#11
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Re: equity - ez for you to answer
[ QUOTE ]
Lets say I am in a hand against 2 opponents. I have the first guy beat 54% of the time. I have the 2nd guy beat 38% of the time. What is my equity against both players? (please explain) ty in advance [/ QUOTE ] It depends on player how often player 1 will beat player 2. If player 1 will never beat player 2 your equity is 38%. This could happen if players 1 and 2 had the same ranking cards but player 2 had a flush draw. You could also be in a situation where player 1 will beat you almost everytime player 2 doesn't. You have AQ, player 1 has AK, and player 2 has QQ. If you end up beating player 2 you'll almost surely lose to player 1. This isn't a perfect example because you can win, but it's possible to have no equity in this spot. let A = beating player 1 let B = beating player 2 P(A & B) = P(A)*P(B|A) = P(B)*P(A|B) If A and B are independant events P(B|A) = P(B) and P(A|B) = P(A). The problem is neither P(B|A) or P(A|B) are specified or can be determined from the given info. |
#12
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Re: equity - ez for you to answer
Not enough information.
I'll use an example to try to show you why. Let's say you have JsTs. Opponent 1 has 33. Thus equity against player 1 is 53.25% Hand Pot equity Wins Ties 33 46.75% 4,743,270 120,354 JsTs 53.25% 5,410,200 120,354 Now let's assume player 2 has AQo. Our equity against player 2 is 39.56% Hand Pot equity Wins Ties JsTs 39.56% 673,184 8,523 AsQd 60.44% 1,030,597 8,523 Our equity against both players is 33.72%. Hand Pot equity Wins Ties JsTs 33.72% 2,761,722 35,007 AsQd 35.46% 2,904,492 35,007 33 30.82% 2,523,303 35,007 Now let's change player 2's hand. We change it to TT, which DECREASES our equity against him to 38.69% Hand Pot equity Wins Ties JsTs 38.69% 1,940,247 94,662 TT 61.31% 3,102,003 94,662 But what happens to our equity against both of them? Our equity in the 3-way pot INCREASES to 34.69% Hand Pot equity Wins Ties JsTs 34.69% 8,321,166 505,188 33 18.50% 4,535,046 89,082 TT 46.81% 11,312,172 505,188 I hope this serves as a counterexample for calculating your equity against two opponents given individual equity vs each. |
#13
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Re: equity - ez for you to answer
T50_Omaha8 is correct.
The key is whether the main uncertainty is whether you will improve or whether the other hands will improve. At one extreme, you have a draw the comes through 38% of the time and gives you the nuts. If it fails, you always lose to hand 2, but you still sometimes beat hand 1. Now you beat both hands 38% of the time, the highest possible amount. Or, suppose your hand never improves. You only win if both hand 1 and hand 2 fail to improve. If the events are independent then your chance of beating both is 0.54*0.38 = 21%. At the other extreme, assume you're down to the river card. 19 of the 42 unseen cards win for player 1 and 27 win for player 2. If that includes all 42 unseen cards (that is, if there are only 4 cards that make both player 1 and player 2 beat you), then you have zero chance of winning. |
#14
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Re: equity - ez for you to answer
[ QUOTE ]
[ QUOTE ] can anybody tell me if he is correct ? [/ QUOTE ] I have to warn you, Gary Carson says I'm insane. I'd hate to be both insane and wrong, but I have to admit it's possible. [img]/images/graemlins/tongue.gif[/img] [/ QUOTE ] Is Gary posting anywhere? I haven't heard from him in a few years. I use to get a lot of feedback from on RGP, however, that has become........well.......you know. |
#15
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Re: equity - ez for you to answer
[ QUOTE ]
[ QUOTE ] [ QUOTE ] can anybody tell me if he is correct ? [/ QUOTE ] I have to warn you, Gary Carson says I'm insane. I'd hate to be both insane and wrong, but I have to admit it's possible. [img]/images/graemlins/tongue.gif[/img] [/ QUOTE ] Is Gary posting anywhere? I haven't heard from him in a few years. I use to get a lot of feedback from on RGP, however, that has become........well.......you know. [/ QUOTE ] He has started a blog: http://www.mathandpoker.com He has some interesting material on the site. RGP may have changed, but Gary has not. He still knows how to hold a grudge, and he still has a penchant for attacking people (as demonstrated by his posts on Ed Miller's blog, http://www.notedpokerauthority.com ). |
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