Ask me anything about poker game theory - Page 4 - Poker Theory

Jerrod Ankenman · 07-24-2012, 10:54 AM

Quote:

Originally Posted by keanosdog

not a theory question but a question on theory itself.

Do you have to understand poker theory to be a successful player?

Well, to be a winner in medium-tough games, you have to understand some things. I mean, it's pretty unlikely you could really win long-term without having some understanding of betting and bluffing ratios, balancing distributions, pot control, etc. But do you have to be able to get through our book? Probably not. There are probably some pretty good players who are just excellent at exploiting their opponents without too much of a theory base. I suspect that very few of the very best players are of this type, however. And pretty clearly they understand things that I don't as well.

keanosdog · 07-24-2012, 12:07 PM

Quote:

Originally Posted by Jerrod Ankenman

Well, to be a winner in medium-tough games, you have to understand some things. I mean, it's pretty unlikely you could really win long-term without having some understanding of betting and bluffing ratios, balancing distributions, pot control, etc. But do you have to be able to get through our book? Probably not. There are probably some pretty good players who are just excellent at exploiting their opponents without too much of a theory base. I suspect that very few of the very best players are of this type, however. And pretty clearly they understand things that I don't as well.

Thanks.

I think I phrased the question badly. What I was really trying to ask is do you have to STUDY poker theory to be succesful.

Take two players like say ivey and dwan.

I'd doubt ivey (could be wrong) spent much time "studying" poker while from what I know of Dwan I'd think he spent a lot of time studying theory as he came up online.

I have no doubt Ivey understands what he's doing (obv) but I would think dwan has more of a background in actual theory.

olavfo · 07-24-2012, 01:19 PM

Strong LHE HU bots exist, but that doesn't mean LHE HU is the simplest game to "solve" through AI programming. What would be the three easiest real poker games (chosen from the online menu) to program a strong AI for? We can cheat a little and assume all games can be played HU with fixed-limit betting.

So let's say you have some finite amount of man hours and computing power available, and your task is to come up with the closest-to-optimal bot possible for some real poker game. Which games would you consider?

Rant · 07-24-2012, 02:11 PM

In NL Hold 'em how is GTO bet sizing affected by stack size?

In other words, if stacks are VERY deep, say 1M BB, how would optimal bet sizing change?

Jerrod Ankenman · 07-24-2012, 02:36 PM

Quote:

Originally Posted by keanosdog

Thanks.

I think I phrased the question badly. What I was really trying to ask is do you have to STUDY poker theory to be succesful.

Take two players like say ivey and dwan.

I'd doubt ivey (could be wrong) spent much time "studying" poker while from what I know of Dwan I'd think he spent a lot of time studying theory as he came up online.

I have no doubt Ivey understands what he's doing (obv) but I would think dwan has more of a background in actual theory.

You could also try to think of it in a Bayesian manner. Pick the top 50 players. How many of them have studied abstract poker theory in a serious way? Now think of the top 5000 players. How many of them have studied? A lot fewer, probably. So does studying help you become really good? Probably, but also being smart helps you to be able to study AND helps you to be really good. So I dunno.

Studying theory isn't strictly necessary but it's hard to see how it will hurt, unless you don't get the right understanding. Then you might wind up adopting supposedly "balanced" strategies which suck and then posting about them on 2+2, "correcting" other players. (I have seen this disturbingly often.)

Jerrod Ankenman · 07-24-2012, 02:41 PM

Quote:

Originally Posted by Rant

In NL Hold 'em how is GTO bet sizing affected by stack size?

In other words, if stacks are VERY deep, say 1M BB, how would optimal bet sizing change?

I don't know.

Some people seem to think that maybe the right bet sizes would get a lot bigger, because they have some idea that bet sizing revolves around getting it all in. I suspect that this is false, that if you have 1M BB stacks most of that money is just almost never in play. But I cannot prove this or even make a terribly convincing argument for it, nor do I even know how to size bets optimally with {20,30,50,100} BBs. The problem seems wicked hard to me, so now I just follow the herd and make a lot of min+smallamt raises and reraises, because it seems effective and then when I ask NL wizards about a hand, they don't roll their eyes at my bet sizing.

Anyway if you have 1M BBs, just ask the other guy to play bigger.

Jerrod Ankenman · 07-24-2012, 02:49 PM

Quote:

Originally Posted by olavfo

Strong LHE HU bots exist, but that doesn't mean LHE HU is the simplest game to "solve" through AI programming. What would be the three easiest real poker games (chosen from the online menu) to program a strong AI for? We can cheat a little and assume all games can be played HU with fixed-limit betting.

