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  #1  
Old 01-25-2014, 04:10 PM
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Default Bayes Theorem in Poker

This is a bit of a head trip but anyway

The actions a player takes makes it more likely that they are that type of player based on the new info we have from their actions

Ok suppose you have a small sample of hud stats on a player that says he is nitty . Now he 3bets you and barrels off every street. There's 2 possible explanations for this

1) He rly is a nit and has a monster hand
2) He is a looser player than we initially thought and is doing it with a wider range

I can't do the maths but the very fact that this action happened makes 2) much more likely than 1) because there's so few combos of hands that player type 1) can take these actions with compared to player type 2) who can do this with maybe 3x as many hands. If he folded pre then that would make our assumption that he's a complete nit slightly more likely

I guess it's a bit abstract but I think it ties in with not putting too much reliance on hud stats and what you've seen BEFORE . What happens now affects the info you had up to this point.

An easier example is an unknown shoves from the sb with 10bb into your bb . Before the hand you might think he doesn't know anything about nash and is only shoving "real" hands , maybe any Ax any broadway , any pair etc . Now the fact that he has actually shoved means that you should alter your perception of him because it's way easier for a player who shoves nash or an even wider range to shove than it is for a player who only shoves value hands to shove . So now with the limited info we have we can go with a new assumption that he's shoving a wider range than we first thought

Thoughts ? Anyone like to deepen my understanding of this plzzzz

Last edited by Frogman3 : 01-25-2014 at 04:15 PM.

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Old 01-25-2014, 05:00 PM
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Need to read this when im not playing.
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  #3  
Old 01-25-2014, 08:28 PM
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A mathematical example is

Random Player in the sb with 8bb . We guess he's either someone who knows about nash and shoving light bvb and is shoving 80% of his hands in this spot . Or we think he may have no clue about shortstack play so as he'll only shove top 20% of hands.

You might guess and say well he's one type or the other so because of that I'll assume he's shoving 50% of hands because that's the mean of 20% and 80% . So if he shoves I'll call X% because I assume he's shoving top 50%

But once he shoves then that actually gives you a lot more info than you first had . The very fact that he shoved makes it much more likely that he is the player who knows about nash than the player who just shoves big hands . Because that player is shoving 4x as many hands as the other type. So now there's an 80% chance that the player is shoving nash and there's only a 20% chance that he's the nittier type.

So now you can say that 80% of the time he's shoving 80% of hands and 20% of the time he's shoving 20% of hands . So on average he's shoving 68% of hands , which means you can call a lot wider than you would against the 50% shoving range we calculated before.

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Old 01-26-2014, 11:41 AM
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Quote:
Originally Posted by Frogman3 View Post
This is a bit of a head trip but anyway

The actions a player takes makes it more likely that they are that type of player based on the new info we have from their actions

Ok suppose you have a small sample of hud stats on a player that says he is nitty . Now he 3bets you and barrels off every street. There's 2 possible explanations for this

1) He rly is a nit and has a monster hand
2) He is a looser player than we initially thought and is doing it with a wider range

I can't do the maths but the very fact that this action happened makes 2) much more likely than 1) because there's so few combos of hands that player type 1) can take these actions with compared to player type 2) who can do this with maybe 3x as many hands. If he folded pre then that would make our assumption that he's a complete nit slightly more likely

I guess it's a bit abstract but I think it ties in with not putting too much reliance on hud stats and what you've seen BEFORE . What happens now affects the info you had up to this point.

