How their bad calls can cost you chips - Implicit Collusion

Just running in and out and caught this. I believe in the original article there was an upper limit to the paradoxical region where player A wants player C to fold correctly so this fits. I think you are zoning in on it but I’m not sure we are at optimal quite yet. At some point the bet sizes become so large that we likely aren’t getting any calls at all, whether we want them or not. Therefore, if we make outsized bets we would lose EV by losing all incorrect calls. I’m still not sure how the pot sizes play into this in the first place. More to think about. How do we locate the sweet spot where we shed the 1 caller but keep the other? More bothersome, how does this play out with more than 2 callers? I’m starting to wonder if there is actually a solution to this at all or whether it simply is an exception to Sklansky and has no optimal solution?

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An excellent article. I am glad you posted it.
Isolating a problematic situation using the psychology of poker and finding the best solutions using math. It reminds me of something I saw a long time ago about playing sixth street in seven card stud.

Thanks for the post.

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The fundamental theorem is about playing as if you could see your opponent’s cards, but in practical terms it seems more relevant to making deceptive plays that disguise your hand (which you know) than to trying to play as if you know your opponent’s hand (which you cannot see).

It seems impossible to come up with an optimal strategy when you never know your opponent’s hand (only range assumptions) and you cannot know what bet size they may be willing to call with any particular hand type.

You could be thinking at meta level 4 while your opponent is on level 2, and you could make the optimal play according to the theorem for the wrong reasons. I think the issue that morton’s theory raises about how equity share of a bet is distrubuted is the most interesting part, but in terms of actually making a bet with a made hand, I think the range-based decision making isn’t altered by the validity of either theorem.

Both these theories were put forth long before hand v range and then range v range were even being discussed. They may have limited applications when competing with players using more GTO-based strategies. Still, there are hoards of players who have not made that shift (and never will), especially at lower levels. I’d think the older strategies and theories are probably as applicable to these games today as they were 20+ years ago.

I’m sorry if my thought processes were a bit foggy earlier. Feels like I’m swimming through Jell-O in my head today. So, in the 1st example we had a situation where it would appear that player A would always want player C to fold, regardless of bet size because of how C’s hand redistributes A’s equity. In the second example, player A still maintains the equity lead, even with player C in the pot. His margin decreases but I’m not seeing how his EV as a percentage of the incremental bet should change based on the size. I’m spit balling here but something about the math seems off to me.

I wish there were more discussions about Morton’s Theorem from the time so that we could see specifically where he thought this condition manifested most prominantly. All we have is the one example from limit and not even a robust discussion about that. It does seem that he found an exception to Sklansky and maybe that was all he was trying to do? When I’m up to it, I’ll try to play around and see if I can find any groups of hands that are more susceptible to this condition than others. You may have picked up on that right away in selecting strong made hands that have very little room to improve post flop vs multiple unique drawing hands. Will we see the same equity redistribution for 2nd pair hands looking to make 2-pair or for pocket pairs looking to pick up sets or is this mostly applicable to conventional drawing hands such as straights and flushes?

Very glad you are enjoying it @SSeville. It was so nice to find something like this - seemingly long forgotten but fairly powerful and relevant (IMO). It may turn out that this was only meant to describe something that had not been previously quantified and that is as far as its usefulness goes. Even if that is the case and there is no optimal counter-strategy, just airing it out and giving it thought would be worthwhile.

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A post was merged into an existing topic: Some reflections on a parallel case

Well, it seems that this topic has been fairly well-received so far. Lots of views, some great comments and I’ve even received some PM’s about it. I am very happy that this bit of poker-theory from the past has generated so much interest. I hope the thread continues to attract attention and that the discussion moves forwards.

To that end, I would like to make sure that everyone knows that their thoughts are welcomed here. No need to PM me, just post directly and lets all enjoy it. I understand that some people may be reticent to post for whatever reason but I’d like anyone and everyone with something to say to participate. If people think this theory is valid, let us know. If others think this is total fallacy, post that. Don’t think you have to be a theory-wonk to get in on the discussion, please. The more the merrier and hopefully we can all enjoy the discussion that follows. All I ask is that posters stay on topic and even if they think a comment is wrong, refrain from making the counter-point personal.

