Eureka

[silkyjonson 1]

Discuss not discuse..................i cant spell at times lolOk so i busted 11th yesterday in the bodog 100 @ 11pm and I went out shortsacked on a coinflip. It seems like I have lost a ton of coinflips in tournies lately when on the overcard side of the equation, and when I've gone through those scenarios over the last month it seemed like the overcard side was lower than expected from common excepted poker probabilities of roughly 50/50. I know this is'nt a big enough sample size but I was just letting my mind wander. So anyways I did'nt give it much thought then went to bed, at like 5am I woke up with a random thought. the 50/50 or 45/55 which is more accurate is the best case scenario for the overcards being that there are none of their 6 cards already out of the deck (only looking at catching one of your 6 needed, not straights and flushes as they don't factor into the equation)Ok i don't know if this has been discussed anywhere else but this is what I came up with.So I came to the conclusion that 45% is the best that it could get, but it could get worse which is obvious. And it gets worse for the 2 overcards because they have to improve and pair to win, which the wired pair does not, even if say 77vs ak some 7's are dead it does'nt effect the scenario as much as the if some A's or K's are out.So I woke up and ran some numbers using a classic coinflip situation of say AKo vs 77. Ok so these numbers are for a full table (10plrs) and we will just concentrate on the 2 players mentioned above. So hypothetically say we were holding the AK and we for some reason knew that the other player held a small pair, and we will ignore betting and just look at the matchup. ok so holding AK there are 50 cards left in the deck and with all of our cards still live in the deck we are 44.612% to win vs 55.388% for the 7's. But realistically there are 50 cards minus the 16 cards the other 8 players are holding, plus another 3 cards that will be burnt so there are 19 cards that are effectively dead and will never make it to the board. So since we are working always in expected probabilities in poker we can calculate the chances of an A or K being in any card out of 50 as 0.12% per individual card. So then we can use this percentage to figure that roughly if we are not eligible for 19 cards that we will on average have 2.28 of our 6 outs lost to us forever from those 19.Ok so we have determined tha 2.28 out of 6 A's and K's are dead to us on avg, so since we cannot use 2.28 we will round down to 2.0 therefore on avg in a full 10 person hold'em table we will have really 4 outs to pair as opposed to 6 which obviously makes a difference in the long run. So using these numbers our new matchup is 64.159% for the 77 vs 35.841% for big slick. So out of all of that I think that the 64/36 in the long run would be more predictive of a full table ring game with unkown cards and not taking into condsideration anything else at all. Also I rounded down from 2.28 so the actual percentage would be slightly even worse for the AKo if we used the 2.28. Of course this has no bearing on say head's up or even 6 handed, but you could still use these numbers to adjust for your expected win % by substituting the numbers and running them out.Im guessing someone like slansky might have touched on this? Although I have'nt seen it in his books or anywhere else, but I guess I was'nt looking for it either, so I just thought I would post my brain fart and get some discussion on this as I know there are some great minds in this forum. I've run through it in my head a few times and it seems valid to me (im not an expert on math or theory by any means

[Jrobb25 0]

nope you've just been bit by the bodog..where worst hand wins

[PMJackson21 0]

So I woke up and ran some numbers using a classic coinflip situation of say AKo vs 77. Ok so these numbers are for a full table (10plrs) and we will just concentrate on the 2 players mentioned above. So hypothetically say we were holding the AK and we for some reason knew that the other player held a small pair, and we will ignore betting and just look at the matchup. ok so holding AK there are 50 cards left in the deck and with all of our cards still live in the deck we are 44.612% to win vs 55.388% for the 7's. But realistically there are 50 cards minus the 16 cards the other 8 players are holding, plus another 3 cards that will be burnt so there are 19 cards that are effectively dead and will never make it to the board. So since we are working always in expected probabilities in poker we can calculate the chances of an A or K being in any card out of 50 as 0.12% per individual card. So then we can use this percentage to figure that roughly if we are not eligible for 19 cards that we will on average have 2.28 of our 6 outs lost to us forever from those 19.Ok so we have determined tha 2.28 out of 6 A's and K's are dead to us on avg, so since we cannot use 2.28 we will round down to 2.0 therefore on avg in a full 10 person hold'em table we will have really 4 outs to pair as opposed to 6 which obviously makes a difference in the long run. So using these numbers our new matchup is 64.159% for the 77 vs 35.841% for big slick.