An easier example is an unknown shoves from the sb with 10bb into your bb . Before the hand you might think he doesn't know anything about nash and is only shoving "real" hands , maybe any Ax any broadway , any pair etc . Now the fact that he has actually shoved means that you should alter your perception of him because it's way easier for a player who shoves nash or an even wider range to shove than it is for a player who only shoves value hands to shove . So now with the limited info we have we can go with a new assumption that he's shoving a wider range than we first thought

Thoughts ? Anyone like to deepen my understanding of this plzzzz
do you read the dayily mail?


jokes interesting read here

if we are under the understanding hes shoving nash and not tight then yh we should ajust our calling radge accordingly like but if we still think hes shhoving value hands BVB value hands should still be any Ax k9s kto jq jt 9js 22+ even a noob know these are big handfs BVB so we can still call like 55+ a2s a9o KJo jts maybe wider vs value like his 10bbs to
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Old 01-26-2014, 12:12 PM
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hmm
sounds counterintuitive at first but it does remind me of the maths used in -http://en.wikipedia.org/wiki/Monty_Hall_problem

for that reason im open to hear more about it
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Old 01-26-2014, 12:31 PM
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From what i understood, your thinking of expanding ranges per position.
In your example your thinking of a typical situation.
Villain is short on SB. We established he is a nit over a sample that exceeds 25 hands (presumably). The issue in this particular spot is that villain could have had the first unopened shoving spot. So what is his steal % from SB/Btn/Co.
If there haven't been any steal spots we can throw our HUD stats overboard and assume villain just didnt got a spot over that small sample.
However if we have those stats, we can accomplish putting villain on a slightly more accurate range.
Calling spots, still means that we need to maintain stack utility (such as FE).
How effective is calling 8BB and winning 60% of the time with a 20BB, while we can have a similar spots with 60% equity vs 20BB stack.
Doesnt that accomplish that you gain 4.8BB (+antes) on average or lose 8 BB.
So future value could equal 7.2BB (losing vs 8BB) gain vs 12BB(vs folding) gain vs 16.8BB (winning vs 8BB).
No matter what we did maintained FE. So at the end we gives ourself a better chance of making more chips, which can have an exponential growth vs the negative of having a stack where we need to win 1 hand to be back in the situation we were in.
Losing - 1 hand behind
Winning - ~2 hands ahead
folding - no chance.

In a nutshell folding is less variance vs calling with decent equity hand gives us a better chance of building a decent with a 20BB stack.
Doing the same for 50BB concludes that calling is more optimal.
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Old 01-26-2014, 01:17 PM
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Hmm no I think that's a different topic entirely

Standard thinking is if we don't know if a player is loose or tight then one action won't change that thinking . For example if player Fred 3bets you then we don't know if he is a nit that's 3betting a very strong range or if he's a looser player that's 3betting a wider range . Bayes theorem suggests that the fact that he 3bet you means you can immediately weight him towards more likely being the looser type of player .

A tight player 3bets 2.5% of hands
A loose player 3bets 7.5% of hands.

So when a player 3bets you can instantly infer that he's 3x more likely to be the loose player type 3betting you with a 7.5% range than he is the tight type to be 3betting with a 2.5% range

So maybe you should react as if he's 3betting 7.5% x 0.75 + 2.5% x 0.25 = a mean 3bet % of 6.25%

Not sure of how applicable it is but I think if you have 60 hands on a guy and have him tagged as a nit but now he 3bets you and triple barrels on a runout such as QJTxx then rather than thinking "oh he's a nit and obv has AK or QQ" you should look backwards and say ok there's very few combos of hands that a true nit can do this with . But there's way more hands that a lag can do this with . So we have to take into account the possibility that our original assessment of him being a nit might not be 100% correct since the actions he took are more likely to be those of a lag player This turns tight folds on our part into marginal calls etc like TT here would be a fold v a triple barrel from a real nit who's never betting the rvr with AA/KK for example (I stole this example from somewhere btw )

Last edited by Frogman3 : 01-26-2014 at 01:20 PM.

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Old 01-26-2014, 02:01 PM
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dont worry frogman, maths geniuses like you and i understand it

lesser players like drj will be trying to get their head around the concept for hours




edit: ill expand 4 dummies...

this is really a "probability vs known info" problem...merging ranges to the looser side because the nitty part of the range is still included in all LAG ranges, villains can be looser than we expect but rarely tighter than we expect (or more accurately, villains will be looser MORE OFTEN than tighter just because loose ranges play more hands than nit ranges)


is what i think its getting at
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Last edited by ouchbadbeat : 01-26-2014 at 02:05 PM. Reason: now im just confusing myself

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Old 01-26-2014, 02:14 PM
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Ouch, Im already 3 steps ahead.

