Different styles for BB defens

[Redeye]

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For the hand in question we have a PFR raisor and a BB defender. The dead money in the pot is the SB. If the blinds were out and two other players were vying for the blind money then what you say would be correct. In this spot there is little dead money, and it will be likely gobbled up by the rake.

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Preflop, the BB defender should not just be viewing the dead money as the small blind. The PFR should be seeing the big blind plus the small blind (1 2/5 SB in the 5/10 game) as dead money whereas the defender is seeing 3 SB + the small blind as dead money. You're getting (3 2/5):1 on your call in the BB making defending with hands like 97s correct. If you we're only getting the small blind as dead money, defending with hands like 97s would be incorrect, IMO.

I think Tolbiny's statement exactly explains the difference when he says:

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The situation only applies when two players are betting and there is no pot. In this case you are each vying for your share of what is in the pot, so both players can make thoeretically +ev plays. The -ev play that allows for multiple +ev plays by both players is the posting of the blinds.


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The guy with AK will make a +EV call because he has odds since there is a reasonable amount of dead money in the pot. However, having a pair gives the defender much more equity per bet and therefore makes money every time he can get a bet into the pot. Therefore, if the defender can c/r the guy with overs, he is making money when doing so even though it bloats the pot making it correct for the PFR to call down with his overs.

[spydog]

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Jeezaz, I don't know why I bothered posting again. Perhaps it is better to stick to e-mail discussions, at least that way I don't have to answer posts as desperately stultifying as this one.

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You and Chief are great posters, let's not get crazy here.

FWIW, this post has gotten quite confusing.

I hope the newbies reading this understand the difference between Pot Equity (which determines whether or not you are making money on your immediate bet or call and doesn't consider pot size) and a +/-EV call (which determines whether or not your call is profitable based on pot size/# of outs).

[naphand]

As I see it, according to TOP we make money from our opponents when they make mistakes. When our opponents correctly call they are not losing money, so we cannot be making money from them. In a multi-way pot made hands -vs- flush draw both players are in a +EV situation, and are making money from the other other player/s who are calling incorrectly. HU the situation is a little less defined, but surely cannot be accurately described two players chasing the (dead) blind money. For a start in a HU battle between PFR and BB defending, the only dead money is the SB and that is going to be gobbled up by the rake pretty quickly once we have a PFR and a flop raise (less the case at higher limits, clearly). This is not a question of PFR chasing dead money, as in most cases that amounts to nothing after the rake.

Note: I just realised that you are referring to the pot as "dead money", unfortunate choice of words as I was thinking dead money from the blinds. OK now it makes more sense.

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...you have pot equity.

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According to TwoDimes in a pair -vs- overcards hand the equity is 76.26:23.74, your approximation of 75:25 is good enough. Now let's see if I can get this straight...

Pre-flop is where the players are "in a battle for the right to the blinds/ante" and pre-flop the PFR has the advantage (for the sake of argument we can ignore pure steal raises with garbage and PP in either hand). So we cannot just assume the defender has equity from the start and over the blinds, he didn't (in most cases, and in particular the one we are discussing here). So pre-flop the PFR was raising correctly with the best hand. The flop wipes the slate clean and the "dead" money is everything in the pot. In this example the pot is 2.25 BB (0.25 BB SB plus 1 BB PFR plus 0.5 BB plus 0.5 Defenders call from the BB). However, you are correct ot point out that the equity also applies to the money going into the pot, pot odds only applies to the money in the pot already.

The money in the pot belongs to no-one but is shared (approx.) 75:25 with the scenario discussed. With 1 card to come it is 86:13.

NB: When the PFR has a hand like A3 and pairs the low card versus TP to defender, the position is even worse at 78:22.

Given the situation where PFR bets and is raised he now has correct pot odds to call the CR. How does he lose money in this situation? From an equity point of view we are saying he owns only 25% of the bets he puts in, however pot odds make it correct for him to call. The money in the pot (much of which was from PF) makes the call correct and PFR is not losing money by doing this, in fact it would be more accurate to say that he has sufficient stake in the pot to justify calling ONE MORE bet. This is the critical point about limit holdem. He is not putting in chunks of money but in increments. After every increment the pot (the "dead" money") grows and his share of it also (at a slower rate than defender). PFR is not losing money by calling, yet defender is making more. However, there is an important consideration here.

