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 Poker Theory General poker theory

03-14-2012, 04:31 PM   #2
wbuster
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Posts: 449
Re: Theory terminology

Quote:
 However, it turns out that in poker, if all players are playing their equilibrium strategies, they will break even in the long-term average sense when we average over all positions in the game.
if all Players would shove and call any two cards they would be break even too, maybe add that point

ty for ya post =)

 03-14-2012, 05:08 PM #3 plexiq veteran   Join Date: Apr 2007 Location: Vienna Posts: 2,006 Re: Theory terminology Looks pretty good, thanks!
 03-14-2012, 05:13 PM #4 Bob147 adept   Join Date: Apr 2008 Posts: 914 Re: Theory terminology sticky at the top imo.
 03-14-2012, 07:42 PM #5 RainbowBright veteran     Join Date: Jun 2007 Posts: 2,344 Re: Theory terminology fwiw, I'm not sure if people would be interested in distinguishing between "hand distribution" and "range". Hand Distribution: All hands for a player before any action is taken on a particular street Range: All hands used by player when taking an action For example, on the Flop: Hand Distribution: All pocket pairs 22+ Betting Range = JJ+ Checking Range = 22 - TT Check-Calling Range = 66 - TT Check-Folding Range = 22 - 66 I'm not sure if it's necessary, but I feel that I get confused sometimes on these boards. thx for doing this.
03-14-2012, 08:56 PM   #6
gedanken
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Re: Theory terminology

Quote:
 Originally Posted by yaqh dominated strategy ...folding the nuts on the river...
Perhaps a more clear example of the definition is how folding first to act is dominated by checking.

03-15-2012, 01:55 AM   #7
Tua
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Posts: 37
Re: Theory terminology

Quote:
good post. btw, i come from a stock/futures (and to a lesser extent - options) trading background and i find poker interesting in a lot of ways. a lot of the game theory carries over, but a lot is quite unique to poker (and trading)

the primary difference i see is that while technically any trade affects the market (even lifting one share from the offer), it has far more minimal effects on the other player's actions vs. poker (obviously) since there might be thousands or millions of players in a future contract in a given day, such that one trade doesn't have the effect that one bet, raise, call or fold does in a poker hand. also, while the futures market is zero sum (like poker) , the stock market is not zero sum.

i have found traders who don't "get" that last point ... which boggles my mind, but it's indisputable

the other difference is that in trading, the "cards" so to speak are the market price at the time (as well as how thin or thick the current orders are on the DOM), but the cards to come are affected by the current actions which is very distinguishable from poker

in brief, in trading, you cannot "force" the game and doing the equivalent of a three barrel bluff will just cause you to lose more money. unless you are soros or something, you cannot appreciably move the market

in poker, you CAN - the market is each individual hand.

can you bluff? sure. people do it on the DOM all the time by flashing fake size to try to get others to react. a market maker can create the illusion of demand where none really exists, in order to move the price. otoh, he (unlike the poker player) has to be there to provide liquidity at all times, whereas the poker player can simply fold

but ultimately, it's most similar in bankroll management (poor money management is amongst the #1 downfall of traders, even if they are very talented at trading itself), in not going on tilt (making emotional/revenge trades will KILL you) and especially in being able to say "i'm wrong and i'm getting out". the best traders are more than willing to take their stop loss. if the market turns around and it would have been a winning trade ... oh well. just like the poker player must fold when he thinks he's beat.

the good trader wants to lose small and win big... "cut your losses short and let your winners ride", so often a winning strategy in trading might only have 30% successful trades, but you still make money.

also, the costs of slippage and commission are similar to the costs of rake.

options guys remind me the most of the internet whizzes because the options guys are VERY comfortable with the math, and with probability curves, and some very complex , galfond'ian if you will , math. the futures guys, ESPECIALLY the pit guys (who are a dying breed) are much more like "feel players" who have great intuition and card sense. they know when they are beat, they are more sensitive to physical tells, and especially for a floor trader, they use their physicality to help execute a trade, just like a live player can use his presence, false tells, etc. to sell his bet.

it's interesting stuff i am seeing here in this forum.

03-16-2012, 11:49 AM   #8
yaqh
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Re: Theory terminology

Quote:
 Originally Posted by wbuster if all Players would shove and call any two cards they would be break even too, maybe add that point ty for ya post =)
Sure, but at that point, each player can improve his expectation by changing his strategy, something which is not true at the equilibrium.

