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Poker Video: Limit Hold'Em by DeathDonkey (High Stakes)

Ok I misread what you were trying to use the AK of clubs to represent. I don't know why you did that instead of just a regular simulation but here you go:

ProPokerTools Hold'em Simulation
21,804,741 trials (Exhaustive)
board: K 7 6
8d 5d 27.09% (5,862,881 wins, 88,483 ties)
20% 24.87% (5,244,406 wins, 360,035 ties)
K9-KQ, AK, K7s, K6s, 76s, QQ-66, Ac*c, Kc*c, QcJc, QcTc, Qc9c, Qc8c, JcTc, Jc9c, Jc8c, Tc9c, Tc8c, 9c8c 48.04% (10,288,806 wins, 372,257 ties)

note that I used top 20% for the first bettor's range since he raised preflop and c-bet, it might be a bit more narrow than that, feel free to tinker with the sim.

So no matter how we arrived at the number, I'm fine with agreeing our equity is somewhere in the high 20%'s and its going to depend a bit on exactly what ranges we assign.

13:2 on the flop are our immediate pot odds, and we have 27%ish equity, those are the relevant numbers. You seem to be mis-understanding the way pot odds work. "Equity" is equity, its our % chance to win the hand accounting for all turn/river combinations against the ranges assigned. I think you are arguing that even though we are getting 13:2 to call now, if we miss on the turn we will have to call another bet (which we will again be getting proper pot odds to call). These add up to make the *effective odds* worse than they appear. This is also called 'reverse implied odds' - these things are straight out of Theory of Poker. What you are neglecting to think about is that part of our equity on the flop comes from the times we just go ahead and hit our hand right on the turn, and heck sometimes they are even drawing dead once we do, and bets are still going to go in. These are 'implied odds'. In some situations its easy to argue that RIO trump IO by a substantial margin, and in other situations its less clear. But even if there are more RIO than IO here it is far from enough to overcome the immediate price when we have 27%ish equity. If our equity were more like 18% it would matter.

You are doing a lot of your analysis incorrectly, and your appeal to authority to Mike Caro is meaningless to me. Either you are misunderstanding something he wrote, or he wrote something wrong. I don't need anyone to tell me that when you start by saying a flush draw will be out 40% of the times based on the hand distributions you assigned (a somewhat unnecessary exercise in the first place), and then you round that up to 2 out of 4 people will hold one (40% became 50% just like that!) and then use the 50% number in your subsequent equation, that you are estimating incorrectly and in your favor. If we accepted your initial combo counting (I already explained why its incorrect which you ignored in your subsequent replies), then the chance that someone holds a flush draw in clubs with 4 opponents would be exactly 40%, not 50%: 40% * 4 people / 4 suits = 40%.

Look, I wrote these postson my iPhone at a casino while waiting to get into a game. I scrawled the math on the back of a casino flyer I had handy with a pen I borrowed from a floorman. I wasn't going for an in depth analysis, but a rough estimation of how often it would happen.

In terms of Mike Caro, he was very dogmatic about it. Back in the 90s, before the poker boom, I had used to listen to his tapes, and on the tape, "Pro Hold'em Secrets" he said:

"Listen. If you flop a open ended straight draw, and nothing else, on a board where there's a flush draw present, you should pass." He then goes on to give an example, and elaborate on his reasoning. "The presence of a flush draw eliminates some of the outs you need to make the hand, and mean you might get the straight beat if you make it. Now you might say that that doesn't happen very often, and you'd be right. But it turns out that it happens just often enough to turn these straight draws from small winners, to small losers."

In a live lecture I attended by Mike Caro, he said you could disregard this point if you happened to hold the Ace of the flush draw in question because it eliminated so many combinations of flush draws. This point is repeated in all the books he came out. For that matter, P. 113 of Bob Ciaffone's Middle Limit Hold'em gives the same advice:
"You should dump a straight draw with a two flush on board and two players betting and raising with other players involved. Two of your outs could be killed, and, if not, redraws get created. The bet could get raised again and you could be multi bet ride on every street."