It is not a question so much of failing to get money in when you are ahead, but a question of where the best value lies. CR the flop may be cool, but bet-calling and CR the Turn could be a lot better. Why? Well it does depend on your read of opponent. If you believe PFR will not fold before the River is it better to get extra bets in on the flop or the Turn? Particularly consider that if the flop is CR the chances of extra bets on the Turn is greatly reduced. The argument that we should put the most in with the best of it is too simple, surely? We do not know for sure we are ahead on the flop or the Turn, cheaper to find out we are behind on the flop but we make less when ahead as well, and given the 86:13 share we have with one card to the Turn I think it is better to set up the Turn raise or 3-bet the flop, which depends on read of opponent. If we think opponent is likely to fold if the Turn misses then clearly CR the flop or 3-betting is preferable, and we must choose according to our read (if opponents always bets flop but rarely 3-bets, or if opponent is very aggressive and will raise overs on the flop).


Addendum
I am still left with the question: how is it PFR is playing correctly and in a +EV situation when calling, when defender can also be +EV by betting. It is to do with the size of the calls versus the pot, of course, but it is still correct to call. As the pot gets bigger and bigger, it becomes more and more correct for prograssively weaker hands to call. It seems like a recipe for WEAK hands to get as much money in as possbile to start with (when they are uncertain of where they stand) so they can call later even as big dogs. Is this how the LAGs survive so long, they build big pots with smaller bets and more opponents, and consequently get better odds to play on through the later streets to draw out (a lot of losses being offset by the folds they get from better hands, of course). Am I missing something or does this make sense? It seems contradictory.

A player calling correctly is not losing money according to the TOP, yet the other player is taking his money? This is counter-intuitive and bloody confusing...yet clearly this can be the case for a caller versus a bettor when there is a pot of sufficient size to play for. The bettor bets according to hand equity (at a basic level, other considerations such as forcing out other players etc. not considered here). A player in 2nd-place bets/raises in order to increase his pot equity in a multi-way pot by folding out other players but NEVER HU unless there is a realistic chance his opponent will fold a better hand, but only calls with the worst of it when his share of the pot (i.e. pot equity), based on his odds of drawing out, justifies it. It is the incremental nature of limit poker allows PFR to call correctly even when a significant underdog and hence maintain a +EV position.

Apologies for the long ramble, but I think I was getting these concepts jumbled. I still find it hard to reconcile the fact that both players can be playing correctly and be +EV. This does not seem possible... [img]/images/graemlins/confused.gif[/img] If every call made is correct, the player cannot be losing money, if he is not losing money the opponent cannot be taking anything from him. So where is the profit? It can only come from other players money already in the pot or where a player is calling incorrectly, such as drawing dead or very thin. Obviously the Flop changes things a lot, and favourites becomes dogs etc., but we cannot consider pre-flop play excluded from pot equity considerations, there is still correct and incorrect play (the blinds being the "pot" pre-flop).

[krishanleong]

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Apologies for the long ramble, but I think I was getting these concepts jumbled. I still find it hard to reconcile the fact that both players can be playing correctly and be +EV. This does not seem possible...

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It's definitely possible. Tolbiny's explanation above was quite good. Here is an example.

Your on the river. Your the BB with a set of aces. SB who is your only opponent has a 4 out gutshot. The pot is 200 dollars because the casino owner dropped 180$ on the table. You slowplayed preflop and the flop. [img]/images/graemlins/cool.gif[/img] When you bet the turn, SB is making a profitable call. But you get ~18 of the dollars going into the pot and he only gets 2. So in the absence of a pot, you are proffiting. Because the pot is so large, his call has a positive expectation. Both players have a +EV move. Moreover just because the SB can call profitably does not mean the BB should NOT bet. He makes money on the last bet.

