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Greenstein's Mathematics Of Poker


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From pg 150 of Ace on the River by Barry Greenstein,"...If several players fold first, Ace-King suited is a favorite over most pairs. (The exceptions are Aces, Kings, and Jacks, and also Tens where one of the Tens is the same suit as Ace-King.) Even Ace-King offsuit is now a favorite against small pairs. The reason for this is that players are more likely to play hands having an Ace or King than those containing smaller cards. Therefore, as players fold, the probability of an Ace or King coming on the board increases"Basically, Greenstein is saying that if in the event that it folds around to you in the small blind and you have AK, you'd be a favorite over a big blind who holds a pocket pair? Am I missing something here?

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From pg 150 of Ace on the River by Barry Greenstein,"...If several players fold first, Ace-King suited is a favorite over most pairs. (The exceptions are Aces, Kings, and Jacks, and also Tens where one of the Tens is the same suit as Ace-King.) Even Ace-King offsuit is now a favorite against small pairs. The reason for this is that players are more likely to play hands having an Ace or King than those containing smaller cards. Therefore, as players fold, the probability of an Ace or King coming on the board increases"Basically, Greenstein is saying that if in the event that it folds around to you in the small blind and you have AK, you'd be a favorite over a big blind who holds a pocket pair? Am I missing something here?
sounds like you quoted it correctly
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sounds like you quoted it correctly
Yeah, but the thing is, if you plug in AKo vs 44 on a poker calculator, it will tell you that 44>AKo. So my question really is am I missing something about that paragraph that Greenstein is trying to say?
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Yeah, but the thing is, if you plug in AKo vs 44 on a poker calculator, it will tell you that 44>AKo. So my question really is am I missing something about that paragraph that Greenstein is trying to say?
He's making the assumption that many non A or K hands are folded so of the remaining cards, there is a higher percentage of A's or K's then from a normal 48 card deck (52 minus AK and the pocket pair).
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From pg 150 of Ace on the River by Barry Greenstein,"...If several players fold first, Ace-King suited is a favorite over most pairs. (The exceptions are Aces, Kings, and Jacks, and also Tens where one of the Tens is the same suit as Ace-King.) Even Ace-King offsuit is now a favorite against small pairs. The reason for this is that players are more likely to play hands having an Ace or King than those containing smaller cards. Therefore, as players fold, the probability of an Ace or King coming on the board increases"Basically, Greenstein is saying that if in the event that it folds around to you in the small blind and you have AK, you'd be a favorite over a big blind who holds a pocket pair? Am I missing something here?
He is saying, theoretically, that if there are a lot of folds in a full ring in front of you, chances are either A) one of the small pair's outs was thrown away, and/or B) since they are folding, they do not hold high cards, effectively giving you better odds, as there are less cards for more outs. Both of those skew odds toward AK because of the way odds are normally calculated. Normally odds are, at the most basic form, outs/unknown cards. If we assume that more cards that are not outs, are mucked by players acting before us, it lessens the 'unknown cards', giving us better odds. Basically greenstein's theory assumes that if we count the mucked cards as non aces or kings, we have better odds.
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if you twodimes AKo v 44 it will assume their are 48 cards to choose from.greenstein is saying their are 40 or less...

if you twodimes AKo v 44 it will assume their are 48 cards to choose from.greenstein is saying their are 40 or less...
actually that's cool....that means pocket pairs lose value in the late stages of tournaments.
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greenstein is saying their are 40 or less...actually that's cool....that means pocket pairs lose value in the late stages of tournaments.
No, it doesn't matter that more cards are dealt, the assumption is that cards are folded that aren't aces or kings.
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i dint read the book but i'll take a stabbarry hypothesizes that with all the mucked cards...most of em must be rags/babies44 loses value against AK if a 4 was mucked (remember we hit a set 20% of the time by the river with two fours left)if 44 is losing value then the AK must be gaining it heads up

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He's making the assumption that many non A or K hands are folded so of the remaining cards, there is a higher percentage of A's or K's then from a normal 48 card deck (52 minus AK and the pocket pair).
and the possibility of a 4 as in someone folding 4-6 being folded if u said ak vs. pocket 4s
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Is this in relation to low limit ring games?If so, I think his point is that at the lower limits many players will play *any* ace, and in some cases *any* king. So by that logic when players fold in front of you they are folding hands that do not contain an ace or a king. (in fact i think it's more reasonable to assume that most players will play any ace...in my experience this is often true.)This logic is pretty dubious, but i think it warrants some thought. If you assumed that all players at a loose low level ring game would play any ace (this isn't too much of a stretch of the imagination) then if 5 people folded in fron of you, you can at least assume that the 3 aces still remain in the deck, with 10 cards less so your odds would improve.

