How bad are the fish?

[alphatmw]

wouldn't the player who sees he has the besyt hand PF just go all in everytime? wouldn't this be the winning strategy?

[pzhon]

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wouldn't the player who sees he has the besyt hand PF just go all in everytime? wouldn't this be the winning strategy?

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First, it would make more sense to play this game in fixed limit or pot limit.

Second, people who think this game is trivial need to look at some actual examples. What's the best hand out of A[img]/images/graemlins/club.gif[/img] 7[img]/images/graemlins/spade.gif[/img], 3[img]/images/graemlins/diamond.gif[/img] 3[img]/images/graemlins/heart.gif[/img], J[img]/images/graemlins/club.gif[/img] 9[img]/images/graemlins/club.gif[/img]? Suppose each has a chance to be on the button. Which do you think should open-push? Assume the stacks are 100 BB.

Spoiler in white:
<font color="white">A7o can push and win the blinds if 33 is in the SB, but not if 33 is in the BB. J9s and 33 should not push with either order of blinds; pushing is worse than folding.</font>

This type of complexity is more common when there are more players.

[bobman0330]

You do realize that the only person to call this game trivially easy is you, correct? Furthermore, you realize that you solved the A7-J9s-33 game with at most 8 twodimes runs?

It's not simple, but the core concept is that even a player in first position can predict what the players later on will do, assuming everyone is rational and has the same incentives. That takes care of the multiway v. HU issues.

The other complexity is that hot and cold equity is not accurate with further betting. This is true, but it would not be impossible to calculate a "flop EV" that takes into account how often hands will flop something they can continue with, and what their aggregate equity is. Again, not trivially simple, but nowhere near the complexity of a really hard game.

I feel confident that given a computer, a large sum of money, and a refresher course in C++, I could write a program to solve any combination of hands.

[pzhon]

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You do realize that the only person to call this game trivially easy is you, correct?

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No, that's news to me. Please give a link to where I said that, or retract your statement. I said the game isn't trivial: "face-up poker is still complicated," and "you'll find it quite nontrivial." You said said face-up hold'em would be "easily quantifiable and predictable," "a straightforward exercise," and "a reasonably easy game to solve." Alphatmw suggested a simple but incorrect strategy for NL face-up hold'em.

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Furthermore, you realize that you solved the A7-J9s-33 game with at most 8 twodimes runs?

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Do you realize I didn't claim to solve that game, since there were more strategies to consider than moving in?
Do you realize that you may have to consider a limp-reraise?
Do you realize that you may have to determine the correct size of a raise?
Do you realize the correct play may depend on the stack sizes?
Do you realize postflop play is nontrivial, too, particularly for limit?

You are just waving your hands, while I have looked at real examples. I am a mathematician, I understand basic game theory, and I'm telling you this is not simple. As far as I can tell, you have made no nontrivial progress. You have simply identified the problem as finite, just like chess. You hope hot-and-cold equities are helpful, but knowing the 1024 equity distributions doesn't tell you how to play the game.

I think this discussion has established that there would be plenty of room to misplay in faceup hold'em. The errors might not be as large as in regular poker, but the standard of play should also be higher, just as in backgammon.

[bobman0330]

If you're a mathematician you should be aware that "straightforward" is not the same as "trivially easy."

In any case, I don't care nearly enough to work out an actual full hand. So judging from your past responses, anything I say that doesn't involve a full solution of an actual hand is going to qualify as just waving my hands or guessing. Nevertheless, if I cared enough to solve face-up poker for 10 hands, this is how I would go about it.

1. first of all, it should be limit, because NL is much more complicated. (On second thought, NL might be less complicated because it would eliminate postflop play. Worth some thought. Also, btw, it seems unlikely that a limp-reraise would ever be correct, just as a check-raise would rarely be correct.)
2. Second, you need a more accurate stand in for hot and cold equity to take into account postflop betting. You'd need both the competing hands and pot size. It's somewhat complicated, but the action on the turn and river is very simple, so that makes it a bit easier. If I were writing a program to determine this modified EV, I would enumerate all the flops, enumerate every hand's winning percentage on each flop, then figure out who has the best hand (they will bet) and whoever has sufficient drawing odds will call. From there, it's easy-ish (not trivial) to calculate everyone's total EV from the flop forward. Summing this up will give each person's total EV given a certain mix of hands and a pot size. I think this step is by far the hardest, but again, I think there are a very manageable number of basic cases, and it's mostly number-crunching.

3. As you mention, there are 1024 possible combinations of people who can take the flop. In practice, you can weed this down a lot by folding badly beaten hands in advance and taking them out of the calculation. Assuming you can't make any shortcuts, you start with the last hand to act, figure out against who he is willing to play and for how many bets (this requires a lot of calculation, but i can think of a lot of ways you can streamline it.) This should also show us what his preferred action should be in each spot.

4. Player 9 is a bit easier, because we know what player 10 will do under each set of conditions. (e.g., if player 10 is always folding, we needn't consider what player 9 thinks if everyone limps, as it won't happen.) Run all the same calculations as for player 10 and figure out what his action is in all the possible scenarios.

5. Repeat again and again and again.

6. You should now know what player 1 is doing, which dictates player 2's action, etc. The postflop action is "straightforward" once the initial pot is straightened out.

7. This is not strictly necessary, but if you feel so inclined, you can make a lot of pointlessly snide comments about a disagreement about how hard it would be to work out a highly theoretical game theory problem.

[pzhon]

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In any case, I don't care nearly enough to work out an actual full hand.


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You do care enough to argue with someone who has worked on actual examples, and is telling you that you don't understand the problem. I don't understand your motivation for that. What makes you think it is a good idea?

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(On second thought, NL might be less complicated because it would eliminate postflop play.

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No, it wouldn't eliminate postflop play. Maybe you would see this if you had actually analyzed the example. According to my postflop estimates, there is an ordering of the hands in which no player will push preflop.

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Also, btw, it seems unlikely that a limp-reraise would ever be correct, just as a check-raise would rarely be correct.)

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That's just a guess.

Whether a limp-reraise or check-raise would ever be correct, these are options. It may be that the possibility of a limp-reraise would prevent someone from making a raise, or call, so the optimal strategy would change if you made limp-reraises illegal. In fact, that happens in one example I have analyzed.

I think it's a waste of time to discuss this with you if you can't be bothered to look at actual examples that contradict what you are saying.

[bobman0330]

I'm having this discussion because poker theory is interesting to me in a way that laboriously running twodimes calculations is not.

The reason I said that NL would eliminate postflop play is because there would almost always be a push on the flop (or at least an uncallable bet). I really can't think of a spot where multiway play would affect this.

In any case, if you feel that I can't bring to this discussion the level of mathematical rigor required by an internet message board thread, then I won't waste any more of your time. I apologize if my ill-considered guesses and waving about of the arms were a distraction from your profound learned contemplation of this weighty matter.

[arod15]

There would still be fish. Look at 7 card People draw into hands hoping for a two pair when someone has a pair showing. Or a for flush. Given every indication in a game like 7 card people still take horrible long term loosing plays. In the end. The game would suck but i suspect there would still be consitient losers. Actually there would haveto be cause if there wasnt the game would end..

[Sasnak]

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This may or may not yield some interesting discussion, but I have a question that has perked my mind a bit. Say hypothetically, Texas Hold'em (or any form of poker for that matter) was played with all hole cards face up for everyone to see. Would there still be consistent winners and losers in this game? Would the only losers be the players that don't understand pot odds and equity, or would a very advanced player still have an edge over a mediocre player that does understand the basic principles?

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Would Ditka be playing?