Random Game Theory Stuff - Page 2

You guys seem to be using a definition where to exploit someone you are required to deviate from GTO. I suppose a definition of that sort isn't necessary wrong, but unlike 1, and 2 above I do think its really terrible.

Example:

You're playing HUNLHE with a GTO strategy. Your opponent is a fish who is shoving allin every hand. Are we exploiting them? Because we aren't deviating from GTO. My answer is very clearly yes, we're both taking advantage of the fact they're using a non-optimal line and we're making a ton of money against them (both 1 and 2 above). We wouldn't be maximally exploiting them, as in we won't be calling shoves with K9 offsuit, but I feel we're clearly exploiting them.

Also we can calculate the maximally exploitative strategy against any given strategy. It probably doesn't exist for full poker, but for toy games the maximally exploitative strategy and the GTO strategy can be equivalent. For example, if our range is only the nuts in a one street game, If its checked to us we'll be betting with both strategies. Our opponents range, whatever it is, doesn't automatically become unexploitable because we aren't deviating.

River play, dogmeat is correct. It is entirely possible that betting 100% of value + bluffs with a 100% checkfold range is better than dividing up ranges. You would only ever have a CR value range if it had the same value as always betting/cf. It could be entirely possible that having 100% check and balanced cr/cc/cf is better.

1 thing is for certain, GTO is not the maximally exploitable solution vs someone playing exploitable. It could be more profitable to CR a lot or never cr.

On January 31 2015 09:07 Highcard wrote: 1 thing is for certain, GTO is not the maximally exploitable solution vs someone playing exploitable.

For full poker this is likely true, but I just gave an example where it isn't true for a toy game.

On January 31 2015 08:29 drone666 wrote: anyone can help me solve this simple toy gaming? I feel a retard lol Show nested quote + The pot is 1, my range is {As, 2s, 2h, 2c, 2d} Your range is {Ks} Highest ranked card wins You are forced to check I can either bet 2, or check behind What is my GTO strategy?

i might have done this wrong but here's what i got. assuming that 'static strategy that gives a logically adjusting opponent over infinite hands the lowest EV' is a good enough definition of GTO, at least for this example. not even sure if that's right anymore lol.

pot = 1
optional bet = 2

1. you check 100%, i have 4 EV (no adjustments)

2. you bet A and check all 2's, in a vacuum gives me the lowest initial EV but once i adjust by folding 100% when you bet, it gives the same result as option 1, but i suppose it's better since it allows for initial adjustment error.

3. you bet 100%. i adjust by calling 100%. i have 10 EV ((4 * 3) - 2)

4. you bet the A and 3/4 2's, i adjust by calling 100%. i have 8 EV

(2's: 1 check = 1 EV, 3 bets = 9 EV. A: -2 EV) = 8 EV

5. you bet the A and 2/4 2's, i adjust by calling 100%. i have 6 EV

(2's: 2 checks = 2 EV, 2 bets = 6 EV. A: -2 EV) = 6 EV.

6. you bet the A and 1/4 2's, i adjust by calling 100%. i have 4 EV.

(2's: 3 checks = 3 EV, 1 bet = 3 EV. A: -2 EV) = 4 EV

even though options 1/2/6 get the same EV, i think 6 is the best because it takes a bigger sample for me to verify your strategy and adjust optimally, so there's a bigger chance for initial adjustment error on my part. also makes me the most indifferent to calling out of all the options.

On January 31 2015 08:30 NMcNasty wrote: You guys seem to be using a definition where to exploit someone you are required to deviate from GTO. I suppose a definition of that sort isn't necessary wrong, but unlike 1, and 2 above I do think its really terrible. Example: You're playing HUNLHE with a GTO strategy. Your opponent is a fish who is shoving allin every hand. Are we exploiting them? Because we aren't deviating from GTO. My answer is very clearly yes, we're both taking advantage of the fact they're using a non-optimal line and we're making a ton of money against them (both 1 and 2 above). We wouldn't be maximally exploiting them, as in we won't be calling shoves with K9 offsuit, but I feel we're clearly exploiting them. Also we can calculate the maximally exploitative strategy against any given strategy. It probably doesn't exist for full poker, but for toy games the maximally exploitative strategy and the GTO strategy can be equivalent. For example, if our range is only the nuts in a one street game, If its checked to us we'll be betting with both strategies. Our opponents range, whatever it is, doesn't automatically become unexploitable because we aren't deviating.

GTO range for calling a 100bb shove doesnt change with villians frecuency thus being MUCH more tight than an exploitive range that should be 50% and ridiculously more profitable

Really interesting article. doesn't change how i understand optimal (NE) play but it does make you think about how to define and understand exploitability. the key insight is that weakly dominated lines exist in full poker and they're very hard to tell from gto lines.

In a 2p2 thread ages ago ike made a great post with an easy to understand analogy: imagine rock-paper-scissors-shitrock. shitrock is the same as rock except it loses instead of draws vs a throw of rock, so rock weakly dominates shitrock and one should never play shitrock, even if one can perfectly balance a shitrock-paper-scissor strategy. similarly in the example one should not build a strategy around shoving turn because it is weakly dominated by an unexploitable two-street bet strategy with the right sizing. and indeed in full-poker, it is extremely difficult / impossible to tell a strategy involving rock from a strategy involving shitrock or how shit the shitrock is.

As for how you define exploitable, i agree with what has been mentioned in the thread that it can be a matter of semantics - meaning being determined by how people use it. the article defines exploitability in an unambiguous and precise way, and according to that definition unexploitability is indeed not as strong as optimal play. But under some other definition (e.g. exploitable is anything that doesn't net the minimax game value) unexploitable == gto. Overall it doesn't matter how you use the words as long as you have the concepts right. There's a fine line between arguing trivially over definitions of words and arguing productively over possible fundamental misunderstandings of the concepts.

