Theory of Poker: Chapters 1-4 Discussion

[sethypooh21]

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Actually we are both wrong. If the house is winning 50.001% of the time and the better is betting 120 bets per hours which is $120,000 an hour then the house is winning 50.001% of that which is winning 60,001.20 an hour and the man is winning $59,998.8 per hour. So you subtract the difference and divide 1B by that. So it takes 416,666,666.66 hours which is roughly 47,564.69 years.

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That's what I had originally, bet then I remembered the .25 extra days per year [img]/images/graemlins/grin.gif[/img]

[jdl22]

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You are playing in a $5/$10 Limit Hold Em game. You have A K . Your opponent has A T . The board is A K 8 2 . The pot is heads up. You bet $10 into a $45 pot. Your opponent calls. According to the Fundamental Theorem of Poker you both gained from this play. How is that possible?

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You have both made a mistake. If you could see his cards you obviously wouldn't bet. Hence you lost 1 bb by making that move. Your opponent in a rakeless game gained that 1 bb. You benefitted because he should have raised. I don't really buy this because if you could see his cards you wouldn't call his raise so it's a moot point anyway.

[jdl22]

The problem with what you guys are saying is that the question cannot be answered. The time it takes for the rich man to go broke is actually a random variable. You can calculate when he should expect to go broke but not when he will. This is what's called a random walk.

[Smokey98]

I'm sure he was just looking for a close estimate, you guys are thinking too much.

[MEbenhoe]

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You are playing in a $5/$10 Limit Hold Em game. You have A K . Your opponent has A T . The board is A K 8 2 . The pot is heads up. You bet $10 into a $45 pot. Your opponent calls. According to the Fundamental Theorem of Poker you both gained from this play. How is that possible?

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You have both made a mistake. If you could see his cards you obviously wouldn't bet. Hence you lost 1 bb by making that move. Your opponent in a rakeless game gained that 1 bb. You benefitted because he should have raised. I don't really buy this because if you could see his cards you wouldn't call his raise so it's a moot point anyway.

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Not to sound mean, but this is entirely incorrect. If you could see that your opponent has a flush draw and don't bet into him you are making a very large mistake. Your opponent has 9 outs for a win out of 44 unseen cards. Therefore if you know what his cards are you will win every time he doesnt hit his flush and fold on the river everytime he makes his flush. What this means is you will gain $10 35 times and lose $10 9 times for a total gain of $260 over the option of not betting. This is a difference of $5.91/hand. This proves that betting is the correct play for you. Your opponent by calling will lose $10 35 times but gain $55 9 times. This means he makes $145 total or $3.30/hand by calling. Lets contrast that with raising. In this case he would lose $20 35 times and gain $65 9 times assuming you call and dont reraise. This results in a total of him losing $115 or -$2.61/hand. Even if you would call a bet on the river every time he hits his flush he still would end up losing $25 on this play or -$0.57/hand. It is clear that the best option here is for you to bet and for him to call.

The fact that you would fold top two pair to a flush draw who raises you and that you don't believe it is correct to bet into him either if you could see his cards are both very incorrect plays and the fact that you feel these are the correct plays suggest you have a lot of studying of the game to do. This again isn't said to be mean but to show you how much in error this thinking is.

Still waiting for the person who's gonna figure out how they are both gaining on this.

[sethypooh21]

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You are playing in a $5/$10 Limit Hold Em game. You have A [img]/images/graemlins/spade.gif[/img] K [img]/images/graemlins/club.gif[/img]. Your opponent has A [img]/images/graemlins/heart.gif[/img] T [img]/images/graemlins/heart.gif[/img]. The board is A [img]/images/graemlins/club.gif[/img] K [img]/images/graemlins/heart.gif[/img] 8 [img]/images/graemlins/heart.gif[/img] 2 [img]/images/graemlins/spade.gif[/img]. The pot is heads up. You bet $10 into a $45 pot. Your opponent calls. According to the Fundamental Theorem of Poker you both gained from this play. How is that possible?

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I think the statement of the question is slightly misleading. Your opponent actually *loses* by your betting. Before your action he has roughly .2 x $45 = $9 in pot equity. By betting, you force him to pay $10 to retain his pot equity, and this would seem to indicate a fold, except that he retains $2 of his own call in equity and "gains" $2 of your bet, so he has to call $10 to retain $13 in pot equity. Thus he "gains" $3 by calling (completely discounting implied odds of course), but is *worse off* by $6 then if you had not bet.