I just wanted to make the point about the value of the equilibrium being 0 only on average over all positions because it seems like that's something people get confused about. I've even seen people solve for the "equilibrium" in a subgame by setting the EV equal to 0, as if EV=0 is the definition of Nash equilibrium.

Quote:
 Originally Posted by plexiq Looks pretty good, thanks!
Quote:
 Originally Posted by Bob147 sticky at the top imo.
Thanks for the positive feedback guys.

Quote:
 Originally Posted by RainbowBright fwiw, I'm not sure if people would be interested in distinguishing between "hand distribution" and "range". Hand Distribution: All hands for a player before any action is taken on a particular street Range: All hands used by player when taking an action For example, on the Flop: Hand Distribution: All pocket pairs 22+ Betting Range = JJ+ Checking Range = 22 - TT Check-Calling Range = 66 - TT Check-Folding Range = 22 - 66 I'm not sure if it's necessary, but I feel that I get confused sometimes on these boards. thx for doing this.
Ah, to be honest, I think I use the terms "range" and "hand distribution" almost interchangably. In particular, to specify the range at the beginning of a street, I usually go with 'turn starting distribution' or 'turn starting range'.

If anything, 'range' is sort of a grouping of hands without any context, whereas 'hand distribution' usually implies a distribution over the various possible hand strengths, which means that there's opponent(s)' range(s) and a particular board involved.

And of course the 'equity distribution' is something specific and different.

But anyway these are kind of poker-specific (not game theory) words, so I wouldn't expect this thread to be authoritative about their meanings. But I am happy to talk about it.

Quote:
 Originally Posted by gedanken Perhaps a more clear example of the definition is how folding first to act is dominated by checking.
Yup, it's true that it's another example, and it's probably more intuitive. However, it's a bit harder to construct a strategy that dominates it. I guess you could take the strategy which is the same except that instead of open-folding, you check and then proceed by only putting any more money in the pot if you get to the river and have the nuts. It should be clear that this strategy does at least as well as the one that involved open-folding, and so it weakly dominates it. (Weakly because it doesn't do strictly better.. it might do the same.)

Quote:
 Originally Posted by Tua good post. btw, i come from a stock/futures (and to a lesser extent - options) trading background and i find poker interesting in a lot of ways. a lot of the game theory carries over, but a lot is quite unique to poker (and trading)
Interesting stuff, thanks for the response.

03-17-2012, 02:16 AM   #9
kamikaze baby
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Re: Theory terminology

Quote:
 Originally Posted by yaqh Nash equilibrium strategies are also known as optimal or game theory optimal or GTO or unexploitable. The fact that "optimal" does not simply mean "maximally exploitative" really seems to trip people up and is thus unfortunate, but that's the language the mathematicians chose, so we're stuck with it.
Very nice post, yaqh, but I just wanted to comment on the above. If you talk to a game theorist (my brother is an economics professor specializing in game theory, so I did ), his or her understanding of the word 'optimal' is completely different from the meaning used in poker theory. An optimal strategy in game theory is not typically an equilibrium or unexploitable strategy; it's a max EV strategy when the game parameters are completely specified (including opponent responses). When people talk about GTO strategy in poker, they really mean minimax strategy, and the misuse of the word 'optimal' has somehow crept into poker-speak and has stuck. It's unfortunate, not only because it's confusing, but ironically because it contradicts the usage from game theory itself.

If you simply google the phrase 'game theory optimal' in quotes, you won't find a single usage of the phrase in any mathematical literature. The only hits you'll get are from poker.

03-17-2012, 02:58 AM   #10
yaqh
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Re: Theory terminology

Quote:
 Originally Posted by kamikaze baby Very nice post, yaqh, but I just wanted to comment on the above. If you talk to a game theorist (my brother is an economics professor specializing in game theory, so I did ), his or her understanding of the word 'optimal' is completely different from the meaning used in poker theory. An optimal strategy in game theory is not typically an equilibrium or unexploitable strategy; it's a max EV strategy when the game parameters are completely specified (including opponent responses). When people talk about GTO strategy in poker, they really mean minimax strategy, and the misuse of the word 'optimal' has somehow crept into poker-speak and has stuck. It's unfortunate, not only because it's confusing, but ironically because it contradicts the usage from game theory itself.
Gah, I didn't want it to be so, but you might be right. Chen and Ankenman definitely use 'optimal' to mean 'equilibrium' in The Mathematics of Poker, though, which may be where the confusion began. I wonder why they did that. I'm going to keep looking for uses of the word optimal in the math literature. I don't trust economists .

