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Server Time: 2/13/2012 11:42:49 AM PACIFIC |
 When to call., P. Liem, 20. Jan 2003 21:00 | ||
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| Hello there, When deciding whether or not to call a bet, should one take into account the amount of money he or she has already put into the pot on previous betting rounds? A little while ago I read one of D. Sklansky's books where he claims that you should not consider the money you've already put into the pot, when deciding your next move. I wonder if I misunderstood, but if I didn't, can someone explain to me why Sklansky is right? Thanks, P. | ||
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| Re: When to call., NiceFella, 20. Jan 2003 22:37 | ||
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| Poker chips have no memory, and they don't have your name on them. Once your chips are in the pot, they don't belong to you or anyone else. It doesn't matter if you put them there or someone else did -- all the chips are the same. Prior ownership of the chips has no bearing on who's going to be receving the chips at the end of the hand. Once I make a bet, I consider those chips *gone*. They're not mine anymore, and the money is lost unless I win the pot. Putting chips in the pot just because you've already put other chips in the pot is a bit like cutting off your foot just because you've already cut off your toe. I don't know if any of this can help you intuitively understand this any better. It's a mathematically sound prinicipal, and this is how I think of it. | ||
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| good money after bad, P. Liem, 21. Jan 2003 13:55 | ||
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| Hey, thanks for the reply. But I'm still unclear. I guess I was looking for someone to explain the mathematics behind not considering the money you've already put into to pot. I'm very new to poker, and having been struggling to get a handle on this amazingly dynamic game. I'm constantly impressed by how the seemingly simple nature of poker leads to great complexity and challenge. So here'e the thing . . . In backgammon the reasoning is different. Backgammon and poker are essentially analogous games. At any point during a game of backgammon you have the option to double the initial wager, your opponent may: 1, accept, game goes on with double the initial stakes; 2, decline, game ends, your opponent loses initial wager; or 3, redoubles, and then you have to decide to . . . etc. As you can see, backgammon is like one long (too long) hand of poker. But when deciding whether or not to accept the double the reasoning used is as follows: Let x be the probability of you winning, let Y be your initail wager. Your expected win, EW, is: EW = x * (2Y); and your expected loss, EL, is: EL = (1 - x) * (2Y); now, if EL - EW < Y, you should accept (i.e., call), otherwise decline (i.e., fold). So backgammon logic says you have to look at Y, which is the money you already put in the pot. Here's my problem: 1. If this is correct for backgammon, why isn't it correct for poker? I can't see any difference between the to games in this respect. You get raised, you estimate your chance of winning, then you look at the money in front of you and decide your move. But backgammon is saying you calculate according to what you've already wagered. 2. If this isn't correct for backgammon, why? I completely understand the principle of not playing, let's call it, "good-after-bad". And I don't, or at least work on, not playing that way. But I'm not talking about the kind of play where you say to yourself, "Aw hell, I've dumped $100 into this already, may as well throw in $20 more." Yeah, for sure that's stupid. But I'm asking, when you're playing well, and starting to get a good grasp on figuring odds, are you sure that you don't want to consider the money you've already put in. I think, in fact, if you play this way, according to the formula above, you'll end up folding more often. So it won't end up being a good-after-bad play. Any thoughts, P. | ||
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| Re: good money after bad, NiceFella, 21. Jan 2003 19:19 | ||
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| I'm not a backgammon player, but I think I understand your explanation of the doubling wager. I'll begin by pointing out that your betting decision is a little complicated as expressed in your equations. You'll notice that EL - EW < Y after substitution becomes (1-x)*(2Y) - x*(2Y) < Y which simplifies to x > 1/2 So your decision to double is really just a determination of whether you have a better than even chance to win the round. Thus the decision to double is decidedly NOT a function of the current bet amount. This is common sense: when you have the best of it, it's in your interest to increase the wager, regardless of its current level. What's important about your equations are their results, not their methods. The expected win and loss are what the gambler cares about. The fact that Y is used to determine these values doesn't imply that Y itself is what is under consideration. If you could calculate these expected values by another method that didn't use Y, the results would be just as valid. The reduction of the decision to x > 1/2 is an example of re-expressing the decision in a manner independent of Y. In any wager, your concern is ensuring a positive expected value. For a simple proposition bet, all you need to calculate this are (1) the amount of the bet, (2) the amount of the potential reward, and (3) the chance of winning that reward. In poker, the amount of the potential reward (pot size) is generated by a complicated series of bets of varying amounts by a varying number of participants. When it comes time to calculate expected value, we don't care about the individual contributions. Only their total is important. In backgammon, we still care only about the size of the potential reward, and not the source of that reward. It's a happy mathematical fact that the "pot size" is so easily computed in terms of the past betting. Don't let that fool you into thinking that your past betting is what you really are examining. I hope that I haven't made any gross errors in this post, and that I haven't caused great confusion or opened any cans of worms :-) I welcome feedback, NiceFella | ||