Krishan

[chief444]

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It is not a question so much of failing to get money in when you are ahead, but a question of where the best value lies. CR the flop may be cool, but bet-calling and CR the Turn could be a lot better. Why? Well it does depend on your read of opponent. If you believe PFR will not fold before the River is it better to get extra bets in on the flop or the Turn? Particularly consider that if the flop is CR the chances of extra bets on the Turn is greatly reduced. The argument that we should put the most in with the best of it is too simple, surely? We do not know for sure we are ahead on the flop or the Turn, cheaper to find out we are behind on the flop but we make less when ahead as well, and given the 86:13 share we have with one card to the Turn I think it is better to set up the Turn raise or 3-bet the flop, which depends on read of opponent. If we think opponent is likely to fold if the Turn misses then clearly CR the flop or 3-betting is preferable, and we must choose according to our read (if opponents always bets flop but rarely 3-bets, or if opponent is very aggressive and will raise overs on the flop).


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naphand,

I agree completely. And I really do hope I didn't offend you too much previously. You seem to be one of the better posters here. I think this is very read dependant as you say. And I also agree that it's not just a matter of getting the most money in NOW (on the flop) but rather what's likely to net you the most throughout the hand. If the opponent's hyper-aggressive I'll sometimes bet knowing he'll raise anything and check/raise the turn knowing he'll bet when checked to almost always. Against some check/raising is probably best. Against others maybe bet/3-bet.

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Addendum
I am still left with the question: how is it PFR is playing correctly and in a +EV situation when calling, when defender can also be +EV by betting. It is to do with the size of the calls versus the pot, of course, but it is still correct to call. As the pot gets bigger and bigger, it becomes more and more correct for prograssively weaker hands to call. It seems like a recipe for WEAK hands to get as much money in as possbile to start with (when they are uncertain of where they stand) so they can call later even as big dogs. Is this how the LAGs survive so long, they build big pots with smaller bets and more opponents, and consequently get better odds to play on through the later streets to draw out (a lot of losses being offset by the folds they get from better hands, of course). Am I missing something or does this make sense? It seems contradictory.

A player calling correctly is not losing money according to the TOP, yet the other player is taking his money? This is counter-intuitive and bloody confusing...yet clearly this can be the case for a caller versus a bettor when there is a pot of sufficient size to play for. The bettor bets according to hand equity (at a basic level, other considerations such as forcing out other players etc. not considered here). A player in 2nd-place bets/raises in order to increase his pot equity in a multi-way pot by folding out other players but NEVER HU unless there is a realistic chance his opponent will fold a better hand, but only calls with the worst of it when his share of the pot (i.e. pot equity), based on his odds of drawing out, justifies it. It is the incremental nature of limit poker allows PFR to call correctly even when a significant underdog and hence maintain a +EV position.

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The only other comment I'll make on the EV math is that even though limit is an "incremental" game, it is a mistake not to anticipate raises and additional action. That is, there are times when instead of making a marginal call you should fold because of the possibility of a raise (ignoring a lot of other factors ie implied odds, overcalls, etc.). Although it really is just a technicality and obviously not the point of your post because generally speaking the preflop raiser isn't really making a "mistake" by betting a ragged flop with A-high or really any two since you will obviously be check/folding at times. But from a "fundamental theorem of poker" standpoint only the opponent is making a mistake in the first place betting the flop.

[kiddo]

The main reason I often checkraise preflopraiser when I hit something from big blind is because if I bet most of the time with a hand he can steal every time I check. Its more important to be unreadable then thinking about small differences in odds, isnt it?


(I am not sure I follow how u can say that when he bets flop with overcards and I got a pair on flop he is not making a misstake. Pair will be ahead 7/8 on turn so almost all money going in is his when he overcards bet. The underdog dont want any more money coming into the pot, no matter how big or small pot is. In this case he will have to invest 1BB to draw for his 6 outs, thats a lot.)

[sqvirrel]

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If every call made is correct, the player cannot be losing money, if he is not losing money the opponent cannot be taking anything from him.