Two problems with this:1. You can't assume any of the 6 'over' cards are dead. In fact given people's propensity for playing any ace, the fact that the action is only two handed makes it more unlikely that an ace was folded, and to a lesser degree, a king.2. You can't ignore the ability of the AK to make straights and flushes, as well as for the pair to be counterfeited. These are viable ways for the over cards to win the hand, and have to be included in any calculation.There seems to be some basic math/probability errors in the theory too, but I'm not an expert by any means. Hopefully one of the math gurus on here will go into more detail.

[Fooney 0]

Slight flaw in your logic.If you remove the 2 outs because they're contained in the 16 cards dealt to players than you must remove them from the cards you can potentially get. It may reduce your outs to 4, but that's 4 out of the remaining 32, not 48. So you either have a 4/32 or a 6/48 which is equivalent.So yes, it is a brain fart, but an understandable one in the middle of the night.

[silkyjonson 1]

Two problems with this:1. You can't assume any of the 6 'over' cards are dead. In fact given people's propensity for playing any ace, the fact that the action is only two handed makes it more unlikely that an ace was folded, and to a lesser degree, a king.2. You can't ignore the ability of the AK to make straights and flushes, as well as for the pair to be counterfeited. These are viable ways for the over cards to win the hand, and have to be included in any calculation.There seems to be some basic math/probability errors in the theory too, but I'm not an expert by any means. Hopefully one of the math gurus on here will go into more detail.

Well there are going to be times when all 6 are dead, and there will be times when all 6 are live, but more likely it will be somehwere in the middle and that is what I have done assigned the probability @ .12% chance that any card out of 50 is an A and a K and then adjusted that to the 19 dead cards.Im not looking at any betting or future action that could tip your hand as to an A or a K I am choosing to ignore that for the analysis, So for discussion reasons just assume that all the other 8 players folded completely random hands.And the AK making straights and flushes has been included in the numbers so that is accounted for, I can show all my math a little later (as I'm going xmas shopping right now) and then some of the math guru's can help me out if there are any problems

[Fooney 0]

A more interesting question along these lines is:Your holding AKo and Player A is first to act and raises (something like 2x or 3x BB) and 2 tight players call before it gets to you. Let's say you put player A on a small pocket pair and want to isolate. Is a push/rearaise a good idea after the 2 tight players called? Even if you successfully isolate against player A what are the chances that the 2 tight players are taking some of your outs with them and should it influence your decision?

[pnambic 0]

While it's true that some of your outs may be gone already, it's immaterial where they are when you fail to get them. Also, the same argument can be made for your opponents redraw outs. If you play around with this in Pokerstove you'll see that it evens out in the end. One interesting thing I came across while playing with this is that for AK vs. 77, with one ace and both sevens out, AK is actually a slight favorite.So, it's bad luck, not bad math. Don't let it get you down.

[silkyjonson 1]

Slight flaw in your logic.If you remove the 2 outs because they're contained in the 16 cards dealt to players than you must remove them from the cards you can potentially get. It may reduce your outs to 4, but that's 4 out of the remaining 32, not 48. So you either have a 4/32 or a 6/48 which is equivalent.So yes, it is a brain fart, but an understandable one in the middle of the night.