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| Re: good money after bad, P. Liem, 22. Jan 2003 12:37 | ||
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| Wow, thanks a lot for the explanation. I think your reasoning is exactly right. I'm embarrassed I didn't even go so far as to do the substitutions. But your math is a bit off. I'll just fix the equation and then comment. So ( (1 - x)*2Y - x*2Y ) < Y reduces to ( 1 - x - x ) < 1/2, -2*x < -1/2, and finally you get x > 1/4 So in backgammon, to call, you've go to have a probability of better than 0.25, which, I think, is the result you want. (I'll explain in a post script so we won't have to bother with something that's not poker related.) Here are the new poker-relevant equations (using the same variable names from the past exchange): EW = x*(P - Y); where P is the pot size, EL = (1 - x)*(Y + y); where "little" y is the amount you have to call, thus we get ( (1 - x)*(Y + y) - x*(P - Y) ) < Y, reducing this we get y*(1 + x) - x*P < 0 So you are right on, the amount of money you've already bet has no bearing on whether or not to call, only the pot size itself in relation to the amount to call. Thanks for all your help, no can of worms here. I guess, in a way, this is all a bit silly, since the real problem is how to calculate x, your probability of winning, which I suppose comes down to an art in the end. Whether or not there's anything left to discuss, I don't know. But any feedback will be great. I'm sure I'll have many more questions in the future. Thanky. --P. P.S. So yeah, in backgammon, if you get all your men off the board before your opponent, he or she has to pay double the current wager. So, that has to be factored in, and I guess it comes out to needing to have more than 0.25 probability of winning. Interestingly, you face the same problem in backgammon as in poker, how to calculate x. In backgammon, of course, everything is exposed, so in principle calculating your probability is easy. That's why backgammon computer programmes can be successful, where poker programmes fail. And, in my humble opinion, it's also what makes poker the fantastic game that it is. | ||
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| Re: good money after bad, NiceFella, 22. Jan 2003 15:38 | ||
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| OK, We're all on the same page here. Thanks for the correction in my algebra ... but this leads me to a surprising thought regarding backgammon. Suppose you're in a position where you figure to have a 60% chance to win the game, and the opponent therefore has a 40% chance to win. If we're right about the math, that means it's correct for *both players* to double. It appears there's more to backgammon than meets the eye. Yikes, keep me out of that game! NiceFella | ||
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| Re: good money after bad, Andrew Wells, 23. Jan 2003 14:33 | ||
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| It becomes correct to ACCEPT a double when you will have the possible opportunity to redouble, it is that factor which makes it correct to accept when you are a 3:2 underdog. Bear in mind that only the player who has accepted the last double has the option to offer a double again. | ||
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| Re: good money after bad, Snorbolus, 21. Jan 2003 19:43 | ||
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| Hello P.Liem The difference between the betting in poker and backgammon is that in backgammon there are a fixed and constant number of opponents (1) for the duration of the betting period. Therefore the ratio between the amount of money that you have already bet and the amount that you stand to win is also constant. That is to say, when you consider the amount of money that you have already bet you are, in effect, considering the "size of the pot". The situation in poker is different because there is no fixed ratio between the amount of money that you personally have already wagered and the size of the pot. Therefore you can not use your previous bets to calculate the pot size. Instead you need to keep track of the pot size during the game and use this information directly. Ultimately you are making the same comparison in both games: how much money am I about to put at risk? how much do I stand to win? what is the chance that I will win if I decide to risk that money? The difference is that in poker (unlike in backgammon), the amount of money that you have already invested is not sufficient information to calculate the amount that you stand to win. I hope that this helps, Snorbolus | ||
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| Re: When to call., Snorbolus, 20. Jan 2003 22:43 | ||
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| You should certainly consider the size of the pot, but never how much of it came from your stack. Indeed, it is best to try to forget about that, otherwise you may be tempted to stay in when you should fold. Sometimes you might want to consider how much aggression you have shown previously in the hand as this affects what the other players put you on. Even then though you have to be VERY careful. You will often be tempted to call a bet or raise instead of folding. Usually when you find yourself thinking about how much of the pot came from your stack you should fold. Snorbolus on 20. Jan 2003 21:00 P. Liem wrote: > Hello there, > > When deciding whether or not to call a bet, should one take into account the > amount of money he or she has already put into the pot on previous betting > rounds? > > A little while ago I read one of D. Sklansky's books where he claims that you > should not consider the money you've already put into the pot, when deciding > your next move. I wonder if I misunderstood, but if I didn't, can someone > explain to me why Sklansky is right? > > Thanks, > > P. | ||
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| Re: When to call., Nathaniel Brous, 20. Jan 2003 22:53 | ||
