[MrWookie47]

Alright. I'm resurrecting this thread. It appears that tinhat is still not satisfied, and I think clarifying the lingering discussion will be for the benefit of everyone in the forum.

I'm unsure of a good place to start my response for good flow, however. I apologize, but I think this is going to be somewhat disjoint. I'm going to try and respond to as many lingering points as I can.

I'm going to kick things off with something I posted in another thread:

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Granted, there are exceptions. I was up against a guy on UB about a month ago who had a PFR of about 5%, but I was iso-3betting him with KJo, A8o, and stuff because he only raised junky hands. He slowplayed his good stuff. There aren't very many of these guys, though. Barring a real read, we can't assign a significant probability to this guy only raising his junk hands.

Just as we do Bayesian analysis when we consider hand ranges, the same math applies to opponent ranges. There's a probability this guy's true stats are 25/2. He might also be 30/10. Or 10/1. Or 40/20. He might be raising from a subset of the top 10% of hands, the 2nd 10%, or the bottom 10%. However, base on the ranges of players who, after 50 hands, have these stats, it's most probable that this guy has a VPIP of 20-30, a PFR of 1-7, and is raising from a subset of the top 10% of hands. Even if you want to completely disregard stats until you have thousands of hands of data on the guy, you're most correct to look at the average player from your database. This would be something like a VPIP of around 35, PFR around 12, and raises from a subset of the top 20% of hands. I'd strongly consider folding against this guy, too.

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It's this Bayesian sort of thinking that will form the heart of everything else I have to say here. We already know how to do this for hand ranges. If we know our villain only caps with AA, KK and AK, we know we're up against AK 57% of the time (assuming we hold no A's or K's ourselves) because of the distribution of cards. We can use this information to look at the board and estimate our chances of winning by figuring how many outs we have (or our opponent has) based on the board post flop scaled by the probabilities that he has a particular hand.

Now, as I stated in that first quote, we can do the same things with our opponents. While in this case we're not concerned with stats, the idea still applies. We're instead concerned with the what I'll call the degree of wonkiness which we assign to our opponents.

You said many times that villains do unexpected things. You posted your had as an example of a highly unexpected outcome in which everyone folded to your (rather wonky in itself) bet. You stated several times that the hand you posted was not an example of how you think we can fold our opponents here. Instead, it was an example of wonkiness and the unpredictability of our opponents. OK.

Here's the thing, though. We CAN, in fact, predict our opponents actions. We have thousands of hands playing against thousands of opponents. We know the mistakes that a lot of people make. We know what set of hands they tend to raise. We know what sorts of hands they tend to call. We know to expect a certain level of wonkiness from an unknown opponent. Thus, we can use our past experience combined with the limited read we have on these opponents, the action so far in this hand, and the board cards, and we can assign an estimated probability to what they're going to do. I think that you and I and everyone else agree, for example, that the probability of betting out and having everyone fold in this hand is negligibly small. There are people who might fold certain hands that the may hold in this spot, but let's look at it from the Bayesian point of view. Most players with most of the hands they might hold in this situation will at least call most of the time. Anyway, that was an easy point. Let's move on.

One of the things you advocated quite strongly was saving "our worst outs." Those outs our for our J's, our 2's, and you even said our straights. From the PM you sent me:

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The compelling factors here (IMO) are pot size and fantastic position on pf 3-bettor. So the 3-outers (A's or 9's) should've been folded by betting into pfr, fully expecting it to be raised, to recover his J/str outs instead of tying ppl to the pot. Now his J/2 outs (what I called his "worst outs") may not be powerful outs but IMO the size of the pot compels one to not be throwing away outs prematurely. He REDUCED his winning chances from 17 possible winning outs down to 9 (cut in half) by (my contention) thinking his only chance was to hit the flush. His crap hand has gone from needing only mediocre improvement to win to a must-hit draw. (The exact outs can be argued but not the reduction) And this is the important point.

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I'm going to talk about saving our J's and our 2's first, because that's easier. First of all, you give us 17 outs if we manage to save these outs. I'm not exactly sure how many outs you're assigning to our J's and 2's in that number. We obviously have 9 outs to the flush, and if we have 6 more for our OESD (I'll cover that later) does that mean we have 2 outs for our J's and 2's? Is it 5 for the OESD and 3 for the J's and 2's (treating them like overcards)? For the conclusion I'm going to draw, the exact number is irrelevant, I suppose, so I'll start with six outs and trim from there.