This is not the case, because the calculations are being made of ak vs 77 with 48 unseen cards which is 6/48, whereas im adjusting and still calculating with 48 but assuming that on avg 2/6 will be dead because really we are not working with 48 but are working with 48-19, so 19 that we are not eligible for. Think about it like this the most outs we can get to pair is 6 (not taking into consideration straights and flushes which are a constant) but we can have less so this will effect our percentage right? So the norm calculation is with 6 but im saying we should adjust to an avg of what the real probability would be. I would be willing to bet a good deal of money that if we ran a deck out cold each time taking out 19 cards and running ak vs 77 with the remaining cards with a 5 card board that the numbers would be closer to the figures i quoted than the 55/45 excepted norm.

[silkyjonson 1]

While it's true that some of your outs may be gone already, it's immaterial where they are when you fail to get them. Also, the same argument can be made for your opponents redraw outs. If you play around with this in Pokerstove you'll see that it evens out in the end. One interesting thing I came across while playing with this is that for AK vs. 77, with one ace and both sevens out, AK is actually a slight favorite.So, it's bad luck, not bad math. Don't let it get you down.

the redraw outs are a good point, I did'nt take them into consideration. These may adjust the percentages but I'm guessing that they are not as significant as the ak scenario but will make a slight difference. good point, and when I come back from shopping I will play around with it a little and see the results. cheers

[PMJackson21 0]

Well there are going to be times when all 6 are dead, and there will be times when all 6 are live, but more likely it will be somehwere in the middle and that is what I have done assigned the probability @ .12% chance that any card out of 50 is an A and a K and then adjusted that to the 19 dead cards.Im not looking at any betting or future action that could tip your hand as to an A or a K I am choosing to ignore that for the analysis, So for discussion reasons just assume that all the other 8 players folded completely random hands.And the AK making straights and flushes has been included in the numbers so that is accounted for, I can show all my math a little later (as I'm going xmas shopping right now) and then some of the math guru's can help me out if there are any problems

You have to assume that some of the dead cards are non-outs. Over the long run the outs to non-outs ratio that exists in the 'nondead' deck would be consistent with the same ratio for the muck. Since both of these would be equal, it makes no difference if you count the avg. number of outs that are dead. In other words, it doesn't make a difference how you count your outs, but how you calculate the probability of using those outs.

[pnambic 0]

2. You can't ignore the ability of the AK to make straights and flushes, as well as for the pair to be counterfeited. These are viable ways for the over cards to win the hand, and have to be included in any calculation.

The straights and flushes are insignificant for AK compared to the pair draws. Try this in Pokerstove:AhKh vs. 7c7s - no cards dead: 47.879% vs. 52.121% - all hearts except the 7h dead: 45.849% vs. 54.151% - all hearts except the 7h and all T-Q dead: 48.686% vs. 51.314% (!) - all hearts including the 7h dead: 52.380% vs. 47.620% (!!) - all hearts including the 7h and all T-Q dead: 58.042% vs. 41.958% (!!!)and for the other side of the coin: - Ac and Ks dead: 39.748% vs. 60.252%That last one is a lot more interesting, as Fooney pointed out above.

[Fooney 0]

This is not the case, because the calculations are being made of ak vs 77 with 48 unseen cards which is 6/48, whereas im adjusting and still calculating with 48 but assuming that on avg 2/6 will be dead because really we are not working with 48 but are working with 48-19, so 19 that we are not eligible for. Think about it like this the most outs we can get to pair is 6 (not taking into consideration straights and flushes which are a constant) but we can have less so this will effect our percentage right? So the norm calculation is with 6 but im saying we should adjust to an avg of what the real probability would be. I would be willing to bet a good deal of money that if we ran a deck out cold each time taking out 19 cards and running ak vs 77 with the remaining cards with a 5 card board that the numbers would be closer to the figures i quoted than the 55/45 excepted norm.

You're wrong and I would gladly take the bet. All's cool though. I tried to explain it and really don't feel like going any farther with it. You just can't remove 2 outs from the equation without removing the 19 cards that correlate to those 2 outs.

[PMJackson21 0]

You're wrong and I would gladly take the bet. All's cool though. I tried to explain it and really don't feel like going any farther with it. You just can't remove 2 outs from the equation without removing the 19 cards that correlate to those 2 outs.