Quote:
 Originally Posted by kamikaze baby If you simply google the phrase 'game theory optimal' in quotes, you won't find a single usage of the phrase in any mathematical literature. The only hits you'll get are from poker.
Well, of course they don't call it game theory optimal in game theory.

Spoiler:

Last edited by yaqh; 03-17-2012 at 03:04 AM.

 03-17-2012, 03:37 AM #11 yaqh Pooh-Bah     Join Date: Aug 2007 Location: mountain view Posts: 5,745 Re: Theory terminology K, here's two game theory books that use 'optimal' to mean 'equilibrium' http://books.google.com/books?id=orO...sec=frontcover http://books.google.com/books?id=fep...sec=frontcover edit: 2 more: http://www.amazon.com/Introduction-T.../dp/0486428117 http://www.amazon.com/Games-Theory-A.../dp/0486432378 Just search inside the book for 'optimal' to verify. If I had to guess, it seems to be a difference between pure mathematicians and economists. Last edited by yaqh; 03-17-2012 at 04:01 AM.
 03-17-2012, 11:36 AM #12 AmyIsNo1 journeyman     Join Date: May 2011 Posts: 304 Re: Theory terminology Gilpin and Sandholm also used 'optimal' when they solved Rhode Island Holdem, which was before MoP was published. http://www.cs.cmu.edu/~sandholm/RIHo...roceedings.pdf
 03-17-2012, 12:28 PM #13 carlop centurion   Join Date: Feb 2011 Posts: 107 Re: Theory terminology Good job, should be sticked or at least linked in the FAQ page for me. As a side note, another possible "dominated strategy" is folding preflop hand XYsuited while raising hand XYoffsuited. If you start folding some of the offsuited and raising the suited hand you gain on every possible spot. Or folding AA preflop (in cash game, in certain spot in sat tournament can be right), opposed to go all-in.
 03-17-2012, 08:44 PM #14 yaqh Pooh-Bah     Join Date: Aug 2007 Location: mountain view Posts: 5,745 Re: Theory terminology We should just outlaw the use of the word optimal in this forum
03-17-2012, 08:52 PM   #15
kamikaze baby
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Re: Theory terminology

Quote:
 Originally Posted by yaqh We should just outlaw the use of the word optimal in this forum

When I spoke to him a couple of days ago, I asked my brother that exact question - is it possible that mathematician game theorists use the word 'optimal' differently from economist game theorists, and he said "I don't think so". I'll point him to the links you posted and see what he has to say!

03-18-2012, 10:20 AM   #16
buggzilla
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Re: Theory terminology

Quote:
 Originally Posted by yaqh equity The equity of a hand or a range is how often it will win at showdown if all betting were stopped and all players checked down to showdown. This frequency is averaged over all the cards that can come and all the ranges involved.
Is this actually the correct definition of Equity? I admit I've always been a little confused about it. Most knowledgeable poker experts and mathematicians will tell you that your hand equity is actually your expected "share" of the pot. But in EV calculations (and on TV!) it's treated just like it's the percentage chance that it will will by showdown.

Per the Pokerstove FAQ, for instance, it says:
"The values generated are all-in equity values. This is not the chance that a hand will win the pot. Rather it is the fraction of the pot that a hand will win on average over many repeated trials, including split pots. The equity for a hand is calculated by dividing the number of "pots" that the hand won by the number outcomes considered. Because two players can split a pot, a player can win fractional pots. Thus, it is possible for a hand to have non-zero equity despite the fact that it cannot win."

So which is it?

To further complicate matters, when we talk about fold equity, most players are actually trying to express the probability that their opponent will fold to a raise.

I'm so confooooosed....

