The idea that bad players are a problem to me is quite silly, i often hear
poker players complaining when a ‘bad’ player wins a hand. They often
ridicule someone for poor play and i just want to strangle them. If someone
is truly ‘bad’ then they are giving their money away to the whole table on
a long term basis.

If you are only able to beat people who are ‘good’ (predictable) then maybe
you’re not as good as you think you are. I am not a good player but i can
spot a sucker pretty quick, and you have to adjust your game accordingly.
Ive been at a table and i sat behind a poor player and i played any hand
that he played regardless of my cards and won pot after pot while ‘better’
players only played when they had a hand.

The true Nash equilibrium hasn’t been found for any poker games, although end-game SnG strategy and HU LHE are very close. That nobody plays close to “optimal” makes exploitative strategies much more profitable in poker at the moment. There have been suggestions that there is no true global Nash-equilibrium in poker for 3+ handed games, although I’m certainly no expert in that. The factor of betting sizes makes NLHE, PLO or others unsolvable for now.

And +1 for Bill Chen’s book!

Also, I agree that Sean is saying “dominant strategy” when he probably means Nash equilibrium strategy.

There is almost certainly a Nash equilibrium solution for the game–an optimal strategy to use if everyone else knew the rules of the game, and was deeply versed in the strategy of the game.

This does not mean that someone who knows a bit about human psychology and real-life strategy won’t dramatically outperform the Nash equilibrium. This is demonstrably true for much simpler games than poker, where the Nash equilibrium is directly calculable. For instance, take the parlor game where you ask everyone to guess a number between 0 and 100, and the winner is the one who gets the closest to 2/3 of the average. Very few people correctly guess the Nash equilibrium value of 0. Therefore, when playing this game in real life, guessing zero is probably a poor play.

Poker, unlike other gambling games under house rules, can be played without losing money to the house. This makes all of the money available to be won by those playing. There are also several different “official” poker games; some quite complicated, some more easily accessed (one of my professional friends has invented and sold two new game variants and earned a great deal of money just from that enterprise). I do not think that a comprehensive unbeatable algorithm can exist for poker, even for the simplest variants, because the game involves human beings playing from irrational perspectives. But i do think professionals’ dominant strategies perform extraordinarily well when pros play against novices. That is one of the reasons big poker casinos have professionals on call when novice high rollers come to town.

I don’t know of any unbeatable algorithm for Hold ‘Em poker, though I concur with the Nash argument that there must be one. In fact, Hold’Em is one the simplest poker games, in a tree-branching sense, and so I wouldn’t be surprised if it’s one of the easier ones to solve. The higher-level question is, what procedure would you use to analyze any arbitrary poker-like game to find its unbeatable strategy? Does this lead to a meta-strategy for solving games in general?

1. This is a blog. Among the various features of a blog is an institutional memory; facts that have been mentioned many times previously may be taken as understood between the writer and audience, even if newcomers might need to catch up a bit.

2. All one has to do is click the actual links to find very explicit statements of my relationship with Jennifer.

3. Loud declarations that you are not uptight tend to convey the opposite impression.

Let’s keep the remainder of the discussion to poker and physicists.

And “dominate” doesn’t mean “beat under any circumstances”; it just means “there is no alternative strategy that does better against every possible opponent strategy.

I am sorry to be a pedant, but that’s wrong or at least a wrong use of pretty basic terminology. A dominant strategy is exactly a strategy that does best, no matter what the opponents do. Most games don’t have dominant strategies. What Nash showed that in a n-person game, there always exist at least one (and maybe more) n-tuples of strategies that are best responses to each other.

Sean, it’s great that you plug your wife’s articles and books, but don’t you think you should add a full disclosure note to let us know that she’s your wife?

The Carroll-Oullette connection is hardly a secret nor news.

I did notice, in your much better half’s post, that the mention of money on the table was only stated in passing. I would offer that the probabilities involving money are very important to understanding the game; afterall, it is what the game is about. Thus, the better minds, include in their calculations, the odds of: winning, winning other pots, the ability to get other money into the pots, the amounts of money on the table, the amounts of money that can come into the game (non-tournament play is where the real money is), and the capacity to cover with side bets of all manner of interests.

Max, all you need to know is “the Spousal Unit”

@Mongoose: Bad players are not a problem for anyone that plays sufficiently many tournaments or cash game hands. Sure, the winner of the WSOP main event is unlikely to be a previously famous player, but that’s just good for the game. It’s still easier to win a tournament with 100 bad players than one with 100 good players.