Just take heart in that you tried to explain it civily. :-)I would love to see the response Sklansky or Carson would give this...Both comical, but on different levels. Gary's would be funny in a light-hearted way, while David's would be entertaining for sheer arrogance/talking down to effect. :-)

[Fooney 0]

Just take heart in that you tried to explain it civily. :-)I would love to see the response Sklansky or Carson would give this...Both comical, but on different levels. Gary's would be funny in a light-hearted way, while David's would be entertaining for sheer arrogance/talking down to effect. :-)

I suppose I was a bit terse there. My apologies, Silky. I'm having a rough day.

[silkyjonson 1]

The straights and flushes are insignificant for AK compared to the pair draws. Try this in Pokerstove:AhKh vs. 7c7s - no cards dead: 47.879% vs. 52.121% - all hearts except the 7h dead: 45.849% vs. 54.151% - all hearts except the 7h and all T-Q dead: 48.686% vs. 51.314% (!) - all hearts including the 7h dead: 52.380% vs. 47.620% (!!) - all hearts including the 7h and all T-Q dead: 58.042% vs. 41.958% (!!!)and for the other side of the coin: - Ac and Ks dead: 39.748% vs. 60.252%That last one is a lot more interesting, as Fooney pointed out above.

This is a big point, that the straights and flushes are not significant compared to the pair draws, one difference is I was using AK off suit which makes a slight difference being less likely to make flushes.Also the number I came up with was 2.28 dead cards on average, and I rounded down thus correcting slightly for dead 7's and other straight and flush cards, though its not a completely accurate calculation though but brings it closer to the actual scenario.

[timwakefield 68]

While it's true that some of your outs may be gone already, it's immaterial where they are when you fail to get them.

I think that sums it up nicely. Whether the aces and kings that you need (or the TJQ you need) are buried at the bottom of the deck or were already folded at the table is, as pnambic said, totally unimportant. The only interest you can have in folded hands is if you think you can 'smell' what some of the players may have folded based on how the hand played out....i.e. 3 limpers, somebody pushes, you can maybe weigh the fact that your AK COULD have less outs vs 77 because the 3 limpers are likely to have had Ax or KQ, KJ, etc.

[silkyjonson 1]

Ok here is an example I will use to put the adjustment into context and get your head around it. Say if you had a job and made a different amount each year, and you made 100k in the first year which is the cap followed by 60k, 80k and 80k in successive years. Now if you had to judge your expected income for the upcoming year, would you say that your expected income is 100k for the year? Or would you say that your expected income is 80k? 100k is the maximum that you could get if you performed at your optimal level, but as shown it can be lower and you would be much smarter to plan for a salary of 80k as opposed to 100k even though 100k is possible.This is my point the percentage you would get on poker stove with no dead cards is the optimal percentage that AK can reach, and though you can kill in the 19 cards that I am assuming dead straight cards, flush cards and the two 7's as a redraw, they are not numerically as significant as having AK outs killed. So I am adjusting for an average amount of outs for AK at a full table which I believe are more indicative. There are going to be times when there will be all the aces out, or other scenarios where you will have 1,2,3,4,5,6 cards still drawing live so I came up with an avg of live cards to pair regardless of any other information which will be actually live. When you make calculations on poker stove it does not run out 8 other hands or burn cards. It still has all A's and K's live which are the major percentage outs for AK my numbers may not be exact as I have not run any trials but hypothetically I think I may be correct. And the major factor is that the AK must improve so it is affected more so then the 77's which do not need to improve to win

[PMJackson21 0]