03-18-2012, 10:49 AM   #17
AmyIsNo1
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Join Date: May 2011
Posts: 304
Re: Theory terminology

Quote:
 Originally Posted by buggzilla Is this actually the correct definition of Equity? I admit I've always been a little confused about it. Most knowledgeable poker experts and mathematicians will tell you that your hand equity is actually your expected "share" of the pot. But in EV calculations (and on TV!) it's treated just like it's the percentage chance that it will will by showdown. Per the Pokerstove FAQ, for instance, it says: "The values generated are all-in equity values. This is not the chance that a hand will win the pot. Rather it is the fraction of the pot that a hand will win on average over many repeated trials, including split pots. The equity for a hand is calculated by dividing the number of "pots" that the hand won by the number outcomes considered. Because two players can split a pot, a player can win fractional pots. Thus, it is possible for a hand to have non-zero equity despite the fact that it cannot win." So which is it? To further complicate matters, when we talk about fold equity, most players are actually trying to express the probability that their opponent will fold to a raise. I'm so confooooosed....
The key phrase in that Pokerstove quote is including split pots. This should probably be mentioned here as well. I also think that it should be called "showdown equity", "all-in equity" or "hot'n'cold equity" instead of just "equity". It's the expected share of the pot if the hands went to showdown with no more betting.

03-18-2012, 11:01 AM   #18
yaqh
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Re: Theory terminology

Quote:
 Originally Posted by buggzilla Is this actually the correct definition of Equity? I admit I've always been a little confused about it. Most knowledgeable poker experts and mathematicians will tell you that your hand equity is actually your expected "share" of the pot. But in EV calculations (and on TV!) it's treated just like it's the percentage chance that it will will by showdown.
It's the "expected share" of the pot if there is no more betting or folding. This is close to the percent chance to win except for the slight difference (as you point out below) caused by the chance of splitting the pot.

Oh, you might be pointing out that some people use 'equity' to refer to a dollar value as opposed to a percent. For example, if you have 60% equity in a \$100 pot, they'll say your equity is \$60. So they're still refering to your expected share in the pot, they're just using the dollar value instead of the percent of the pot size.

Quote:
 Originally Posted by buggzilla Per the Pokerstove FAQ, for instance, it says: "The values generated are all-in equity values. This is not the chance that a hand will win the pot. Rather it is the fraction of the pot that a hand will win on average over many repeated trials, including split pots. The equity for a hand is calculated by dividing the number of "pots" that the hand won by the number outcomes considered. Because two players can split a pot, a player can win fractional pots. Thus, it is possible for a hand to have non-zero equity despite the fact that it cannot win."
Yea you're right, I was a bit sloppy (i.e. wrong ) in OP since I neglected split pots. We should say that equity is the chance of winning plus half the chance of chopping.

03-18-2012, 11:27 AM   #19
yaqh
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Re: Theory terminology

Quote:
 Originally Posted by carlop As a side note, another possible "dominated strategy" is folding preflop hand XYsuited while raising hand XYoffsuited. If you start folding some of the offsuited and raising the suited hand you gain on every possible spot.
I'm not sure that this is actually true, due to card elimination effects if nothing else. Here's an example that's even kind of realistic:

Consider the heads up no limit game where the SB minraises or folds his button and then, if he minraised, the BB shoves or folds.

In this case, at small/medium (say, 20BB) stack sizes, BB might be shoving a range with mostly big cards and smaller suited connectors (but not small, unsuited cards). In this case, minraising, say, 65o is better for the SB than raising 65s. The reason is that they're both going to be folding to a shove, but BB's slightly less likely to shove if SB holds 65o since 65o blocks twice as many of the BB's 54s,56s,67s combos.

So, the SB's steal is slightly more likely to work with 65o than 65s which makes raise/folding 65o better than raise/folding 65s. And so, if it's close, there definitely could be a situation where SB should be raising 65o but open-folding 65s.

03-18-2012, 12:05 PM   #20
carlop
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Posts: 107
Re: Theory terminology

Quote:
 Originally Posted by yaqh The reason is that they're both going to be folding to a shove, but BB's slightly less likely to shove if SB holds 65o since 65o blocks twice as many of the BB's 54s,56s,67s combos. So, the SB's steal is slightly more likely to work with 65o than 65s which makes raise/folding 65o better than raise/folding 65s. And so, if it's close, there definitely could be a situation where SB should be raising 65o but open-folding 65s.
65o is better than 65s only because it blocks one more combo of 65s (2 instead of 1).
vs 54s or 76s every 65 (off or suited) has the same blocker effect.
Eg. if I hold 6h5s or 6s5s there exist 3 combo of 54s in any case (5h4h, 5c4c, 5s4s).