Some of you know that I am experiencing a bit of a medical thing. This leaves me at times unable to fully engage in what I think is an interesting subject here. I would appreciate any and all help in keeping the discussion going and to developing a clearer grasp of what Morton put forward. Does it help explain certain behaviors or perceptions? Does it apply as much to NL as it seems to for limit games? If it has validity, are there counter-strategies to maximize our expectations? Lots of questions so far and not many answers so there are many ways to contribute if you’d like.

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I think there are three ways of playing poker. Power play, get a hand pair, shove in big bet and get rid of as many calls possible, get a trip on the flop get even more aggressive. Second the gambler’s way, play in total, assess your hand based on flop, turn and river, across the table and across the deals. If not all some. Third is in line with Sklansky’s principle: Play your hand in accordance with others hands. There will be little hybrid, mostly stemmed on one principle.

People playing in one way, the other ways of playing may look donk. Analysis of one method may not be applicable to others, may not even make sense.

Added 1:
Probably you have to add fourth category, normal/natural play: you have a good hand, the bet is right, you call, bet is low you raise and the bet is too high you fold.

Added 3:
Another category could be judgement play. Players judge their hand to be a good winner, and bang a big bet. Hand need not be the best. Some of the good players in Replay play this. Another small variation in Replay (elsewhere too, idk) is donk intuition. Some of the woman folks do this and pull out miracle winners.

Added 2:
After writing this I am thinking of many other ways. One is that I have seen players placing everyone’s cards and orchestrating the bets. Seen players who bet on what you don’t have. All quite artistical. Some are mathematical. Some are folky.

Well, you can’t categorize every play, but these seem the major categories.

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Sorry to hear that. Hope poker helps. It does many a times.

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Its true that this theory tries to find an optimal bet size. In my opinion, we don’t know anything about opponent’s hand. All we know is the probability of our hand making. We have to make a bet size based on that only. I don’t know how that goes.

There can be different way of finding the bet size : Take my case for example. I bet only one BB irrespective of the hand I hold. Be it AA or 27o. I believe in post flop. But faced with a big bet, I will call upto 5-6BB if I hold AA or KK. I will fold over that bet even I hold an AA. I will call 4BB for QQ, high card seq and suited (A10s). 3-4BB any card seq and suited. 2-3 any card seq or suited. 1-2 for any card. Assuming a good stack size of 50BB.

I do two things here. One I don’t look at the pot size. Betting based on expected return on pot value makes you an aggressive better while the probability of winning being the same. But I don’t demerit the advantage in this. Two I only see my stack size and the bet. Or I see how much of the stack I will lose in case I lose the hand. This is my way of playing, looking at others play I believe that’s what many do.

Putting these two, I get a constant mathematical ratio of 0.25. Having an AA with 40% probability, I am willing to bet 1/10th of my stack (0.1/0.4). With no hand which has say 10% probability I am risking say 1/40th of my stack (0.025/0.1). This ratio can be called risk factor. For a given percentage of probability of winning how much percentage of stack one is willing to risk. If you bet above this factor you may make someone to fold. This is different line of thinking but its prevalent, at least intuitively, as you have quoted in one of your messages:

I don’t know how much this is going to help, but my bit anyway.

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Thanks for contributing to the discussion. No, we don’t know their exact cards but neither did we under Sklansky’s FTOP. The development of range-based approaches to the game may have made some of these older paradigms somewhat dated in application. However, they still hold fundamental truths - or at least we thought they did until Morton found some exceptions :slight_smile: However we approach the game, looking into the minds of those who came before us can only be beneficial to our understanding of it.

You guys are talking about mathmatical calculations here for replay poker land of the miracle last card straights, flushes, and full houses now this is funny l.o.l.

We are actually talking theory in general but I’m glad we gave you a chuckle. Something for everyone on this thread I guess :slight_smile:

If you took the time to read through it, you would have noticed that part of this theory could help explain why there is the perception of more bad beats here than normal. Yes, it is play-chip poker and you can only go so far with it in terms of mimicking cash-play but the basic precepts remain the same. As a matter of fact, the whining we see here mimics live 1/2 games very nicely.