Just reverse the decision with the extra information
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Old 01-26-2014, 02:19 PM
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i just hate dutchies tbh

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Old 01-26-2014, 02:24 PM
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Yeh maybe I overcomplicated it trying to put the maths into it

If an unknown player shoves from the co with 10bb . Before the hand we don't know if he's loose or tight . So we might think to call him with a medium range

BUT the fact that he shoved makes it much more likely that he's a loose player than a tight one because loose players will shove more often than tight players and he shoved therefore its most likely he is a loose player. So we should call with a medium-loose range rather than the medium range we first thought

It's going backwards

Before the hand

We are 50/50 on if he is a loose or tight player
In theory we would call a medium range giving him 50% chance of being loose and 50% chance of being tight

During the Hand

He shoves
Loose players shove more often than tight players
Therefore he is more likely to be a loose player than a tight player
Now we can assess he is 75% likely to be a loose player and 25% to be a tight player (made these numbers up but you can use bayes theorem to get actual numbers - google it , it's complicated)
We can call with a medium-loose range which matches our new perception of him

Last edited by Frogman3 : 01-26-2014 at 02:26 PM.

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Old 01-26-2014, 02:30 PM
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pretty sure i nailed it before drj started hating on me

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Old 01-27-2014, 09:05 AM
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I personally don't display hud stats unless I have a significant sample on the player. In one way that eliminates the problem (by sweeping it under the carpet no less).

If no stats are displayed I generally consider them as a noob prone to mistakes/bad plays - often by playing too tight/too loose. I would certainly call LP shoves fairly wide against them, not so much because bayes' tells you too, but more because most of such shoves by there very nature are often pretty wide. Many players will look to coax more out of the top hands, so we're already primarily looking at a range that is minus at least AA-QQ
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Old 01-27-2014, 12:35 PM
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Not sure why you are making it so complicated. I think you forget that the current action, or hand, counts to the past history when it comes to the statistics of play. I.e if he 3-bets me this hand and had 33% 3-bet before this hand started, his actual 3-bet percentage is 50% now (2/4 spots instead of 1/3).

You also forget that for HUD stats to be even approaching 100% reliability, you need a shitload of stats. Like even 2000 hands is not enough for me to just blindly look at the stats and make a decision (which you should never do, really). It's also about the spot, how I have been playing against this player and what I think of him and the way he plays.

The way I use the HUD is for an indication of player type, and to see if he is new-ish at the stakes and game. The main number I look at is really aggression factor since that is a statistic that is based on every hand played, as opposed to 3-bet or 4-bet stats which occur fairly rarely for most players even over 2-3k hand samples.

Also, the game constantly changes, since the way people play doesn't remain constant. So you always have to keep in mind that the way your opponent is playing now may be completely different from the play-style which you have seen before, be it that he may be just trying something new, or has been looking at videos/coaching. I think it is more important to make a judgement of what kind of player he is, i.e changing it up, than to blindly look at spots and the way he has acted in those spots prior to this. This is where I guess this theorem kind of comes in, since he is in some spots more likely to indeed be mixing it up, as it is unlikely that he has the ultimate nut hand to beat you in this spot. If you think that the fact that it is unlikely for him to have it in this spot, plus the fact that you think he is capable of changing it up, then you can of course change your play.
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  #15  
Old 01-27-2014, 12:43 PM
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I think this has some merit to it. But whereas regs / competent players will tend to have logic and mathematics behind each decision, a random may decide to do something on the spur of the moment. They might want to double or bust, they may be card dead and get bored so they open/ jam wider or whatever. The problem with randoms is they don't necessarily have a consistent range in each spot imo because their play can change based upon many factors (at least possibly can).
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Old 01-27-2014, 01:21 PM
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It's not really relevant when you have a lot of info on someone , it's more relevant when you have little to no info . Like a player new to the table 3bets you 1st hand and proceeds to triple barrel . It's much more likely this is a loose player who is doing this with a wide range than a tight player who has happened to find a monster . Just because a loose player will have much more combos of hands to do this with and therefore will do it much more often

Yeh I guess it's obvious but most people would react like " well I don't know anything about this guy so I have no idea what his range is" . So they call down with a respectable or medium range that is aimed towards him being an "average" player . But you should be calling down with a lighter range because he's weighted to being more likely to be a loose player than a tight or average one , just from his actions in this very hand.