Ok here is an example I will use to put the adjustment into context and get your head around it. Say if you had a job and made a different amount each year, and you made 100k in the first year which is the cap followed by 60k, 80k and 80k in successive years. Now if you had to judge your expected income for the upcoming year, would you say that your expected income is 100k for the year? Or would you say that your expected income is 80k? 100k is the maximum that you could get if you performed at your optimal level, but as shown it can be lower and you would be much smarter to plan for a salary of 80k as opposed to 100k even though 100k is possible.This is my point the percentage you would get on poker stove with no dead cards is the optimal percentage that AK can reach, and though you can kill in the 19 cards that I am assuming dead straight cards, flush cards and the two 7's as a redraw, they are not numerically as significant as having AK outs killed. So I am adjusting for an average amount of outs for AK at a full table which I believe are more indicative. There are going to be times when there will be all the aces out, or other scenarios where you will have 1,2,3,4,5,6 cards still drawing live so I came up with an avg of live cards to pair regardless of any other information which will be actually live. When you make calculations on poker stove it does not run out 8 other hands or burn cards. It still has all A's and K's live which are the major percentage outs for AK my numbers may not be exact as I have not run any trials but hypothetically I think I may be correct. And the major factor is that the AK must improve so it is affected more so then the 77's which do not need to improve to win

I understand what you are trying to say, but you can not assume what is in the muck, other then what Tim referred to in his last post.There are numerous threads like this in the google archives, and I would assume 2+2 (if i could ever use their search function properly), and the conclusion never changes. If you feel that you have found something original, I'd email Sklansky, Carson, Ferguson, or someone along those lines and ask their opinion. Matt Matros or Bill Chen would probably be more accessible (and more nice about it then Carson or Sklansky :- ) ), so maybe they would be better options.

[silkyjonson 1]

I think that sums it up nicely. Whether the aces and kings that you need (or the TJQ you need) are buried at the bottom of the deck or were already folded at the table is, as pnambic said, totally unimportant. The only interest you can have in folded hands is if you think you can 'smell' what some of the players may have folded based on how the hand played out....i.e. 3 limpers, somebody pushes, you can maybe weigh the fact that your AK COULD have less outs vs 77 because the 3 limpers are likely to have had Ax or KQ, KJ, etc.

Yes so if you are saying that sometimes you can smell the A's then you are in a way agreeing with what I'm saying but don't realize it. Even if you can't smell them you would be a fool to think that there are never any A's or K's out against you in any hands that you play. So why not try to make an accurate adjustment of the cards out against you given a certain number of hands, on any average hand.Yes it is totally unimportant where those cards are I am not denying that, but if you can arm yourself with an expectation that will get you to predict how many are still actually live in the deck.When playing blackjack card counters are adjusting to the expected probability of a shue being loaded with the cards they want or do not want thus being advantagous for them. this is because the shue adjusts as cards are dealt out, thus making it better or worse because of the cards remaining, my logic is that it is the same in poker some times being better or worse, not being able to see these cards you cannot count the actual outs you have left but you can predict an average between the most optimal and least optimal, not knowing which it is. The difference is between blackjack and poker you cannot see the cards dealt out, if you see an exposed card is an ace you should probably fold more often, but if you do not have this advantage you can still make a guess as to that there may be some already dead.

[silkyjonson 1]

I understand what you are trying to say, but you can not assume what is in the muck, other then what Tim referred to in his last post.There are numerous threads like this in the google archives, and I would assume 2+2 (if i could ever use their search function properly), and the conclusion never changes. If you feel that you have found something original, I'd email Sklansky, Carson, Ferguson, or someone along those lines and ask their opinion. Matt Matros or Bill Chen would probably be more accessible (and more nice about it then Carson or Sklansky :- ) ), so maybe they would be better options.

I agree you cannot assume what is in the muck, but you cannot assume what is not in the muck also and that is what the 6 outs does, it assumes that no aces or kings are in the muck, but I think (i dont know but im trying to figure out) that you can make a prediction that in the long run will bring you closer to the actual event that out of 19 cards not eligible for the flop some of them will be aces and kings and I cannot predict exactly how many but I can get closer to the mean I believe.You have a good point I think I will email some of those guys and maybe they can lead it in in one way or the other, as they have more experience in these mathematical game theory problems than I do. And Im sure this cant be original someone must have come to this conclusion and its driving me nuts but if it is wrong I want to know why.