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haha, probably because 1/2 live is rigged as well. the dealer always gives aces to the person who tips him most :stuck_out_tongue_winking_eye:

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As it relates to the game played here and the constant comments about how chasers always win, I think this theory applies (multiway pots). While each of the individual actions may have been wrong, the collective actions turn out to be “right”. In effect, the table collectively plays defense against the raiser, who presumably has the best hand at the time. Any one of the calls heads-up would be +EV for the player with the best hand. However, if you string incorrect actions together, you wind up with 2 things happening. 1st is that after a few incorrect calls, the remaining players have such a good price to call that their chasing really isn’t - they have been given the correct price to continue. 2nd, In cases where you have 1 incorrect call and 1 correct call, you can have situations where the best hand’s equity is disproportionately negatively impacted by the incorrect call, to the benefit of the player calling correctly. @JoeDirk pointed this out as a possibility in an earlier post and it appears that he was correct in his statement.

So, while there may not be any optimal solution to the scenarios envisioned by Morton, I think the explanatory power of his theory does help us understand some of the things we all see when playing here. It would stand to reason that if his theory was meant to explain multiway pots in looser games, it would apply very well to much of the play on this site.

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believe theory has merit but only in limit games.

I’m interested in your thoughts on this. The example Morton gave was in limit and he was talking to Mike Caro about opening strategies in limit but he addressed Sklansky in the context of NL (regarding exceptions in the FTOP). My thinking so far has me leaning towards it could impact limit games by altering strategies but that it still has some explanatory power in NL games. How do you see it? Do you think it is totally irrelevant to NL or just that it loses some ability to help with developing strategies there?

After raking my head for couple of days I found this simple solution.

Substituting n bets instead of one bet in Player B’s expectation we get:

4/46 * (p+2n) - 42/46 * (n) = 0;

Solving this we get p/n = 8.5

If p/n ratio is under 8.5 its not beneficial for B to chase. Over this ratio its beneficial for him. By adjusting the bet so that p/n is under 8.5 makes the chasing unbeneficial for B.

Similar calculation will lead to p/n = 6.5 for you to benefit from B’s chasing. Over which you are not benefited. Under which you are benefited. Keeping the p/n under 6.5 by adjusting the bet makes you benefit from B’s chase.

Similar calculation I tried to do to see whether Morton’s argument contradicts with Sklansky’s argument. I couldn’t succeed because it entirely depends on player A’s style of betting (assuming chase and benefit is only between you and player A), whether he goes by pot, probability or stack. I just stopped it because I couldn’t model player A’s betting. At my fist calculation they are breaking even: Make a high bet collect the bets or let it roll and collect the bets based on the winning hand. I am not sure, the calculation is not complete.

Added:
The argument of the above calculation goes like this: There is a big pot, and three players are playing. One with a good hand (you), one with a probable hand (player A) and one with average hand (player B). This big pot will attract player B to chase. According to Morton’s argument, his chasing will not be beneficial to you. So, how do you stop him from chasing. That can only be achieved by betting big, which will reduce B’s expectation. What is the optimal size of the big bet, which is found by slightly modifying Morton’s calculation.

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Thanks @narench - good stuff.

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going thru the above analysis it seems Mortons theory does work…the only problem here is this cannot be explained to the players ranked 10k to 40k who have filtered into the 50k tournies and are simply blinded to chase anything…firstly they cannot calculate odds,to them is what they see…gut shot,need runner runner,need two cards to make flush,no problem will go for it…even when you bet big to avert a chase you cant stop an idiot from calling your hand,he doesn’t know any better…but I must also tell you…this site gives you the benefit of the chase more often than not you will hit…they constantly do it as its worked in the past…do you think he even knows what to read what the opponents are holding…absolutely no way…hes married to his chase no matter what…i can understand this theory but for most players playing 50k and below tourneys its rocket science…its like asking a child to start reading astro physics at the age of 5…if you put the above into prospective in a big ticket game It makes more than logical sense to apply…but you have to take into consideration that when you play with the same players everyday for years you have a certain yardstick and a good read on them before putting mathematical odds into play…so this is another prospective…most players play the same hand the same way for years…don’t change the pattern unless short stacked or large stacked (then hes limping in with J3.92,38 etc…stealing blinds that’s all part of the game…
Then there are stages of the game wherein you don’t risk even an AA at the start (im talking of real solid players) as its too early in the game to get knocked out…so to say risking 40% of your stack is a fair bet…
ofcourse the same AA later in the game more often then not you do go all in as limpers are too many…and if you are grinding your way you need one of those to kick in…there is another time you will play the AA with 40% of your stack would be if you in the midst of the bubble…keeping a low risk…

Mortons theory can be applicable even on a real table more so to say…playing the same players everyday you will still play the player first then bring in the math…but a very good theory no doubt in the long run of play.

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