So let's say you have some finite amount of man hours and computing power available, and your task is to come up with the closest-to-optimal bot possible for some real poker game. Which games would you consider?

Well, the smallest games, naturally. I guess those are 2-7 single draw and draw high (they only have two rounds of betting and one draw!). LHE is probably next. Stud games are awful, so many streets. Omaha is also awful, a ton of hand types and the easy simplifications really mess up the game.

beeny · 07-24-2012, 04:19 PM

What do you think about the trend of finding GTO of NLHE cash games by breaking the game down street-by-street? Does it come close to what an actual GTO strategy might look like?

For example, a 3xbb button steal is profitable with any two cards if it works 67% of the time, so the theorists find the ranges where the blinds defend enough that opening any two cards on the button isn't outright profitable. Consequently, the button must defend enough of his range so that he can't be 3-bet from the blinds with any two cards and instantly lose money.

AnJo280 · 07-24-2012, 07:33 PM

1vs1
player a minbets 100%
player b calls 100%
Player a c-bets halfpot 100%
player b folds 33,33....% to c-bet.
both players check turn and river.

Who´s +ev and what if player b calls exactly 50%
I have trouble calculating how nonSD exploitable people are who call too much pre but fold too much postflop.

R Gibert · 07-24-2012, 07:50 PM

The following is a very slightly edited copy of an email I sent to my friends. I'm not sure if this has much practical value, so I'm curious about your assessment.

Quote:

I wrote a program that calculates optimal bluffing and optimal calling frequencies at the river and stumbled across a special situation.

As usual, I will be making some unrealistic assumptions in order to tease out an interesting insight, but I feel a little lazy today and will not spell them all out. Instead, I will count on you guys, Alan excepted, to use your brains and infer them.

Here's the situation. You're at the river and Villain has a large vbet range of say 64%. Hero has a 100% bluff catching range. The pot is $100 and Villain pots it. Well it turns out that for a pot size bet, Villain should vbet 64% of the time, bluff 32% of the time and fold the remaining 4% of the time. Few players mix their vbets and bluffs in the proper ratio and this is partly, because they are playing by feel and partly, because they want to be exploitive.

Now here is the thing I noticed. Against an opponent who folds too often, Villain should bluff more often. However, more often in this case means going from bluffing 32% of the time to only 36%. Villains vbet range plus bluff range cannot exceed 100% of course. So Villain cannot make a significant amount of money exploiting a Hero that folds too much.

From Hero's point of view, this creates an opportunity. If he does not know whether Villain bluffs too often or not often enough, Hero can simply assume the latter, because there is very little downside to being wrong. This means that if hero always or mostly folds, there is a decent chance he will be playing exploitively. BTW, for the example I've outlined, the optimal ratio of folds to calls for Hero with his bluff catchers is 50%.

Here are a few numbers from my program:

Code:

Pot [100.00]? 
Bet [100.00]? 
vbet  [0.50]? .64
bluff [0.32]? 
call  [0.50]? 

Pot = $100.00
Bet = $100.00
vbet = 0.64
bluff = 0.32
call = 0.50

EV = $96.00


Pot [100.00]? 
Bet [100.00]? 
vbet  [0.64]? 
bluff [0.32]? .36
call  [1.00]? 0.0

Pot = $100.00
Bet = $100.00
vbet = 0.64
bluff = 0.36
call = 0.00

EV = $100.00


Pot [100.00]? 
Bet [100.00]? 
vbet  [0.64]? 
bluff [0.32]? .16
call  [0.00]? 

Pot = $100.00
Bet = $100.00
vbet = 0.64
bluff = 0.16
call = 0.00

EV = $80.00

With optimal vbet/bluff/calling ratios,
Villain's EV = $96
Hero's EV = Pot - $96 = $4

With Villain bluffing all his air and Hero always making the wrong decision by always folding, Villain's EV goes up from $96 to $100.

With Villain not bluffing often enough—say 16% as illustrated by my program— and Hero always folding, Villain's EV goes down from $96 to $80.

So by Hero always folding, He risked doing $4 worse to possibly doing $16 better. A 4 to 1 ratio. Good money odds that make it a good gamble. Of course, if Villain realizes what is going on, he can simply pocket the $4. However, I haven't seen this idea anywhere, so Villain's realizing this is going to be at the very least, rare.

Presumably, Villain might sort of catch on to the fact that Hero sometimes folds too much and start bluffing more often, but he will probably not realize how he was previously getting exploited. This means that Villain may start bluffing too often in situations where Hero's downside to folding is not small and the trick does not apply. In these situations, Hero can then be exploitive by calling more often.

bobf · 07-24-2012, 07:57 PM

Quote:

Originally Posted by slowjoe

Have you solved [0,1] vs [b,1] where 0 < b < 1?

