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  #11  
Old 12-28-2005, 10:42 PM
cbloom cbloom is offline
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Default Re: 5/5 NL...Doing Business????

Actually that math is messed up. Stupid algebra! Anyhoo, I think the correct result when you correctly add the odds of hitting both is something like (N - 1)/(44*43*2) , which is very small so pretty irrelevant unless the pot is huge.
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  #12  
Old 12-29-2005, 10:33 AM
derick derick is offline
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Default Re: 5/5 NL...Doing Business????

[ QUOTE ]

The game is fantastic. A lot of passive calling stations and players who are willing to go broke with TPTK or even less.

[/ QUOTE ]

Getting invited back is so +EV you want to fit in.

Do business.
Get the money.
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  #13  
Old 12-29-2005, 02:42 PM
scdavis0 scdavis0 is offline
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Default Re: 5/5 NL...Doing Business????

cbloom,

It's amazing to me that you could spend so much time working out the math on this and still come up with the wrong answer. I hope for your sake that your post is some sort of joke. I'll let you spot the error in your logic.

Running it once, twice, thrice, the whole deck -- it does nothing to EV.
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  #14  
Old 12-29-2005, 03:03 PM
scdavis0 scdavis0 is offline
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Default Re: 5/5 NL...Doing Business????

Here's a reasonable formulation in the case of ONE out.

Let S = size of the pot

If you run it once your EV = S/44

If you run it twice, one of 3 things will happen

1. You'll miss twice
2. You'll hit the first board but miss the second
3. You'll miss the first board but hit the second

To get our overall EV, we simply sum the product of each probability by the percentage of the pot we will receive should they occur.

Scenario 1 -- miss twice:

We will miss on the first card 43/44. Given that we missed the first card, we will miss the second card 42/43. The product of these probablities is 21/22. We will miss both boards 21/22 and receive zero.

Scenario 2 -- hit 1st and miss 2nd

We will hit on the first board 1/44. Given that we hit the first board, we will miss the second board 43/43. The probability is therefore the product -- 1/44. In this case we get half of the pot.

Scenario 3 -- miss the first but hit the second

We will miss the first board 43/44. Given that we missed the first, we will hit the second 1/43. The product of these is again 1/44.

Our overall EV is therefore:

EV = (S * 21/22 * 0) + (S * 1/44 * 1/2) + (S * 1/44 * 1/2)
= S/44

Thus running it twice with one out does NOTHING to EV. For fun, solve it generally for any number of outs!

(If anyone cares to see the general solution I'll be happy to provide)
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  #15  
Old 12-29-2005, 04:07 PM
pokerjoker pokerjoker is offline
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Default Re: 5/5 NL...Doing Business????

Allin on turn with villian having 1 out and the cards are resuffled inbetween tries.

Heres an easy equation w/o algebra.

1/44 x 1/44 =villians chance of winning

43/44x43/44 =your chance of winning

chance of tie (1/44x43/44)x2

if you don't do it twice then

43/44 u win
1/44 villian wins


I dont feel like mathing this out 'cause I have no calculator here.
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  #16  
Old 12-29-2005, 04:24 PM
scdavis0 scdavis0 is offline
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Default Re: 5/5 NL...Doing Business????

cards are generally not reshuffled

although it doesn't matter if you do
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  #17  
Old 12-29-2005, 04:58 PM
cbloom cbloom is offline
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Default Re: 5/5 NL...Doing Business????

Umm, sc if you do the general numbers I think you'll find the EV difference is

(N - 1)/(44*43*2)

in the case of 1 out there is indeed no difference, but with more than 1 out there is a difference.
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  #18  
Old 12-29-2005, 05:24 PM
TheWorstPlayer TheWorstPlayer is offline
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Default Re: 5/5 NL...Doing Business????

there is no difference.
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  #19  
Old 12-29-2005, 05:32 PM
scdavis0 scdavis0 is offline
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Default Re: 5/5 NL...Doing Business????

Wow you are actually defending your math.. I can ensure you that you are embarassingly incorrect

Ahem.. to quote you

[ QUOTE ]
The difference is ((N/44) - 1)/86. If you somehow had > 44 outs
it would be +EV to draw twice (silly), and the less outs you have the worse it is. In the extreme case of having only 1 out,
you lose 1.1% of the pot in EV by drawing twice !!

[/ QUOTE ]

You say something about having greater than 44 outs (which is impossible with 44 cards left in the deck), then you provide this formula. You give no reasoning for why your math should break down with exactly one out.. in fact you point out with exasperation how bad of a deal it is if you are the one with one out.

I'll provide the general solution for any number of outs -- if that STILL doesn't satisfy you then I'll show you the error in your own calculations.

Then if that is no longer enough, I'll agree to meet you and we can deal out a scenario where we run it twice and I have two outs. Just give me a 0.1% edge on the payout. Bring your whole bankroll!

EV of running once = S*x/44

S = size of the pot
x = number of outs

4 scenarios:
1. miss twice
2. hit 1st / miss 2nd
3. hit 2nd / miss 1st
4. hit twice

I won't bother calculating the probability of scenario 1 since you have zero EV in this case.

2. hit 1st miss 2nd

(probability hit 1st)*(probability missing 2nd given that you hit 1st)

x/44 * (43 - (x-1))/43 = x/44 * (44-x)/43 = x/44 * (44/43 - x/43) = x/43 - x^2/(43*44)

3. I'll spare the math as it should be obvious the answer is equivalent to scenario 2

4. Hit twice

(probability of hitting 1st) * (probability of hitting 2nd given that you hit 1st)

x/44 * (x-1)/43 = x/44 * (x/43 - 1/43) = x^2/(43*44) - x/(43*44)


Total EV of running twice:

let 'term x' = result for above calculation for scenario x

EV = S*term2*(1/2) + S*term3*(1/2) + S*term4

= S*(1/2)*(x/43 - x^2/(43*44)) + S*(1/2)*(x/43 - x^2/(43*44)) + S*(x^2/(43*44) - x/(43*44))

= x/43 - x^2/(43*44) + x^2/(43*44) - x/(43*44)

= x/43 - x/(43*44)

= (44*x)/(43*44) - x/(43*44)

= (43*x)/(43*44)

= x/44 = EV of running once
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  #20  
Old 12-29-2005, 05:43 PM
TheWorstPlayer TheWorstPlayer is offline
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Default Re: 5/5 NL...Doing Business????

my way was shorter, but nice post.
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