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Originally Posted by durrrr
if you play a strategy that is the most optimal were i to know it... then ur gonna lose a lot- b/c its pretty easy to figure out what that is, and i can play similarly back but exploit occasional spots
There are no 'occasional spots' where you can exloit a GTO HU NL bot! This is the very definition of Game Theory Optimal Strategy. Assuming a fixed stackdepth and each player having to both play from the SB and BB and a finite number of betsizes, by Nash's Theorem there exists a mixed strategy that will not lose in expectation.
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and you won't be sure if I'm doing that. if you then adapt ur play based on how I'm playing u aren't playing GTO anymore (GTO is a strategy that doesn't need to be adapted).
I dare durrrr to come up with one hypothetical spot where he could exploit the GTO strategy. Since he did already in the 2011 thread I will use that one to show why he is wrong, but he is free to come up with another example.
http://forumserver.twoplustwo.com/sh...&postcount=200
Quote:
Originally Posted by durrrr
edit: assume i raise- bot reraises, i 4b, bot calls. we're 100,000,000bb deep. on river the board is t98hhhxx and i have j6hh. the bot can't ever really have q7hh for both blockers, so if theres enough aggression i can bluffshove for 50,000 times the pot or w/e and he'll need to fold (100m bb's yo), but he can't ever do the same to me b/c he doesn't know i can't have q7hh. this is a super complicated example that'd obv almost never come up, but its a clear equity advantage for me. also if the bot calls some % then i don't need to ever bluffshove, but i get paid off some % for 50,000 times the pot- where the bot never does. more simplistic scenarios come up but they aren't free equity they carry risk. i hope sauce bet w/ me before i posted this example
On the river with a Th9h8hxx board given the action durrrr's range will consist of Jh6h X percent of time and he will shove 50,000 times the pot 100% with it.
And with positions reversed (i.e. the GTO bot on the button) and the same board and action till the river the bot will have Jh6h Y percent of time.
Now durrrr makes the assumption that - mostly given preflop 4bet, since one would expect Qh7h not to fold too quickly on Th9h8h - does have Qh7h with exactly 0%.
He does never state how often he would have Qh7h in the same spot! I will come back to this later, since it can be used against durrrr's argument.
The bot has Jh6h with the optimal frequency of Y percent and will shove it with a Z percent frequency, if this optimal frequency was 100% then durrrr would not exploit the bot since he plays this spot exactly the same. If this frequency is lower then durrrr is bluffing away his 100,000,000bb too often.
Also the bot will call a 50,000 times potbet on the river with his bluffcatchers with a frequency that is (roughly) proportional to the inverse of the size of the bet. So when he bluffs for 50,000 times the pot he will win 1 potsize 49,999 times and lose 50,000 times the pot 1 time vs the hands that would've called a potsized riverbet (clearly these numbers are not exact but just an indication since I don't know the GTO strategy for 100,000,000 HU NLHE and furthermore they are based on a comparison to a 1x potbet for simplicity where is it conceivable that optimal betsize is much larger). Winning 1 unit 49,999 times and losing 50,000 units one time equals losing 1 unit one time, which is (again roughly) the same as losing to the better hands at showdown when checking.
Also note that Qh7h is not the only bluffcatcher that the bot will have in his range. If he would only bluffcatch with Qh7h then his GTO opponent (and durrrr when he copies this strategy) could make twoway bets with {KhJh, AhJh} by shoving them, folding out the ace high flush, the 7h6h straightflush and boats (to which they lose), and get calls from Qh7h (which they beat). Hence these hands need to bluffcatch also.
But most importantly, by turning these strong hands AhJh, KhJh, Jh6h into a bluff will lose expectation compared to the strategy of the GTO bot. durrrr thinks he can do something special that the bot cannot do (i.e.
shoving some combo's in a certain spot with a certain frequency) but once you write it out for
what it really is you don't even need to understand Nash's Theorem to see that durrrr is mistaken here. Everything durrrr can do the bot can do also.
Back to how often durrrr calls the 4bet with Qh7h. If durrrr does have Qh7h with the same 0% frequency as the bot, then clearly the bot can do the same to durrrr (i.e. bluffshoving Jh6h with a 100% frequency when this has a higher expected value than playing it for value).