Let's give you exactly what you want. You lead, and UTG raises. How happy are we if we hit a J or a 2, really? Well, that depends on UTG's range of hands. He LRR'ed, however, so that gives him some inherent wonkiness. AA-JJ is a good start, however, as those hands are all consistent with a LRR and a raise on the flop. Given what we now know, he can have AA 6 ways, and KK-JJ 3 ways each, a total of 15. AK might also make this play, that's 12 hands. Unfortunately, hitting a J or a 2 does absolutely nothing for us against those hands. We're still losing. There may still be hope, however. Now we're into that wonkiness. LRRs are often done for stupid reasons with stupid hands, so how many effective wonky hands should we include. We can't list them explicitly without a better read, but we can give them a proportionate probability. For my purposes here, I'll give them 27 hands, so 50% of the time UTG was just wiggin' out with his LRR. Now, how often can we expect to win against that range if we hit a J or a 2? Well, LRR's that were done for stupid reasons are often done out of spite with a hand that wanted to see a cheap flop and is now mad, or else villain is thinking "may as well build a big pot," and raises. There are a lot of Ax, Kx, Qx, Jx, and PP hands that might do this. If we hit a J or a 2 against these sorts of hands, we're still not winning much of the time. Furthermore, he raised. He likes his hand. There's a probability that he's a maniac, but we don't have such a read yet. We bust out our Bayesian analysis of our opponents and conclude that, while there's now a larger than usual probability that this guy is a raving lunatic, most players raise the hands they like here, and even loons can hold K's and Q's. In my estimation, I'll say there are two effective hands in his range against which we'll win if we a J or a 2. Two hands out of 54, and that's with a very high degree of wonkiness assigned to this guy. Since our J and 2 outs are only good 2 times out of 54, 3.7% of the time, each J and each 2 remaining in the deck is only worth 0.037 outs, for a total of 2/9 of an out. Furthermore, since we can't raise if we hit one of these, but we still have to call down if we hit them (since we are considering them outs, after all), we're going to be paying off a lot. I am going to further discount them because of how much we stand to lose even if we hit. One ninth of an out should be sufficient, but I'll round to a tenth of an out to make things easier.

How much is this worth to us? Well, we can use the good ol' multiply by 4 rule to estimate what percentage of the pot we own with our tenth of an out -- 0.4%. Scaled by the pot size means that these outs have added 0.062 SB to our equity. That's pretty darn small. Let's compare this to pumping a flush draw. If we have a nut flush draw, and we bet out and get two callers, we gained approximately 2% of all bets that went in (neglecting full house redraws), or 0.06 SB. Huh. Look at that. These J and 2 outs are a little bit better. If, say, we were to c/r and trap 2 opponents for 2 SB each, though, pumping the flush draw nets us more, and if we trap 3 or 4 opponents, life is better still.

Unfortunately, in this hand, we don't have 35% equity from our flush draw. The chance that villain has a set on this board is fairly high, based on our Bayesian analysis above. Consequently, the equity from our flush draw is markedly lower than 35%. The Q[img]/images/graemlins/spade.gif[/img] isn't a great out, and villain has a redraw even if we hit a clean spade on the turn. Giving us, say, 7 outs is a little more reasonable, perhaps on the conservative side. Thus, we'll need more opponents in order to pump our flush draw for value, denying us the EV I cited earlier from pumping. Seven outs gives us 28% equity, so we need 3 opponents minimum. If we can c/r a field of 3 opponents, even with our reduced equity, we should gain more by pumping our draw rather than keeping our J and 2 out equity. That is, if we only have a flush draw. Speaking of which...

Saying we forfeit our straight outs by c/r'ing the field is grossly fallacious. If we hit, there's a good chance we're chopping with someone, and there's a full house redraw against us (like the flush), but we can't just throw them out, no matter how many players are still in the hand. If we turn a non spade A, we have the nuts! The nuts is not a function of how many players are in the hand. The nuts just wins pots, plain and simple. There's a pretty good chance we chop with another J, unfortunately, but that's how it goes. So I say we give ourselves 3 additional outs for our OESD, no matter how many remain. We don't always chop if we hit an A, but we don't always win if we hit a 9 (AJ, boat). We get those outs no matter how many are in the hand. Furthermore, why on earth do you think that we can keep them clean if we bet and UTG raises. Hell, no J is folding on this board without a very high wonkiness factor. UTG has been shown to have such wonkiness, but his wonkiness has been raising, not folding. If we bet and UTG raises, the pot is offering 18.5:2 for any A's to come along, too. They're not folding their gutshots, typically. As we have all seen, the mistake made by most opponents is going too far with marginal hands. If we see people everyday call 2 cold with gutshots in a small pot, why do we think there's a reasonable chance they'll fold when they're getting the right price? There's a chance, sure, but that chance is very small, and the equity we gain from this chance is going to be small compared to the value of pumping our 7+3 out draw. While I set out to show that the value we gain from UTG raising the field is negligible (I think I gave it a rather generous treatment, in fact), I think now that it's more effective to show that that the value we gain from pumping our draw is much greater than anything we gain from trying to get HU with UTG or trying to fold everyone. I'm going to end here, but let me know if you or anyone else has any further comments.