Can it be solved analytically?

If S is the bet size, F(x) is Prob(player 1 hand <= x), G(x) = Prob(player 2 hand <= x). For the non-degenerate cases... player 1 value bets [0,v] and bluffs [b,1] and player 2 calls [0,c] where 0 < v < c < b < 1

If I didn't make any mistakes... the indifference equations are
[1] G(c) = 2G(v)
[2] G(b) = (1+s)G(c)
[3] F(v) = (s+1)/s(1-F(b))

[1] makes player 1 indifferent to betting/checking at v. [2] makes him indifferent to checking/bluffing as b. [3] makes player 2 indifferent to calling/folding at c.

In your example, changing your b to k because I'm using b already [0,1] vs [k,1]
F(x) = x
G(x) = (x - k) / (1 - k) for x in [k,1] and 0 for x in [0,k]

Subsituting F and G into the indifference equations... the rest is algebra.

Pretty sure that even with "black box" F(x) and G(x) this can be solved quickly non-analytically using binary search methods, but it is probably kind of messy since F and G do not have to have inverses.

Jerrod Ankenman · 07-24-2012, 08:18 PM

Quote:

Originally Posted by beeny

What do you think about the trend of finding GTO of NLHE cash games by breaking the game down street-by-street? Does it come close to what an actual GTO strategy might look like?

For example, a 3xbb button steal is profitable with any two cards if it works 67% of the time, so the theorists find the ranges where the blinds defend enough that opening any two cards on the button isn't outright profitable. Consequently, the button must defend enough of his range so that he can't be 3-bet from the blinds with any two cards and instantly lose money.

Well, it's better than guessing for sure. How much does it look like a real GTO strategy? Probably not very much. But it is a reasonably logical bound: you can't play any tighter than X otherwise there is an obvious exploitive response.

Jerrod Ankenman · 07-24-2012, 08:21 PM

Quote:

Originally Posted by AnJo280

1vs1
player a minbets 100%
player b calls 100%
Player a c-bets halfpot 100%
player b folds 33,33....% to c-bet.
both players check turn and river.

Who´s +ev and what if player b calls exactly 50%
I have trouble calculating how nonSD exploitable people are who call too much pre but fold too much postflop.

I don't really understand this, is it holdem? Am I supposed to like do these calculations? There should be software for this, I don't have any special expertise. Or maybe someone else will help you.

Jerrod Ankenman · 07-24-2012, 08:30 PM

Quote:

Originally Posted by R Gibert

The following is a very slightly edited copy of an email I sent to my friends. I'm not sure if this has much practical value, so I'm curious about your assessment.

Seems like what you wrote is basically right about the relative upside/downside of deviating in one way or another and the difficulty the other dude will have in perceiving your deviation and exploiting it.

The hidden idea might be: what are you doing on the river with 64% value bets? How come you only have folds in addition to your bets and bluffs, what about checking for a showdown or checking to induce a bluff, etc? If these things exist, you could have done better on previous streets by expanding your distribution, etc.

Jerrod Ankenman · 07-24-2012, 08:36 PM

Quote:

Originally Posted by bobf

If S is the bet size, F(x) is Prob(player 1 hand <= x), G(x) = Prob(player 2 hand <= x). For the non-degenerate cases... player 1 value bets [0,v] and bluffs [b,1] and player 2 calls [0,c] where 0 < v < c < b < 1

If I didn't make any mistakes... the indifference equations are
[1] G(c) = 2G(v)
[2] G(b) = (1+s)G(c)
[3] F(v) = (s+1)/s(1-F(b))

[1] makes player 1 indifferent to betting/checking at v. [2] makes him indifferent to checking/bluffing as b. [3] makes player 2 indifferent to calling/folding at c.

In your example, changing your b to k because I'm using b already [0,1] vs [k,1]
F(x) = x
G(x) = (x - k) / (1 - k) for x in [k,1] and 0 for x in [0,k]

Subsituting F and G into the indifference equations... the rest is algebra.

Pretty sure that even with "black box" F(x) and G(x) this can be solved quickly non-analytically using binary search methods, but it is probably kind of messy since F and G do not have to have inverses.

Wait, equation 1 isn't right. X bets all the hands up to k with impunity, and only then does Y start winning anything on his calls. So G(v) - k = k - G(c), or G(v)+G(c) = 2k.

I stopped proofreading there because I am lazy.