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DanielNegreanu

The Odds Are Almost Always In Favor Of A Monster Draw

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*EDIT: I'm a bit retarded, feel free to rid this post for giggles, but I am so wrong it's not funny*Daniel, I have to commend you on this post, if you ever read this *Unlikely* because this post was the reason I registered.There is so many things wrong here, I don't know where to start. *Ooooh I can see the flame war already*Daniel, as a professional poker player, I am sure you are aware of this, in fact this is an advanced strategy rarely if EVER discussed in poker books, is it because the Poker pro's don't want you to know it? Maybe, I doubt that somehow. I just think it's one of the cardinal things in poker you just don't talk about.Lets look at a nice 9 person table situation *which lets face it, if you play MTT's is where you are going to spend most of your time*. Lets say early position doubles, plays really tight, and everyone folds except for you, in the bb, you call with your 6 7hThe flop comes down with the 'Monster Draw' 3h 8h 9sYou have 15 outs. wow, percentage wise, you have the best hand.But do you really believe no one else held a single heart?how about a 10?how about a 5?in 9 handed, assuming you get headsup flop action. 17 cards are out that you don't know what are. 22 cards are already out, 5 of which you know. just under HALF THE DECK is already in play, including folded cards and the first burn. Now let me ask you thisDo you really have 15 outs? On a good day you would have 13-15, an average day 11, and a bad day, 8 or less.Should you put all your money into the pot when you are behind? ----Next problem I have with this post. So many problems with this one.

Your odds to win the hand with only one card to come decrease dramatically. A hand with 15 outs after the flop is a 56 percent favorite, but if you don't improve on the turn, that number drops all the way down to 34 percent.
See this is why I hate, loathe, disgust poker calculators. They are completely unrealistic, firstly: I have a problem with 56 changing to 34. I'm not saying which one is wrong here, because I frankly don't care, but your percentage chance should be more or less halved with only one card to come *so 56 goes to 28ish or 34 should be 68 to improve on the turn* But listen guys, rather than use a 'odds calculator' why don't you just use some simple maths in your head.After the flop 22 cards out of a 52 card deck have been used, that means that if you have exactly 15 outs still in that deck *good luck kiddo* since there are 30 cards left in the deck, what do you imagine your odds are that you will hit your card on the turn? 30 cards, divide by 15, hmmm...I don't know if I can work that out.You have a 50% chance to make your hand on the turn, assuming you have all your outs still in the deck. what's amusing is that, if the turn card doesn't help you, and you still believe you have 15 outs by some godly fate, there is now 28 cards left in the deck, 15 of which can help you. Your chance to hit on the river increased even more.I'm not trying to say my odds and math are correct *Though basic year 9 math we learn in school says it is* But I am trying to say that Daniels here *I'm not blaming daniel, I'm blaming whatever odds calculator he used* are.---In closing. When thinking about decisions like these, PLEASE figure out how many cards are already out, and adjust your outs to go with that. There is a good chance you really only have about 10, sometimes more, sometimes less on a full 9 handed table, 10 outs....hmm, decent favorite indeed.*The poster admits that she is probably going to get flamed massively for this post, and as such has allowed users to send her e-mails. The poster also admits she might get banned for this post, but she hopes it isn't the case*

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I don't think anyone gets banned for trolling, DonkeySchool.

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Actually I'm not trying to bait anyone into an argumentative response, I seriously feel that there are massive massive problems with what daniel posted *shrugs*

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Okay, I made this post elsewhere, since poker is a game of making educated guesses on what people hold *it's how you put your opponent 'on a hand'* why can't you go one further.Which of these two statements is more likely to be true in regards to those that folded1 - One of my opponents folded a heart, 10, or 52 - None of my opponents folded a heart, 10 or 5No you cannot 'know' what your opponents folded, just like you can't 'know' your opponent has AA or KK, but you can make educated guesses to the point,

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From a site where I wanted to find out wether or not I made a retarded post or not :club:

To explain further so you might understand, because you dont know what the unseen cards are, you have no idea how many are outs and how many are bricks. In calculating outs, it makes no difference that other players may be holding some of them, there are 47 unknown cards (on the flop) and you can no more discount the unknown cards in players hands or the muck than you can the remaining cards in the deck. On TV you may see the calculations take into account which outs are no good based on what others have (and true, this is a more accurate calculation), but since you dont know what those are when youre playing, you cant take them into account in doing a mathematical estimation of your chances to hit your needed cards. Your post in the DN forum made reference to your chances "going down" more with each additional person at the table, because they may hold the outs. What youre not seeing is that taking those hidden cards into account could improve your chances as well. Each one that isnt an out gives you a slightly better chance to hit your draw, and each one that is an out lessens your chances. But again, that doesnt matter unless youre watching on tv and know what the other cards are. Sorry, but your theory that discounting outs based on other players unknown holdings is not a well kept secret of top professionals that you stumbled upon - you just werent thinking about it the right way. Hope this clears it up instead of confusing you more.Also, your point on DNs forum that the odds for you to hit your outs should be precisely halved for hitting on the turn, as opposed to the river is incorrect. Without going into heavy math, hitting on the turn is X in 47 (unknown cards), where X is your number of outs. From turn to river, one more card is exposed, and if it isnt your out, then one more card is known, and since it wasnt one that you wanted, your outs are now X in 46, which makes a bit of a difference. Your odds of hitting it on the river if you didnt get there on the turn will be a bit more than half of your chances of getting there, flop to river. Or in other words, your chances of hitting your out on the river are slightly better than your chances of hitting on the turn (assuming you missed on the turn).
I guess I should apologize to daniel, but I figure in the long run I sent more traffic to his forum ;)Please forgive my moronic post,DonkeySchool