On January 31 2015 08:29 drone666 wrote: anyone can help me solve this simple toy gaming? I feel a retard lol Show nested quote + The pot is 1, my range is {As, 2s, 2h, 2c, 2d} Your range is {Ks} Highest ranked card wins You are forced to check I can either bet 2, or check behind What is my GTO strategy?

if you bet, villain has to call 2 to win 3, so he needs to be good 40% of the time to call (2/(2+3) = 0.4).

You minimise his maximum possible EV by making him indifferent between calling and folding, so your ratio of value to bluffs has to be 60:40, or 3:2. Always bet the ace for value - you have an ace 20% of the time so 20% of your river actions will be valuebets. That means 13.33% of your river actions have to be bluffs (3:2 value/bluffs ratio), leaving the other 66.67% for checking back.

You have a deuce 80% of the time and your overall required riv bluff freq is 13.33%, so you want to bluff 16.67% of the time you have a deuce (0.133/0.8) and give up the remaining 83.33% of the time. A practical way to get to that frequency might be to pick a suit - let's say spades. You will bluff two thirds of the time when you have the 2s and never with the other deuces. Look at your watch and bluff if the second hand is between 0-40seconds.

This is what the article linked in op refers to as using the indifference condition to solve a simple toy game. It's interesting to know that solving real poker is far less simple, when there are multiple streets, multiple possible betsizes and the possibility opponent can raise.

thanks Romm3l,
I wasnt understanding why I had to bet one deuce 66% of the time, I knew I had to be bluffing 40% when Im betting but didnt know how to get to that number lol

There's no such thing as deviating from GTO in order to become unexploitable.

The only thing a GTO strategy guarantees is that you won't lose money.

On February 05 2015 04:28 MARSHALL28 wrote: There's no such thing as deviating from GTO in order to become unexploitable. The only thing a GTO strategy guarantees is that you won't lose money.

Well you will lose rake/2 if both play GTO, right?

On February 05 2015 04:28 MARSHALL28 wrote: There's no such thing as deviating from GTO in order to become unexploitable. The only thing a GTO strategy guarantees is that you won't lose money.

wat?

GTO is always unexploitable, but there are an infinite (or finite by sizing amounts) number of unexploitable non-GTO plays

I guess I just disagree with the author of the blog.

Maybe I'm completely wrong but here's how I see it...

The purpose of a GTO strategy is to breakeven at worst against every other strategy possible. If the goal is to breakeven, how do we improve on it? By becoming more break-even ?

Baal,

You and the article seem to be saying that there are multiple unexploitable strategies and that GTO is the strategy that is completely unexploitable while at the same time being the most exploitative...

Do you see the logical contradiction here? (you can't have an exploitative strategy and be unexploitable)

Maybe I don't know what I'm talking about, if somebody is sure I'm wrong please go ahead and explain to me.

considering abusing mod status and changing the title of this thread to "Smart People Nitpicking Over Semantics"

On February 06 2015 18:14 Daut wrote: considering abusing mod status and changing the title of this thread to "Smart People Nitpicking Over Semantics"

dont think thats what im doing at all. i think there's an actual argument here.

didn't the author provide an example of 2 unexploitable play in a simple example where one was GTO and the other one was not?

isn't that enough to prove you wrong marshall?

On February 06 2015 20:41 Fayth wrote: didn't the author provide an example of 2 unexploitable play in a simple example where one was GTO and the other one was not?

No, because the author is using a wacky definition of exploit. One of his "unexploitable" strategies has a better EV than the other against the best possible counterstrategy.

On February 06 2015 16:13 MARSHALL28 wrote: The purpose of a GTO strategy is to breakeven at worst against every other strategy possible.

That isn't what a GTO strategy is, but it is a characteristic of the sum of GTO strategies for a rakeless, hu, FLHE game with resetting stack sizes.

For asymmetrical starting conditions, ie one player has an immediate advantage over the other, for example sb vs bb, there still exist GTO strategies, but one those (the bb's), will lose money.

So a player playing optimally (GTO) from the bb can still lose money to a player playing sub-optimally from the sb (due to starting conditions).

On February 06 2015 21:16 NMcNasty wrote: Show nested quote + On February 06 2015 20:41 Fayth wrote: didn't the author provide an example of 2 unexploitable play in a simple example where one was GTO and the other one was not? No, because the author is using a wacky definition of exploit. One of his "unexploitable" strategies has a better EV than the other against the best possible counterstrategy.

How is there a counter strategy to GTO?

On February 06 2015 21:45 NMcNasty wrote: Show nested quote + On February 06 2015 16:13 MARSHALL28 wrote: The purpose of a GTO strategy is to breakeven at worst against every other strategy possible. That isn't what a GTO strategy is, but it is a characteristic of the sum of GTO strategies for a rakeless, hu, FLHE game with resetting stack sizes.

There is a GTO solution for every game of poker.

On February 06 2015 21:16 NMcNasty wrote: Show nested quote + On February 06 2015 20:41 Fayth wrote: didn't the author provide an example of 2 unexploitable play in a simple example where one was GTO and the other one was not? No, because the author is using a wacky definition of exploit. One of his "unexploitable" strategies has a better EV than the other against the best possible counterstrategy.

I still dont get what is not clear, shoving turn with a balanced bluff to value ratio is unexploitable meaning the opponents call or fold has the same EV yet that strategy is not GTO.