From your perspective, you start with $36 in pot equity. This is good. However, it can get better by betting. You either force your opponent to forfeit his $9 (essenitally giving you $9 for free), or to pay $10 of which you "own" $8, so betting gives you either $45 or $52 in equity, returning $16 on a $10 investment.

So each play is positive for the individual player, but the overall play is "more positive" for you then for him.

[Leavenfish]

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Actually we are both wrong. If the house is winning 50.001% of the time and the better is betting 120 bets per hours which is $120,000 an hour then the house is winning 50.001% of that which is winning 60,001.20 an hour and the man is winning $59,998.8 per hour. So you subtract the difference and divide 1B by that. So it takes 416,666,666.66 hours which is roughly 47,564.69 years.

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I hate to say it, but you are wrong. All of you. Why? No man can live 47,000 years! It is physically impossible. Now, if the term android had been used.... [img]/images/graemlins/laugh.gif[/img]

[BugsBunny]

What type of game conditions would make this strategy optimal?

Having a huge ante isn't enough, in and of itself. The right conditions would have more to do with game texture than ante size. The only type of game where I can think of that it would make sense to try and win the most pots is a game where all the pots are roughly the same size, and small as well.

If you have large pots (either constantly or at least semi-frequently) then winning 1 large pot can give you enough ammo to wait for a long time to wait for another opportunity to take another large pot. You're investing a small amount per round (be it antes or blinds) in comparison to the size of the pot.

If the pots are all small though then the per round cost starts to eat at your stack, and the only way to make money is to win lots of the small pots. If all the pots tend to be small then the opponents are all probably very weak-tight, making it relatively easy to steal lot's of antes/blinds or the initial pot.

High antes/blinds or small antes/blinds it doesn't really matter. What matters is the pot size in relation to the size of the antes/blinds.

[BugsBunny]

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Why is Mathematical Expectation important to a poker player?


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Because the mathematical expectation of a given hand/situation is what determines what a players correct move is. If it's negative he shouldn't continue to play. If it's positive he should. A player only wants to commit money when he has the best of it, meaning his expectation is positive.

Understanding expectation can help you deal with bad things happening. Even if you lose a hand you still make money long term, if the play was correct. You realize that your earn is simply your expectation times the amount of time played, as long as you continue to play correctly.

Now here comes the challenge working in what you should have learned about Mathematical Expectation and hourly rate:

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On p. 11 Sklansky quotes Bob Stupak, “Having one-thousandth of one percent the worst of it, if he plays long enough, that one-thousandth of one percent will bust the richest man in the world.” We won’t use Bill Gates for this example, but assume a man with a $1 billion bankroll is playing a dice game in which the house has a 50.001% to 49.999% edge. If this man bets $1000 per roll of the dice and rolls 120 times per hour how long will it take him to go broke? Explain your answer. (Have fun with the math on this one)

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It depends [img]/images/graemlins/smile.gif[/img]
He, personally, will never go broke. If his descendants keep playing they'll eventually go broke after approximately an average of 1440 generations (assuming a generation is 33 years, and there's 365.2425 days in a year. (the length of the year will also probably change in that time)

Now this can also be +- a few generations depending on the standard deviation, but the chapter doesn't get into that at all so we'll just leave it alone.

Breakdown:
He's losing an average of 0.02 dollars per hand

1,000,000,000/(120 * .02) = 416666666.666667 hours
416666666.666667/24 = 17361111.1111111 days
17361111.1111111/365.2425 = 47533.1077602171 years
47533.1077602171/33 = 1440.3972048551 generations (give or take)

[jdl22]

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Not to sound mean, but this is entirely incorrect.

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No worries. What we're trying to do is discuss the book, if I'm wrong rip into me.

On this problem I was way off. My board reading skills are pretty bad apparently because for some reason I thought it was the river. Looking again I'm fairly embarassed because there appear to only be four cards out. Now I'll go back and read the rest of what you said.

edit: Wow, good call, I was even farther off on what I thought the problem said. Firstly I thought that the hero in the question had AT and it was the river betting round. I need to read these problems more carefully. Obviously you shouldn't fold this if you are the guy with AK. [img]/images/graemlins/blush.gif[/img]