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*EDIT: I'm a bit retarded, feel free to rid this post for giggles, but I am so wrong it's not funny*Daniel, I have to commend you on this post, if you ever read this *Unlikely* because this post was the reason I registered.There is so many things wrong here, I don't know where to start. *Ooooh I can see the flame war already*Daniel, as a professional poker player, I am sure you are aware of this, in fact this is an advanced strategy rarely if EVER discussed in poker books, is it because the Poker pro's don't want you to know it? Maybe, I doubt that somehow. I just think it's one of the cardinal things in poker you just don't talk about.Lets look at a nice 9 person table situation *which lets face it, if you play MTT's is where you are going to spend most of your time*. Lets say early position doubles, plays really tight, and everyone folds except for you, in the bb, you call with your 6 7hThe flop comes down with the 'Monster Draw' 3h 8h 9sYou have 15 outs. wow, percentage wise, you have the best hand.But do you really believe no one else held a single heart?how about a 10?how about a 5?in 9 handed, assuming you get headsup flop action. 17 cards are out that you don't know what are. 22 cards are already out, 5 of which you know. just under HALF THE DECK is already in play, including folded cards and the first burn. Now let me ask you thisDo you really have 15 outs? On a good day you would have 13-15, an average day 11, and a bad day, 8 or less.Should you put all your money into the pot when you are behind? ----Next problem I have with this post. So many problems with this one.See this is why I hate, loathe, disgust poker calculators. They are completely unrealistic, firstly: I have a problem with 56 changing to 34. I'm not saying which one is wrong here, because I frankly don't care, but your percentage chance should be more or less halved with only one card to come *so 56 goes to 28ish or 34 should be 68 to improve on the turn* But listen guys, rather than use a 'odds calculator' why don't you just use some simple maths in your head.After the flop 22 cards out of a 52 card deck have been used, that means that if you have exactly 15 outs still in that deck *good luck kiddo* since there are 30 cards left in the deck, what do you imagine your odds are that you will hit your card on the turn? 30 cards, divide by 15, hmmm...I don't know if I can work that out.You have a 50% chance to make your hand on the turn, assuming you have all your outs still in the deck. what's amusing is that, if the turn card doesn't help you, and you still believe you have 15 outs by some godly fate, there is now 28 cards left in the deck, 15 of which can help you. Your chance to hit on the river increased even more.I'm not trying to say my odds and math are correct *Though basic year 9 math we learn in school says it is* But I am trying to say that Daniels here *I'm not blaming daniel, I'm blaming whatever odds calculator he used* are.---In closing. When thinking about decisions like these, PLEASE figure out how many cards are already out, and adjust your outs to go with that. There is a good chance you really only have about 10, sometimes more, sometimes less on a full 9 handed table, 10 outs....hmm, decent favorite indeed.*The poster admits that she is probably going to get flamed massively for this post, and as such has allowed users to send her e-mails. The poster also admits she might get banned for this post, but she hopes it isn't the case*
this has to be one gigantic level....or the worst post ever