That's something you also seem to be neglecting in this video. You're saying that the hero is paying 2 versus 13, but you don't really know that because his call doesn't close the action. Folding a straight draw in the face of a flush draw was just one of the maxims I learned poker with. And, hey, maybe it's wrong. But we're talking about the reflections of people (one of them very math oriented) who played a great deal of live, limit Hold'em for a living.

I'm sorry if you disapprove of my rough analysis. If you must be technically correct, let's look at this specific hand. Our hero holds no clubs. The flop has two. There are 47 unseen cards, and 1081 ways to draw two from 47. There are 55 combinations of two clubs, so the chances of having a flush draw simply pulling two cards from the deck are 55/1081 or .05%. If our four opponents have completely random hands, then the chances of having a flush draw out is 20%.

But that analysis, while correct, isn't all that damn useful, because they don't have random hands. The four opponents hold hands they chose to play, and are those who remained from a field of 8 opponents. The chances that one of the eight opponents held two clubs, would be .05x8 or 40%. So what are the chances that one of them chose to take the flop? That depends on their selection criteria, and now things start to get subjective. If we say that people would want to play all suited Aces (10 combos) and Kings (9 combos) from any position, plus QJ, QT, Q9, JT, J9, T9, 98, 87, 76 and 56(which I'm not counting because of the board in this specific case), T8, T7, and 97 then we'd have 32 combos. 32/1081 = 3% x 8 opponents = 24%

I'm not sure what the thinking is of Caro, but I think it goes something like this. You're not getting odds versus one opponents, and against two, one of them will probably have a flush draw. Of course, at this point, we're really reduced to making educated guesses about what it would take for our opponents to continue on a two flush board, but heavy action would logically indicate that our hero has closer to 20% equity than 32%.

When you're getting 13:2, you have the odds to call with your OESD even if you know that one player has the flushdraw 100% of the times. Odds of 1:6.5 + implieds and 6 outs is a call.

Hi preston,

Just wanted to say that disagreeing with you isn't anything personal. You are good at articulating your arguments, and obviously know how to count combos and whatnot, I just think some of the things you are analyzing are misguided (preflop stuff here for instance, knowing how often a flush is out just doesn't sway the decision nearly as much as you seem to think), so I'm taking time and writing long posts because I want you to change your mind about the flop being a fold, and I want to convince others that may be reading that folding the flop is bad poker.

I looked through some of your old posts on DC and you seem like a good guy, I play in LA a lot myself, maybe I'll see you around some time. I think you are just holding onto the Caro maxim a bit too hard. If the pot were smaller, it would be way more worthwhile to consider folding the flop, not just because of the possible flush draw, but just because of the good old pot odds that wouldn't be nearly so attractive. It also isn't really a surprise that poker advice from the 90s or even more recently might be incorrect or out of date, books written a couple years ago certainly suffer from that too, and I'm sure I can find videos I've done on DC that I would now disagree with my play as my game has evolved.

When you're getting 13:2, you have the odds to call with your OESD even if you know that one player has the flushdraw 100% of the times. Odds of 1:6.5 + implieds and 6 outs is a call.

In this hand it really is just this simple, I have to agree.

Hand 1- I think I would reiterate what DD said, that you should be bluffing by c/r here because you would play your value hands the same way. I would expect the turn to get checked through rarely, so going for a c/r makes sense. Also, I think c/r this exact hand is probably going to result in bluffing too much here. I would generally play this hand passively and not (as you both seemed to conclude) look to semibluff the flop. Although I think if you would like to bluff the turn, you should do it with a c/r, I think you should probably limit your bluffs here to 78. Mostly because adding in combinations of 58s means you will probably be bluffing too often on this board, into 3 people. So, if I had to pick some type of hand, the better open ended straight draw seems to be a better candidate, because our equity will just be stronger on the turn, even though our relative hand values are almost exactly the same.

Just another advantage to the c/r in hand 1 is that if it goes bet,raise and gets back to us we can easily fold without wasting any bets knowing we have no fold equity and are drawing dead.