[Fooney 0]

I'll try one more time just because it's kind of amusing that you can't quite grasp this. You seem like a real bright guy you just seem to have a blind spot on this one.Let's say you ended up all-in pre-flop AKo vs 77 and at that point all the players and the muck cards were placed face up for everyone to see. And just as you predict, there is one A and one K (2 of your outs) shown to be dead.What does this do to your odds of hitting 1 of your outs?Nothing.Because you may only have 4 outs but there are now only 29 cards left for you to draw from. Whether it's 6 outs from 48 or 4 (3.72 by your calculations) from 29 it's roughly the same.If your going to remove the 19 dead cards from consideration, you have to remove them from your calculation.

[pnambic 0]

When you make calculations on poker stove it does not run out 8 other hands or burn cards. It still has all A's and K's live which are the major percentage outs for AK my numbers may not be exact as I have not run any trials but hypothetically I think I may be correct. And the major factor is that the AK must improve so it is affected more so then the 77's which do not need to improve to win

Well, I did run the calculations, and reported on them above. And as reported, the equity calculated for the "no dead cards" case is the average - as is only reasonable. If both remaining 7s are dead, AK is a 57:43 favorite, nonwithstanding that it needs to improve.The only interesting application of the various observations made in this thread was mentioned by Fooney and timwakefield: when you find AK and you have a raise and a call or two in front of you, it's probably not a good idea to squeeze-push if your opponents are reasonably tight and you suspect Ax or high broadway to fold, and a pocket pair to call. Good advice, with or without the math, I'd say.

[Jeepster80125 0]

[timwakefield 68]

Yes so if you are saying that sometimes you can smell the A's then you are in a way agreeing with what I'm saying but don't realize it. Even if you can't smell them you would be a fool to think that there are never any A's or K's out against you in any hands that you play. So why not try to make an accurate adjustment of the cards out against you given a certain number of hands, on any average hand.

The cards which are folded around the table are no different, in the statistical way that they relate to your hand, from the cards at the bottom of the deck. It doesn't matter if, on average, one or two or more of your outs will be folded, as far as you are concerned they are still live, since you have no way of knowing where in the deck or in the muck they are.

[MasterLJ 0]

I agree you cannot assume what is in the muck, but you cannot assume what is not in the muck also and that is what the 6 outs does, it assumes that no aces or kings are in the muck, but I think (i dont know but im trying to figure out) that you can make a prediction that in the long run will bring you closer to the actual event that out of 19 cards not eligible for the flop some of them will be aces and kings and I cannot predict exactly how many but I can get closer to the mean I believe.You have a good point I think I will email some of those guys and maybe they can lead it in in one way or the other, as they have more experience in these mathematical game theory problems than I do. And Im sure this cant be original someone must have come to this conclusion and its driving me nuts but if it is wrong I want to know why.

No it does not assume 0 A's or K's are in the muck.It's like this.In order to "observe" this problem you'd have to know the cards of the people at the table. If you know what other people have folded, then the odds change since now there are fewer unknown cards (it becomes 6 outs out of LESS cards total ). A solid example:77 vs AKCalculate the outs for AK: 6 cards out of 48 unknowns help him (let's just focus on pairs).Give a dude a random hand at the table of : J3os that we somehow know he mucked.Now calculate AK's odds: 6 cards out of 46 help him. He now has BETTER odds.Rewind time, make J3os dude have A2 insteadNow calculate AK's outs: 5 cards out of 46 help him.So, the ~45% is actually the average expected outcome of AK vs 77 given ALL CASES of what goes into the muck. For every time you know someone folded a hand that hurts your outs, there's another time where they folded a hand that helps your outs, which averages out to be the percentages everyone cites (45/55 etc).Hope that makes sense. It took me a long time to wrap my head around it.