But it is not impossible that there are spots where the bot never has the nuts and durrrr's range is stronger to the point where durrrr can shove a wide range or even his entire range and the bot has to fold everything. Once you understand this you will understand that any such example spot that you can come up with is just as useless as the Jh6h on Th9h8h spot.
This does not prove that durrrr could exploit the bot since the bot can always do the same. And furthermore these situation will come up very infrequent (if ever).
One example would be that durrrr 2x potbets the turn and the bot calls, and on 70% of rivers durrrr will shove and the bot must fold and when the bot hits his 30% good rivers he has exactly 0 implied odds. The bot must win the pot 40% of times to make up for the 2x potbet call on the turn but only wins 30%, a contradiction since the bot only makes optimal calls on the turn.
We can conclude that against a GTO bot there will be no such spots where you can bluff him of his entire range without a cost. The cost will be either money lost in expectation on previous streets by playing too loose or too tight and losing more in common spots than you can make up with the very rare spots.
This is likely the same situation as the Qh7h call preflop, say it loses 5bb on average when you call. And 1 in 1,000,000 times (the Th9h8h runout with given action) you lose a 200bb pot on the river to a shove that you cannot call since you don't have Qh7h does not mean you got exploited since 5bb >>>>> 200bb/1,000,000.
http://forumserver.twoplustwo.com/sh...&postcount=212
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Originally Posted by durrrr
Quote:
Originally Posted by Yuth
In your J6s example the GTO bot would assume you bluff there with nut blockers and adjust its range as such. Meaning he'd still fold 99.998x% of all his range except randomly show up with the A hi flush. And it would be a breakeven strategy.
i could fold 100% of the time to his shove tho, so this means id never need to bluff the bot, and would get paid off .002% of the time w/ my straight flush (obv itd take a while to realize- but when playing for eternity i just made equity).
This is clearly wrong, if you always fold anything but QhJh to a shove the bot can exploit you by bluffshoving any Jh in this spot. Which in turn would be highly exploitable since you could then call with any hand that has over 50% equity against his {JhX | not a valuehand} range on the river. So he will bluff with a much lower but optimal frequency.
If you only get paid off 0.002 percent of the time with your straightflush against his bluffcatchers that would've called a 1x potbet 100 percent of the time you don't make any money by shoving, at least not in expectation!
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point is in this spot i have an edge on the bot. once u admit i have an edge in one spot, u can quickly deduce (think for 15min) how its gg bot
This logic would've been correct if you had an edge in just one spot.
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(hint if he calls x% i can bluffshove more when i have a blocker to that x etc- if x is high to account for this i can just never bluff). the bot in my j6s example could never bluff if the situation was turned b/c it's risking 50,000 times the pot and it doesn't know i dont have q7hh (and if it makes assumptions like that... think for 15min... gg bot).
His calling frequency of x percent is optimal against your optimal range. Note that the GTO bot implicitly 'knows' your range since it knows it's own range in the same spot and how to play against it. Deviating from the optimal range (for example calling too many 4bets with Qh7h) will by definition not make you any profit, at least not in expectation.
It is very likely that with 100,000,000bb stacks the bot will have combo's that can make or block the nuts on even the rarest spots to protect itself from 50,000x potbets. Qh7h has this property but it is not even the best bluffcatcher in this rare Th9h8h example as I've explained with the twoway bets.
If Qh7h was a hand that could win 100,000,000bb more than X/100000000 times by calling Xbb at a certain point then for sure the bot would make that call with a positive frequency.
- cliffs:
- durrrr thinks that whenever his range is stronger than his opponent to the point where he could shove his entire range to get 100% folds in a Xbb pot in a spot that occurs with frequency Y will always weigh up to the cost of building your range up in a way that deviates from the optimal mixed strategy, when in reality the cost of building your range up like that will be always >= X*Ybb by the very definition of optimal strategy;
- durrrr makes the mistake by thinking in terms of hands in a vacuum and not in terms of expected winrate of a certain mixed strategy against another mixed strategy;
- durrrr owes me at least $5k for all the propbetfish action that he is not gonna give to other HS regs after reading my post.