The minor effect of blocking one more combo can change the equilibrium in toy game restricted without post-flop game, but I think that in complex game having more equity if you saw a flop is a lot better.

But you are right, this is only "almost dominated", so not so usefull.

03-18-2012, 12:18 PM   #21
yaqh
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Re: Theory terminology

Quote:
 Originally Posted by carlop 65o is better than 65s only because it blocks combo of 65s. vs 54s or 76s every 65 (off or suited) has the same blocker effect. Eg. if I hold 6h5s or 6h5h there exist 3 combo of 54s in any case.
Ah, yea you're right.

Anyway, as far as the definition of 'dominated strategy' goes, the thing to keep in mind is that it really means 'better (or at least as good) versus every possible opponent strategy'. So you have to consider even the really wacky ones where, say, Villain is folding all hands preflop except for 32o.

As far as the opening suited vs unsuited hands example, maybe Villain plays well in general except that he's retardedly terrible on 4-flush boards: he open-folds his flushes but goes all-in with all non-flush hands. In this case, your unsuited hands are probably more valuable than your suited ones since you have twice as many flushdraws.

Anyhow, removing dominated strategies from consideration can help you make a lot of progress towards solving some games, but I don't think it's particularly useful in poker.

03-18-2012, 09:36 PM   #22
yaqh
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Re: Theory terminology

Quote:
 Originally Posted by yaqh Anyhow, removing dominated strategies from consideration can help you make a lot of progress towards solving some games, but I don't think it's particularly useful in poker.
Someone mentioned Liv Boeree, and I was reminded of my favorite example of a game that can be solved simply by eliminating the dominated pure strategies.

Scary stuff.

03-19-2012, 05:42 AM   #23
kamikaze baby
old hand

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Re: Theory terminology

Quote:
 Originally Posted by yaqh K, here's two game theory books that use 'optimal' to mean 'equilibrium' http://books.google.com/books?id=orO...sec=frontcover http://books.google.com/books?id=fep...sec=frontcover edit: 2 more: http://www.amazon.com/Introduction-T.../dp/0486428117 http://www.amazon.com/Games-Theory-A.../dp/0486432378 Just search inside the book for 'optimal' to verify. If I had to guess, it seems to be a difference between pure mathematicians and economists.
Okay, I showed these links to my brother, and he said roughly the following (this might turn into a bit of a game of 'broken telephone' since I'm repeating things second-hand, but I hope it's more or less accurate )

* at a glance, the first book never defines how it's using the word 'optimal'; the second is a translation from Russian and uses all kinds of funny language; and the last two are archaic and use a lot of outdated terminology;

* in economics, the word 'optimal' would be reserved for two situations. The most common usage would be when discussing a well-defined optimization problem (not poker) in which there would be an optimal solution. The other would be a more casual usage of the term in a game where there is a clear best strategy;

* instead economist game theorists would use more precise language to describe a strategy - they would talk either about a 'best response' strategy' (that would be what we call an exploitative strategy) or a 'minmax strategy' (which is what we call a 'game theory optimal strategy')

* in contemporary game theory, there are almost no pure mathematicians working in the field, outside of mathematical biology. Most research is done in computer science and economics. So while he conceded that there may be some specialized vernacular that is only used among pure math game theorists, that isn't the group that is writing most of the papers about the field;

* the one caveat he mentioned is that zero-sum games like poker are of very limited theoretical interest in contemporary game theory. So if there is some specific terminology in use for that one class of games, he might not be familiar with it. But I think he'd be surprised if that were true.

Anyway, long story short, he still views the usage of the word 'optimal' in poker theory with a lot of suspicion, and says that his game theory colleagues would never use the word the way we do. Take that for what you will!

 03-19-2012, 10:18 AM #24 yaqh Pooh-Bah     Join Date: Aug 2007 Location: mountain view Posts: 5,745 Re: Theory terminology Sounds good, thanks for looking into it. I think I'll just try to avoid using the word in the future myself. It has led to a lot of confusion around here...
 03-19-2012, 10:52 AM #25 RustyBrooks Carpal \'Tunnel     Join Date: Feb 2006 Location: Austin, TX Posts: 24,378 Re: Theory terminology I've stickied this. I'll be monitoring it from time to time. If there are any questions about additions or modifications feel free to put them in this thread and we'll try to address concerns. Might be nice to add links to some of the better game theory threads also?

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