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| I am sure someone else will be able to answer your question more clearly than myself, but, since I am here... You actually do want to take into consideration the money you have put in the pot, BUT, only in relation to the pot as a whole. Your contribution is not overly significant. If you are beat, drawing thin or dead, who cares how much you have invested already? He words it that way to make a distinction, so you do not throw good money after bad. Invest in David's "Theroy of Poker." He covers your question in depth. If you have read it, read it again. It is a lot to absorb at one time. The only glaring exception to this rule is in tournament play, where you have already pot committed yourself and must throw your remaining money in on the long shot. I hope this helps. - Nathaniel Brous | ||
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| Re: When to call., P. Liem, 21. Jan 2003 14:01 | ||
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| Hey, could you take a look at the reply I sent to NiceFella. Because you're the only person who actually said you *should* take into consideration the amount of money already in the pot. I'd like to get a debate going on this, and figure out the best "mathematical" solution to the problem. Thanky --P. on 20. Jan 2003 22:53 Nathaniel Brous wrote: > I am sure someone else will be able to answer your question more clearly than myself, > but, since I am here... > > You actually do want to take into consideration the money you have put in the pot, > BUT, only in relation to the pot as a whole. Your contribution is not overly > significant. If you are beat, drawing thin or dead, who cares how much you have > invested already? He words it that way to make a distinction, so you do not throw > good money after bad. Invest in David's "Theroy of Poker." He covers your question > in depth. If you have read it, read it again. It is a lot to absorb at one time. > The only glaring exception to this rule is in tournament play, where you have already > pot committed yourself and must throw your remaining money in on the long shot. I > hope this helps. - Nathaniel Brous | ||
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| Re: When to call., Nathaniel Brous, 21. Jan 2003 19:07 | ||
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| I apologize if I have misled you. Please read my post again. I apologize for stating the obvious. I only meant that when you determine your overall odds (good bet, bad bet), the money you put in must be included. It is not a separate entity. The money in the pot belongs to the pot, until it is awarded. Unfortunately, I can't help you with the math, but can give you a decent example to think over. Two identical holdem hands. In one, you are heads up (both blinds) preflop, and in the other all ten people see the flop. In the first you have put in 50% of the money, the other 10% of it. Assuming you have a nut flush draw, which one do you prefer to chase with? Sorry for the confusion. -Nathaniel on 21. Jan 2003 14:01 P. Liem wrote: > Hey, could you take a look at the reply I sent to NiceFella. Because you're the only > person who actually said you *should* take into consideration the amount of money already > in the pot. I'd like to get a debate going on this, and figure out the best > "mathematical" solution to the problem. > Thanky --P. on 20. Jan 2003 22:53 Nathaniel Brous wrote: > > I am sure someone else will be able to answer your question more clearly than myself, > > > but, since I am here... > > > > You actually do want to take into consideration the money you have put in the pot, > > BUT, only in relation to the pot as a whole. Your contribution is not overly > > significant. If you are beat, drawing thin or dead, who cares how much you have > > invested already? He words it that way to make a distinction, so you do not throw > > good money after bad. Invest in David's "Theroy of Poker." He covers your question > > in depth. If you have read it, read it again. It is a lot to absorb at one time. > > The only glaring exception to this rule is in tournament play, where you have already > > > pot committed yourself and must throw your remaining money in on the long shot. I > > hope this helps. - Nathaniel Brous | ||
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| Re: When to call., P. Liem, 22. Jan 2003 12:49 | ||
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| That's a good question, I think. My gut instinct would be to chase with more people in the pot. Is that right? However, practically speaking, when your flush doesn't come up, you've got to decide what to do. The more people in the pot the harder it is to win by bluffing, plus you may have to face more raises. So, is it clear cut that you'd want to chase with more people in? --P By the way, I think we worked out the math (confirming what you say), which, if you're interested is in a reply post to NiceFella. on 21. Jan 2003 19:07 Nathaniel Brous wrote: > I apologize if I have misled you. Please read my post again. I apologize for stating the > obvious. I only meant that when you determine your overall odds (good bet, bad bet), the money > you put in must be included. It is not a separate entity. The money in the pot belongs to the > pot, until it is awarded. > Unfortunately, I can't help you with the math, but can give you a decent example to think > over. Two identical holdem hands. In one, you are heads up (both blinds) preflop, and in the > other all ten people see the flop. In the first you have put in 50% of the money, the other > 10% of it. Assuming you have a nut flush draw, which one do you prefer to chase with? Sorry > for the confusion. -Nathaniel | ||
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| Re: When to call., Piers, 21. Jan 2003 10:11 | ||
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| You do not need to know how much money you have put in the put, its just cluttering up your memory forget it. What you do need to know is how much money is in the pot. If you want to take Poker seriously you should practise and practise until you can keep track of the pot size with the minimum of overhead. | ||
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