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The player calling IS losing money. His ownership of the pot relative to his investment is reduced. So while he may be making correct calls when behind, his winnings over the long haul will be lessened because he is losing money on each new bet.

[naphand]

Now you are cheating, casino owners do not do this... [img]/images/graemlins/ooo.gif[/img]

Actually, I was going to use this example, except it was a random observer (Note: this is not possible on-line). It actually is correct as an example and I think I got it in my addendum above (edited while you were posting, I suspect). The question is, where does the profit come from? In your case it is the casino owner, mostly. If both players are playing correctly, they cannot be losing money even in the same pot. The profit must, therefore, come from the blinds or from other players (playing/drawing incorrectly, according to TOP).

So I am back again to the notion that if your opponent is drawing correctly he is not losing money. His pot equity is less, but his proportion of it still covers his bets (short-term losses). He will win the pot enough times to recover his losses long-term with a profit. If he is not losing, how is opponent winning from him?

So we are back to profiting from TOP mistakes, which does include betting the flop with overs when opponent has a pair. His call (to a CR) is still correct though and cannot be losing money for him, as it is not a mistake according to TOP. It must be then, although defender (who holds a pair on the flop) is taking 75% of PFR's money on each bet, PFR is recovering more than this from his 25% stake in the pot. The flop bet is a loser, but even this TOP mistake is a long-term profitable play, which makes matters even more confusing. Clearly then if we are to profit from PFR we must extract additional bets from him.

Now something else occurs to me. Say PFR bets every street and Defender just calls down? PFR is making a TOP mistake on every street by betting. If Defender bets out the flop and PFR just calls down (calling correctly, assumng the pot is big enough), PFR makes no TOP mistakes as he calls correctly each time, yet the net result is the same. The pot is the same size at SD and each player put in the same money. Why are they different? You can argue that Defender made a TOP mistake by never raising, yet his pot equity was the same and the $$ in the bank were the same. How does "profiting from TOP mistakes" fit in with this, when in one case PFR makes 3 mistakes to Defenders one, and the in the other both played correctly? Profit identical.

[ddubois]

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How can both players be in a +EV situation?

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The pot.

[naphand]

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The underdog dont want any more money coming into the pot...

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Yes and no. The underdog would like to draw FREE as this is the most favourable position. However, there are plenty of occasions when facing a bet when drawing, that calling is still profitable; it is an easy call. With 25% equity in each bet going in and only 1 opponent we are taking the worst of it, but with a 4-handed pot every bet going in is breaking even (ignoring for amoment how pot equity changes according to number opponents).

I can see how if we put in 50% of the bets in a given round with only 25% equity we appear to be losing money. When we put in 1 BB with 25% equity, we are losing 0.5 BB (2 BB goes in, 1 BB from each player, of which we own 25% or 0.5 BB, we paid 1 BB for a net loss of 0.5 BB).

If there were an infinite, or even just a LOT of betting rounds, then this loss would really add up and chip away at our profitability. But pre-flop PFR was the favourite and put in 1 BB as the favourite against Defender (the equity would be different (TwoDimes shows 97s -vs- overs as 40:60). PFR has made an "equity profit" on Defender pre-flop, which further reduces his losses, as well as on the SB. This "profit" is only hypothetical as the flop now changes everything. But the "dead" money on the form of the residual pot from the pre-flop action now exists.

With sufficient $$ in the pot for PFR to call and profit from calling, he is not losing money on any given call. Calling the flop CR with better than 6.67:1 odds is correct and so profitable, as it would be on the Turn. Calling one card on the flop with correct 1-card odds and folding the Turn without proper odds is also profitable. Folding with correct odds is unprofitable and a losing play, calling with correct odds is a winning play. PFR is not losing $$ by calling correctly.

Technically,calling two more bets as a big dog is a loss, but if the correct odds are available to draw then how can this be a losing play? Looking at all bets together we can say "ah yes he out in 2 BB as a dog". But he did not put in 2 Bb at once, he drew to live cards which arrive with sufficient frequency to make calling profitable long-term. So how can you say calling correctly is a losing play?