where two players don't have an incentive to change their strategy.
A simplified way of looking at how a solver works: If you have player1 and player2. You would start with some strategy. Then have player2 exploit player1. Then have player1 exploit player2's new strat. Then player2 exploit player1. And keep going back and forth until ...
I coded some python to generate every hand. As it seems to work okay for a regular deck (13 ranks, 4 suits), I think I can trust the numbers. For comparison, here's what it says for a regular deck (also, the odds printed are rounded down to an integer).
1098240 one pair or 1 in 2
123552 two pair or 1 in 21
54912 three of a kind or 1 in 47
It would have no effect on flushes or straights. Pairs I don't know. Have to work out the math.
A short deck is different in that it increases the likelihood of pairs and triplets and straights. Flushes once again I'm not sure. Have to work out the math.
Some interesting info.
As the number of suits increase, boats/quads drop a lot of value. A deck with more than 16 suits would value straights over boats. If you removed a suit to make a 3-suit deck, straights would outvalue flushes.
As the number of ranks increase, flushes drop value (and conversely gain value when the reverse occurs) while the rest of ...
In poker, there are never identical situations, because even if you play with the same cards and the same opponent for days, you will end up creating history and dynamics between you.
However, you will end up facing decisions similar to what you have faced in the past. And yes, in the long run if you want to be balanced and unpredictable you will end up ...
I am probably one of the few people with significant experience in all three fields (mathematics, Machine Learning (and AI), poker).
To answer is it known, the answer is probably not yet. There are two approaches to beating an imperfect information game with AI. The first has really nothing to do with Nash Equilibrium. The first is basically in a way, a ...
Book recommendations are kind of out of scope.
A Sit & Go is a mini tournament. Because of the payout structure a chip you lose is worth more than a chip you win. You need to stay alive. You should be more selective about your hands.
Players like Negreanu will play a range of hands and go for pot control. He has some books out.
Old school ...