Ok maybe a crap example here but I knew zero about this player. You might think yeh std call but if it's weighted 50/50 towards him being a tight player or a loose aggressive player then it's maybe a fold on the turn given that JT got there as well as the obv possible sets or slowplayed KK/AA . But given that just from his actions it's much more likely he is a loose aggressive player then it makes it a call down imo

Pokerstars Hand #110778318196: Tournament #850815018, $20+$2 USD Hold'em No Limit - Level I (10/20) - 2014/01/26 12:04:25 ET
Table '850815018 110' 9-max Seat #4 is the button
Seat 1: jayjayme (3000 in chips)
Seat 2: on3fl3wov3r (2990 in chips)
Seat 3: kefffff (2970 in chips)
Seat 4: PocketAcesA5 (3000 in chips)
Seat 5: Agent Bear (2980 in chips)
Seat 6: klatsu (3000 in chips)
Seat 7: kinkladze030 (3000 in chips) is sitting out
Seat 8: valeryan1999 (3000 in chips)
Seat 9: leon091083 (3060 in chips)
Agent Bear: posts small blind 10
klatsu: posts big blind 20
*** HOLE CARDS ***
Dealt to Agent Bear [Qh Qs]
kinkladze030: folds
kinkladze030 has returned
valeryan1999: folds
leon091083: raises 20 to 40
jayjayme: folds
on3fl3wov3r: folds
kefffff: folds
PocketAcesA5: folds
Agent Bear: raises 80 to 120
klatsu: folds
leon091083: calls 80
*** FLOP *** [8d 9c 4s]
Agent Bear: bets 140
leon091083: raises 180 to 320
Agent Bear: calls 180
*** TURN *** [8d 9c 4s] [7h]
Agent Bear: checks
leon091083: bets 540
Agent Bear: calls 540
*** RIVER *** [8d 9c 4s 7h] [7d]
Agent Bear: checks
leon091083: bets 2080 and is all-in
Agent Bear: calls 2000 and is all-in
Uncalled bet (80) returned to leon091083
*** SHOW DOWN ***
leon091083: shows [5h As] (a pair of Sevens)
Agent Bear: shows [Qh Qs] (two pair, Queens and Sevens)
Agent Bear collected 5980 from pot
*** SUMMARY ***
Total pot 5980 | Rake 0
Board [8d 9c 4s 7h 7d]
Seat 1: jayjayme folded before Flop (didn't bet)
Seat 2: on3fl3wov3r folded before Flop (didn't bet)
Seat 3: kefffff folded before Flop (didn't bet)
Seat 4: PocketAcesA5 (button) folded before Flop (didn't bet)
Seat 5: Agent Bear (small blind) showed [Qh Qs] and won (5980) with two pair, Queens and Sevens
Seat 6: klatsu (big blind) folded before Flop
Seat 7: kinkladze030 folded before Flop (didn't bet)
Seat 8: valeryan1999 folded before Flop (didn't bet)
Seat 9: leon091083 showed [5h As] and lost with a pair of Sevens

  #17  
Old 01-27-2014, 02:08 PM
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To make it more relevant to apply stats.

