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View Poll Results: If you voted Rep, was your reason.... | |||
Family Values - Religion | 3 | 12.00% | |
Dem Scandals - Individ. character | 0 | 0% | |
Military - Iraq | 5 | 20.00% | |
Branding - loyalty | 0 | 0% | |
Economy - taxes | 12 | 48.00% | |
Poker | 5 | 20.00% | |
Voters: 25. You may not vote on this poll |
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#31
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Re: Something I\'ve been thinking about
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A coin-flip is a coin-flip, no matter how the problem is broken down. That's a large part of the beauty of equity calculations. They abstract away the details of individual hands and give us a broader understanding of what's going on. [/ QUOTE ] Ok, but does being all-in with 90% equity have higher variance than being all-in with 50% equity? I think that's the crux of the OP |
#32
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Re: Something I\'ve been thinking about
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Ok, but does being all-in with 90% equity have higher variance than being all-in with 50% equity? I think that's the crux of the OP [/ QUOTE ] At the time the decision is made, we're never all-in with 90% equity. That's the key. When we decide what to do, we have 50% equity. |
#33
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Re: Something I\'ve been thinking about
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Say you buy a lottery ticket $2, and you have 1/10000 to win $19 998. It's the only price. This situation is a coinflip but it has a lot more variance than a head-or-tail coinflip. [/ QUOTE ] Being laid the right odds to take a bet and equity are not the same thing. In your lottery example, you do not have 50% equity, even though the bet is break even. |
#34
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Re: Something I\'ve been thinking about
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So 1 has 0 variance. [/ QUOTE ] No. Once we are called, it's true that the outcome is certain, but we don't know what hand he has. From our perspective, we win the pot 1/2 the time and lose the pot 1/2 the time. Thus, we're flipping a coin for the pot, and this will be true for any range against which we have 50% equity. So the distribution of outcomes is the same in all 5 cases, and hence the variance must also be the same. |
#35
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Re: Something I\'ve been thinking about
Ok look, mathematically, if I'm right, examples 2 and 3 have the same variance, which are the 2 situations where variance is higher while number 4 comes 2nd while 1 and 5 have no variance.
E(X) = SUM(px) V(X) = E(X^2)-(E(X))^2 For 1 : E(X) = 0.5 V(X) = 0 For 2 : E(X) = 0.5 V(X) = 0.125 For 3 : E(X) = 0.5 V(X) = 0.125 For 4 : E(X) = 0.5 V(X) = 0.0625 For 5 : E(X) = 0.5 V(X) = 0 |
#36
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Re: Something I\'ve been thinking about
[ QUOTE ]
Ok look, mathematically, if I'm right, examples 2 and 3 have the same variance, which are the 2 situations where variance is higher while number 4 comes 2nd while 1 and 5 have no variance. E(X) = SUM(px) V(X) = E(X^2)-(E(X))^2 For 1 : E(X) = 0.5 V(X) = 0 For 2 : E(X) = 0.5 V(X) = 0.125 For 3 : E(X) = 0.5 V(X) = 0.125 For 4 : E(X) = 0.5 V(X) = 0.0625 For 5 : E(X) = 0.5 V(X) = 0 [/ QUOTE ] That would be true if our decision point were after we knew which actual hand villain holds. Since we don't, we can't break it down like that. That is, the variance is dependent on the amount of uncertainty at the time the decision is made. The underlying composition of that uncertainty doesn't matter. |
#37
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Re: Something I\'ve been thinking about
[ QUOTE ]
Ok look, mathematically, if I'm right, examples 2 and 3 have the same variance, which are the 2 situations where variance is higher while number 4 comes 2nd while 1 and 5 have no variance. E(X) = SUM(px) V(X) = E(X^2)-(E(X))^2 For 1 : E(X) = 0.5 V(X) = 0 For 2 : E(X) = 0.5 V(X) = 0.125 For 3 : E(X) = 0.5 V(X) = 0.125 For 4 : E(X) = 0.5 V(X) = 0.0625 For 5 : E(X) = 0.5 V(X) = 0 [/ QUOTE ] If you use E(X) = SUM(px), then you should be using: V(X)=SUM(x-E(X))^2*px. Edit: and how the hell did you get E(X)=0.5? [img]/images/graemlins/confused.gif[/img] |
#38
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Re: Something I\'ve been thinking about
[ QUOTE ]
[ QUOTE ] Ok look, mathematically, if I'm right, examples 2 and 3 have the same variance, which are the 2 situations where variance is higher while number 4 comes 2nd while 1 and 5 have no variance. E(X) = SUM(px) V(X) = E(X^2)-(E(X))^2 For 1 : E(X) = 0.5 V(X) = 0 For 2 : E(X) = 0.5 V(X) = 0.125 For 3 : E(X) = 0.5 V(X) = 0.125 For 4 : E(X) = 0.5 V(X) = 0.0625 For 5 : E(X) = 0.5 V(X) = 0 [/ QUOTE ] That would be true if our decision point were after we knew which actual hand villain holds. Since we don't, we can't break it down like that. That is, the variance is dependent on the amount of uncertainty at the time the decision is made. The underlying composition of that uncertainty doesn't matter. [/ QUOTE ] I honestly didn't understand what you said but while writing my answer I found what was wrong in my reasoning. Assuming it's an all-in situation, half the time we're winning, half the time we're loosing, in every situation, it's that simple. You're right imo. |
#39
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Re: Something I\'ve been thinking about
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half the time we're winning, half the time we're loosing, in every situation, it's that simple. [/ QUOTE ] Exactly. [img]/images/graemlins/smile.gif[/img] |
#40
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Re: Something I\'ve been thinking about
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Edit: and how the hell did you get E(X)=0.5? [img]/images/graemlins/confused.gif[/img] [/ QUOTE ] sit 2 : E(X) = SUM(px) = (2/3)*(0.75) + (1/3)(0) = 0.5 Aint this right? |
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