How their bad calls can cost you chips - Implicit Collusion

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.


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


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.


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:


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.

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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From what everyone has said so far, it seems like Morton’s theorem does hold for NL, but that because bet sizing is variable, there is a “zone” where the theorem applies, below which the caller is getting the right price to call and above which the original raiser is getting more value from a call than a correct fold.

If this zone does exist, I don’t think it actually is an exception to Sklansky’s theorem because if you could see both opponents’ hands you could still bet an optimal size that is above the zone. My understanding of Morton’s theorem is that it is specific to drawing hands and is related to the relative change in equity that occurs by having additional players in the hand. That makes it very difficult to create any kind of “solution” because the change in relative equity will differ based on the exact holdings, which can never be known. Plus, giving your opponents a price that they will mistakenly (or even correctly) call rather than betting so large that your opponents will always correctly fold is also a factor if the bet needs to be extremely large to be above the zone. The theorem does seem to provide some support for the idea of betting large to get value and protect a made hand rather than trying to extract medium value by having draws continue, but that is just my interpretation based on the few examples I have looked at. It is cool to think about and makes things complicated, but taking a balanced line that can account for range-based situations with missing information still seems like the best approach.

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Well said, roughly say 94% of the good game is achieved by good poker game sense and careful play. Rest 6% is the champion space. These kind of calculation helps and fine tunes the play to climb up the 6%. These things make significant difference in tournaments, ring is a different game.

OK, good discussion going on. It seems that there is general agreement that Morton’s Theorem has validity and has some relevance to NL (though probably more to Limit games). There also seems to be general agreement that one of the ways to counter the behavior is through increased bet sizes, though it has also been pointed out that this “solution” brings about a whole other set of problems with it.

For the purpose of the games played here, lets try to fold in one more concept and see where that goes: Fold equity. I think it is safe to say that fold equity is minimized in most games here. People love to call. If you combine Morton’s Theorem, with a partial solution of increasing bet sizes, and the general under-realization of fold equity here, doesn’t this help describe much of what we see in terms of extremely large pots for the strength of the hands played? If you need to increase your sizings to counter what Morton’s Theorem suggests and add in reduced fold-equity, then it stands to reason that pot sizes will bloat rapidly as the player with say AA tries to navigate a field of 3-4 players seeing a flop.

I think this is a logical view but I’m happy to be corrected if I’m missing something. Taking this line as valid for the moment, I can then see how the issue of “bad beats” becomes more dramatic here than in theoretically optimal poker. Not only do people have more premium hands cracked because of the multiway pots but the times when they are cracked tend to be in larger pots than would be called for relative to the strength of the hands (1 pair, sets, …). It is one thing to have your AA cracked in a 30-40BB pot and quite another to have 100+BB wiped off your bankroll in a single hand.

My thinking is that this may be another way of explaining why people are so convinced bad beats are more prevalent here than elsewhere. Part of that belief certainly comes from the overall looser play we see but I think the size of the pots in which these bad beats happen influences players’ perceptions. Premium hands get cracked all the time, everywhere. What may be different here is that when they are cracked, because of Morton’s Theorem and reduced fold-equity, those pots are of a greater magnitude than they should be. That combination creates a general perception that bad beats are more prevalent here than they should be. The reality is that there may be some increase in frequency but a large increase in pot sizes when they occur.

Hope this makes some sense and look forward to hearing what others have to say about it.


Morton’s theory and increasing bet size, they are not different. It’s the way to implement Morton’s theory. If increasing bet size is partial then Morton’s theory is also partial. He nowhere mentions fold equity.

Morton’s theory itself difficult to implement, it assumes you know the opponent’s cards. You don’t know them. You can only assume opponent has 30% draw. Then how are we going to know their fold equity.

These theories should be viewed as a theoretical basis than implementation, which may lead to implementable solutions. In which case you can add fold equity to Morton’s theory.

Morton’s calculation itself gives a high bet size. Say you are in a six seater holding AA at BB position. You have a probability of 50%. Everybody bets 1BB. when your turn comes you see a pot size of 6BB. Say you want to jam any hand under 40%, which includes most of the hands, you need to bet 12BB.

(6 + n) * 0.4 - n * 0.6 = 0 -> n = 12BB.

12BB is large enough a bet to deter many loose hands, and protect your AA. I am not sure under what circumstances one should include fold equity.


BTW I have developed small formula to find bet size n in terms of pot size P to block a given probability p (in case its useful) :

(P+n) * p - n * (1-p) = 0 -> n = [p/(1-2p)] P

You want to block a hand of probability 40%, you need to bet twice the size of the pot (0.4/(1-0.8)=2). For probability of 30%, you need to bet 3/4th of the pot (0.3/(1-0.6)).

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Hey @narench - Agreed. I was just trying to add another concept to what we seem to have agreed on with respect to Morton’s theorem. If increasing bet sizes is a partial solution under “normal” circumstances, then in circumstances where fold-equity is minimized, bet sizes need to increase even further. I think this is a logical step to take in trying to explain behavior and perceptions with regard to this site (and looser games in general). I did not mean to suggest Morton had explicitly mentioned fold-equity as part of his theory. Sorry for any confusion and thanks for your continuing contributions to this topic.

I am sorry too. I got little cheesed off.

I have to put in a word here, in case my statement “If increasing bet size is partial then Morton’s theory is also partial” makes any misgiving. Its unfair to discuss whether Morton’s theory is partial or not. Intention was only to hypothesis a shut down bet for the loose hands. Not to find any complete solution.

But I feel your idea is correct in saying considering pot equity only is partial. There could be more to it. Say, people holding AA usually bet in the range of 5BB, generally the pot size of the initial round. Its enough to shut down the hands under 30% probability. But still people call with hands below this probability genuinely. So there is something more to it, it could be relatively large stack, post flop equity change or something else, like fold equity, rather unfold equity.

Good thinking. But I feel its going deeper than it should.

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