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No, it doesn't matter that more cards are dealt, the assumption is that cards are folded that aren't aces or kings.
umm, whatwhat are you talking about...more cards being dealthold'em: not stud, not omaha, not pineapple
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Yeah, but the thing is, if you plug in AKo vs 44 on a poker calculator, it will tell you that 44>AKo. So my question really is am I missing something about that paragraph that Greenstein is trying to say?
Don't forget to factor in your raise. If it has folded to you and you are in the cut off you will, naturally, raise. Position plays a large part in his theory, I believe. The blinds will think you are trying to steal and will call with a small pair but if the flop comes with a couple overcards to the small pair they should fold to a modestly aggressive bet. Thus the more powerful hand even if the flop missed you.
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Don't forget to factor in your raise. If it has folded to you and you are in the cut off you will, naturally, raise. Position plays a large part in his theory, I believe. The blinds will think you are trying to steal and will call with a small pair but if the flop comes with a couple overcards to the small pair they should fold to a modestly aggressive bet. Thus the more powerful hand even if the flop missed you.
That's not even close to what he was talking about.
umm, whatwhat are you talking about...more cards being dealthold'em: not stud, not omaha, not pineapple
I didn't understand your original statement, then.
actually that's cool....that means pocket pairs lose value in the late stages of tournaments.
Why does any of this mean that pocket pairs lose their value later in the tournament?
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BG is right, you can infer that the As and Ks are still live based on the folds.This type of rational becomes even more powerful in Razz

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I believe Barry has a masters degree in mathematics. Ive also heard this theory argued the other way, or differently. That if you hold a big hand in late position you are more likely to be up against a big hand behind you because all of the poor hands have folded. I would say Barry may be on to something here. If he has been making these kinds of assumptions throughout his career it has served him well so far.

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actually that's cool....that means pocket pairs lose value in the late stages of tournaments.
This is not the case. Pocket pairs go up in value late in a tournament because your stack to blinds/antes ratio has shrunk (your M).
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I think it is safe to say that if there are limpers in front of you, then your AK is probably weaker than probability would dictate, because there are probably some Ax or Kx in there.His theory having no limpers makes AK more of a favorite shows a serious lack of understanding of probability, I believe. The AK being a slight underdog is based on having all unseen cards unknown. Therefore, the other people NOT having As or Ks is already factored in, in effect. He was trying to make a semi-valid point, but appears to have drawn some incorrect conclusions.

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His theory having no limpers makes AK more of a favorite shows a serious lack of understanding of probability, I believe. The AK being a slight underdog is based on having all unseen cards unknown. Therefore, the other people NOT having As or Ks is already factored in, in effect. He was trying to make a semi-valid point, but appears to have drawn some incorrect conclusions.
No, you're the one who's wrong. If we assume that no A's or K's are folded, the odds of our AK winning go up. It's pretty simple really, but what should you expect from General.
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I think it is safe to say that if there are limpers in front of you, then your AK is probably weaker than probability would dictate, because there are probably some Ax or Kx in there.His theory having no limpers makes AK more of a favorite shows a serious lack of understanding of probability, I believe. The AK being a slight underdog is based on having all unseen cards unknown. Therefore, the other people NOT having As or Ks is already factored in, in effect. He was trying to make a semi-valid point, but appears to have drawn some incorrect conclusions.
No way does that make AK weaker.The value from AK comes when you flop TP and stack someone who is dominated.
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Why does any of this mean that pocket pairs lose their value later in the tournament?
maybe they don't lose value but i need to think more about the implications. the idea is based on this:as the tourney progresses hands like AT or AJ become more playable for resteal pushes and squeeze plays, but these hands are simple preflop mucks from EP earlier in the tourney...in other words you're getting more info later in the tourney than earlier when there are multiple folds in front of you. maybe pushing in LP with 8s or 9s would not be correct in certain situations based on stack sizes...
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I think I understand Greenstein's comments. Just to illustrate an extreme case, I ran AKo vs 44 using {2c 5d 8h 4s 9c Th 6s 7c 8d 7s 4c 3d 6h Tc 6c 2s} as dead cards, ie 8 ppl folded garbage hands with no paint. AKo has 70.3% equity vs 29.7% of 44. However, that's a really extreme case. You can also trivially construct a case where AK is a huge underdog.Perhaps I should tell you guys that Greenstein gave the heading "Some Interesting But Not Too Useful Mathematical Facts" for the paragraph I quoted in my original post.

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