Our Hud indicates that villain is stealing 50% from Btn over a sample size of 2 (18-26 hands).
In Bayesian theory if villain is raising unopened the next time from the Btn his stat is 67%, while our HUD will indicate 50%.
While if 10x our sample, then it would mean that villain is stealing from Btn 52% instead of 50%.
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  #18  
Old 01-27-2014, 02:17 PM
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I'll reply with my great feedback on this after I have smoked the 42nd joint of the day. BRB
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Old 01-28-2014, 12:39 PM
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Not that I wouldn't call down in that situation perhaps, but with no info I don't quite understand what bluffs he can actually have that didn't get there by the river that didn't pick up enough SD value ott to stop bluffing w/? There's no FDs and he can genuinely have all 3 sets plus the most likely straight draw got there. I guess he can have JJ TT and be valuing worse or be a nutter w/ like A9. Not sure how many bluffs he has. That's all kinda besides the point was just interesting.

In terms of this as a general theorem, I think it's so easy to find out things about players really quickly online even with no hands or history by perhaps doing a sharkscope search or whatever that most of the time in a close tight situation you aren't totally totally in the dark if you don't want to be and I think that this theory is based upon us literally having no information available as in perhaps if a average age average height average build person comes and sits at a live table and doesn't say a word to us and then jams 10bb in from the c/o in a turbo. In that situation (taken with a pinch of salt as clothes etc could perhaps give things away) we would have practically no info.

Online even knowing things like how many games they've played what their ABI is even if we cannot see exact profit/ loss can lead us to perhaps fairly accurately assume certain things about our opponents even with no real HUD stats available. That could also be myself massively overating these things but I mean if a guy has played 5k games w/ a $20 ABI it would probably be fair to assume he's got more clue than the guy who's played 150 games w/ a $4.5 ABI.

I can see the offset of this being the argument that assuming ones has a clue and then assigning characteristics to them (they could be TAG or LAG e.g.) can also be a problem but in certain spots especially nash spots one would assume one that knows the game better has a better idea of jamming ranges in a spot and if we're talking strictly nash based a general player type is irrelevant a jam will either be profitable in a situation or not.
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  #20  
Old 02-08-2014, 05:44 PM
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Quote:
Originally Posted by no1yidmax View Post
Not that I wouldn't call down in that situation perhaps, but with no info I don't quite understand what bluffs he can actually have that didn't get there by the river that didn't pick up enough SD value ott to stop bluffing w/? There's no FDs and he can genuinely have all 3 sets plus the most likely straight draw got there. I guess he can have JJ TT and be valuing worse or be a nutter w/ like A9. Not sure how many bluffs he has. That's all kinda besides the point was just interesting.

In terms of this as a general theorem, I think it's so easy to find out things about players really quickly online even with no hands or history by perhaps doing a sharkscope search or whatever that most of the time in a close tight situation you aren't totally totally in the dark if you don't want to be and I think that this theory is based upon us literally having no information available as in perhaps if a average age average height average build person comes and sits at a live table and doesn't say a word to us and then jams 10bb in from the c/o in a turbo. In that situation (taken with a pinch of salt as clothes etc could perhaps give things away) we would have practically no info.

Online even knowing things like how many games they've played what their ABI is even if we cannot see exact profit/ loss can lead us to perhaps fairly accurately assume certain things about our opponents even with no real HUD stats available. That could also be myself massively overating these things but I mean if a guy has played 5k games w/ a $20 ABI it would probably be fair to assume he's got more clue than the guy who's played 150 games w/ a $4.5 ABI.

I can see the offset of this being the argument that assuming ones has a clue and then assigning characteristics to them (they could be TAG or LAG e.g.) can also be a problem but in certain spots especially nash spots one would assume one that knows the game better has a better idea of jamming ranges in a spot and if we're talking strictly nash based a general player type is irrelevant a jam will either be profitable in a situation or not.

actually there is a bit more, may not get the info you are looking for but you can get enough to al least make a prelim guess.

how are his cheques stacked..?
how is he sitting in his chair..?
where are his arms...?
where is he looking..?
who is is watching the closest..?
where is he looking on the flop..?
how often does he check hole cards..?
does he make any premature moves..?
is he listening to music..?
is he busy texting..?.... I love the ole fake text not really paying attention play..

just some of the ways you can get info on an unknown......

 


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