Probability And Hand Cobinations

[Dirtydutch 9]

I was watching some HULHE sweat videos the other day (one of the Stox guys), and he was using (and poorly explaining) the probability of hand combinations to determine if his opponent was on a busted draw or whatever often enough for different plays to be more profitable than others. Can someone explain to me, like you're talking to a retard, exactly what I need to consider while doing this, and what types of situations I would find where this is practical and appropriate? Any kind of tutorial or dialog here would be great.

[trystero 0]

http://www.flopturnriver.com/phpBB2/forum/...etc-t75711.htmlhas an introduction to this idea. Galfond expands upon that with his concept of G-Bucks:http://www.bluffmagazine.com/onlinefeature/gbucks.aspSection of most relevance is this,

I’m trying to get you to recognize how many hand combos make up a certain hand. For instance, when you think someone has a set, there are only three possible combos of each set, whereas there are twelve hand combos of top pair-top kicker. So, if someone takes a line where he has to have a set or a bluff, realize how unlikely it is that he has a set. Similarly, suited hands are much less likely than unsuited hands.

[Dirtydutch 9]

Awesome. Thanks.(I heart OMGCA)

[FizzbinPro 0]

Good couple of articles. Really goes deeper into why one should bluff when it makes sense that a good hand is held, rather than randomly. Great for learning to better understand ranges. Thanks for the links.

[DinkDonk 1]

The G-Bucks article is excellent. Read it several times.Ok I kind of have a rule against discussing any important strategy publicly, so I'll keep this a little rough, but I just want to give an example of how important this can be in Limit Hold Em Dutch.Ok. Let's say we're in a 6 Max LHE game. We are in a game we are familiar with and have stats/knowledge on several of the players. We are dealt AhTh in the cutoff and it is folded to us. We raise and the BB calls. Having played thousands of hands with him we know he will defend about 55% of his hands from the BB vs. our steal raise. For the sake of argument, we will say the top 55%, so he's got any ace, any pair, K5o+, K2s+, Q7o+, Q2s+, J7o+, J4s+, T8o+, T6s+, 98o+, 96s+, and 56s+. However, let's say that he would 3 bet us with the top 10%, so we remove 88+, AJo+, ATs+, KQo, KTs+, and QTs+. At this point in the hand we have our hand (AhTh, for now we are going to discuss just our hand vs. his range and ignore our theoretical range) vs. his 45% (not the top 45%, remember). There are 2.5 BB in the pot (we will ignore rake and assume 1/2 blind structure) and we are heads up.That is the information we have at our disposal.The flop comes down Jh9s2c and our opponent checks to us. We will say he does that with 100% of his range as that is generally not far from true vs. a standard opponent. We bet (as we will probably do with 100% of our range in this spot) and our opponent raises us. This will narrow his range significantly. We know that he will raise us with any pair, and any straight draw. This narrows his range down to 33-77, A2o, A9o, A2s, A9s, K9o-KJo, K2s, K9s, Q8o-QJo, Q2s, Q8s, Q9s, J7o-JTo, J3s-JTs, T7o-T9o, T7s-T9s, 98o, 95s-98s, 78o, and 78s, minus all combinations including the Ah or Th. Since I'm lazy I will just assume we have enough equity and implied odds to continue in the hand so we call. There are now 4.5 BB in the pot. Our opponent holds a very specific percentage of his original hand range.The turn comes the 3h. Our opponent bets. We know that this specific opponent will bet with all of his range that he raised the flop with, including his draws. We also know that he will never fold a pair, even if we raise the turn and bet the river (or if we call the turn and raise the river). If he has a pair he is going to showdown. We also know that he will bet the river regardless of what comes. If he is raised, he will fold all of his missed draws, and call with all of his pairs. So we decide to call with our nut flush draw and live pair outs. (The best play here is a discussion for another time.) There are now 6.5 BB in the pot. Our opponent has the same range as he did after the flop raise and turn bet.The river is the 7s. Our opponent of course bets again, as we knew he would do with 100% of his range. There are 7.5 BB in the pot, so we need to win the pot 1 in 8.5 times, or around 12% of the time, to make a call correct on the river. The way we find this is by counting the combinations of hands that he has that we 1. Beat and 2. are beat by. I'll put my counting (which will most likely come out wrong as its 5:30 and I'm tired) in spoilers so you can feel free to do the math (Use pokerstove and don't forget to count out dead cards) on your own and post your results. Hands that beat us

He can have 24 combinations of pocket pairs14 combinations of unsuited Ax's4 combinations of suited Ax's 18 combinations of unsuited K's 6 combinations of suited K's18 combinations of unsuited Q's6 combinations of suited Q's34 combinations of unsuited J's24 combinations of suited J's23 combinations of unstuied T's7 combinations of suited T's9 cominations of 98o12 combinations of suited 9's9 combinations of 78o3 combinations of 78s=187 combinations of hands

Hands that we beat

9 combinations of KTo21 combinations of unsuited Q's4 combinations of suited Q's=34 combinations of handsSooooo, of his 221 hands, we beat 34. This means that we are a 5.5 to 1 underdog to his range of hands (we win the pot a bit over 15% of the time). The pot is laying us 7.5 to 1, making this a slam dunk call. ( And justifying why I'm such a showdown monkey)

Granted, this problem was made up entirely off the top of my head and in an actual game we will never have such good information about what an opponent will have/do, but this is a common situation in LHE and is well worth studying if you want to improve at the game. If this is helpful to anyone, please say so, because if I'm posting it for no one's benefit, I will have good justification for going back to my self-imposed strategy silence.

[Dirtydutch 9]

Very helpful. I had figured most of this out from reading the OMGCA article and staring at the wall for a minute, but this is more specifically the answer I was looking for, and I'm sure unless I'm the dumbest person alive that I've been playing this long and hadn't looked into this (very possible), this should help a lot of people who don't feel like wading through 8 pages of more advanced Galfond awesomeness. You're on today, Dink.

[DinkDonk 1]

Very helpful. I had figured most of this out from reading the OMGCA article and staring at the wall for a minute, but this is more specifically the answer I was looking for, and I'm sure unless I'm the dumbest person alive that I've been playing this long and hadn't looked into this (very possible), this should help a lot of people who don't feel like wading through 8 pages of more advanced Galfond awesomeness. You're on today, Dink.

Everyone should reallly realllllly be reading this if they want to improve (though I hope most people don't). He goes into soooo many more details and variables that I'm unwilling to help spread. But, yeah, play around with pokerstove and run these scenarios so that they are second nature. You'll usually come to the same conclusion and say Zomg A high! I can't fold!, but at least you'll know that it's correct and you'll understand why.

[trystero 0]

It's a shame Galfond doesn't write more. I think he's one of the best writers out there (really gets into why we should do what we do).

[Zach6668 513]

Who was the Stox guy?If it was TheBryce, I recommend going back to some of his early videos, and/or his class room videos where he talks about combos.If it wasn't TheBryce, then I strongly recommend deleting every video that doesn't include TheBryce.