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Also, your point on DNs forum that the odds for you to hit your outs should be precisely halved for hitting on the turn, as opposed to the river is incorrect. Without going into heavy math, hitting on the turn is X in 47 (unknown cards), where X is your number of outs. From turn to river, one more card is exposed, and if it isnt your out, then one more card is known, and since it wasnt one that you wanted, your outs are now X in 46, which makes a bit of a difference. Your odds of hitting it on the river if you didnt get there on the turn will be a bit more than half of your chances of getting there, flop to river. Or in other words, your chances of hitting your out on the river are slightly better than your chances of hitting on the turn (assuming you missed on the turn).
It's not even just that, because the difference between X in 46 and X in 47 is negligible (usually within 1%, for smallish values of X). Other factors can come into play between the turn and the river, some of which positively impact the probability and some of which negatively impact the probability.One such instance is the possibility of going runner-runner that is included in the turn probability, but not included in the river probability where you did not improve. For instance, suppose that you hold 6h-7h, and the flop comes 3h-8h-9s. (This is essentially the scenario that Daniel brings up to start this thread.) In addition to the fifteen outs of any 5, any 10, and any heart (remembering not to double-count the 5h and the 10h), you can also win the pot by hitting running cards of 6-6, 7-7, or 6-7. The probability of these events occurring is (5/46) * (4/45), which contributes approximately 1% to the turn probability.But the biggest factor in contributing to the percentages in this case has to do with the fact that your turn percentage is discounted because improving twice is irrelevant. Unimproved on the turn, you have a roughly 33% chance of winning on the river (15/46). But let's think about what this is really saying about the turn probability:The turn probability incorporates two factors: you improve on the turn, in which case the river is irrelevant (except for the case of drawing the 9h, where the opponent may have redraws to a full house) OR you don't improve on the turn and improve on the river. Notice that the second possibility requires that two distinct events happen: you have to not improve on the turn AND you have to improve on the river.The first possibility is relatively easy to calculate: you improve on the turn with probability 15/47 (approximately 32%).The second possibility is more difficult: the first event has probability 32/47 (it's the remaining probability from the first possibility above) and the second event has probability 15/46. So the probability of both happening is 32/47 * 15/46 (approximately 22%).So the probability of winning on the turn is approximately 54% (it's the sum of the previous two probabilities), while the probability of winning on the river is approximately 33% (the 15/46 we calculated earlier).In other words, since improving on the river really only matters in cases where we didn't improve on the turn, and this only happens about 2/3rds of the time, the win percentage for the turn is only approximately 5/3 (1 + 2/3) times the win percentage of the win percentage for the river. Indeed, the approximation 5/3 * 33 = 55 is pretty darn close to the 54% that we got calculating the probability more authentically.But I should caution you: that 2/3rds approximation really only worked for that specific case (outs on the turn = 15). When the number of outs is relatively small (say 4), then the probability that we make it to the river unimproved is significantly larger. Note that the probability of winning with 4 outs on the river is 9%, where as the probability of winning with 4 outs on the turn is closer to 17%, almost exactly the double that you originally expected. That's because our multiplier in this case is 1.91 (1 + the .91 probability that we didn't improve on the turn), and 1.91 itself is really close to 2.Anyway, hopefully, that clarifies a little more of what's going on between those percentages.

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Dam I knew I should have paid more attention to math in school. Maybe I'll send a copy of this to my son so he will.

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It's not even just that, because the difference between X in 46 and X in 47 is negligible (usually within 1%, for smallish values of X). Other factors can come into play between the turn and the river, some of which positively impact the probability and some of which negatively impact the probability.One such instance is the possibility of going runner-runner that is included in the turn probability, but not included in the river probability where you did not improve. For instance, suppose that you hold 6h-7h, and the flop comes 3h-8h-9s. (This is essentially the scenario that Daniel brings up to start this thread.) In addition to the fifteen outs of any 5, any 10, and any heart (remembering not to double-count the 5h and the 10h), you can also win the pot by hitting running cards of 6-6, 7-7, or 6-7. The probability of these events occurring is (5/46) * (4/45), which contributes approximately 1% to the turn probability.But the biggest factor in contributing to the percentages in this case has to do with the fact that your turn percentage is discounted because improving twice is irrelevant. Unimproved on the turn, you have a roughly 33% chance of winning on the river (15/46). But let's think about what this is really saying about the turn probability:The turn probability incorporates two factors: you improve on the turn, in which case the river is irrelevant (except for the case of drawing the 9h, where the opponent may have redraws to a full house) OR you don't improve on the turn and improve on the river. Notice that the second possibility requires that two distinct events happen: you have to not improve on the turn AND you have to improve on the river.The first possibility is relatively easy to calculate: you improve on the turn with probability 15/47 (approximately 32%).The second possibility is more difficult: the first event has probability 32/47 (it's the remaining probability from the first possibility above) and the second event has probability 15/46. So the probability of both happening is 32/47 * 15/46 (approximately 22%).So the probability of winning on the turn is approximately 54% (it's the sum of the previous two probabilities), while the probability of winning on the river is approximately 33% (the 15/46 we calculated earlier).In other words, since improving on the river really only matters in cases where we didn't improve on the turn, and this only happens about 2/3rds of the time, the win percentage for the turn is only approximately 5/3 (1 + 2/3) times the win percentage of the win percentage for the river. Indeed, the approximation 5/3 * 33 = 55 is pretty darn close to the 54% that we got calculating the probability more authentically.But I should caution you: that 2/3rds approximation really only worked for that specific case (outs on the turn = 15). When the number of outs is relatively small (say 4), then the probability that we make it to the river unimproved is significantly larger. Note that the probability of winning with 4 outs on the river is 9%, where as the probability of winning with 4 outs on the turn is closer to 17%, almost exactly the double that you originally expected. That's because our multiplier in this case is 1.91 (1 + the .91 probability that we didn't improve on the turn), and 1.91 itself is really close to 2.Anyway, hopefully, that clarifies a little more of what's going on between those percentages.
Great post TheMathProf... thanks for being so detailed.

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I don't think anyone gets banned for trolling, DonkeySchool.
Cant believe I missed DonkeySchool's post. Id just add that nobody gets banned for not having a clue about probability, but if they did, DonkeySchool would be up for a lifetime ban.

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I love when people comment on the plays of someone making decisions for millions of dollars.Paul did quite well for himself. :club: The power of a monster draw is in acting first. Making the other player make a tough decision for his/her chips.If they call - ok you are a favorite but you still have to hit. If they fold - you made a profit without a made hand.Win Win

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