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HELP! math thinking, Mark Barnett II, 16. Oct 2003 09:58
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ok math problem i think im missing something somewhere.
few posts below talks about having openended straight flush draw in NL HE.
he figures 17 outs *actually 15 but either one works* and calls an all in bet on the flop thinking he has over 50% chance of making his hand
now assuming he is right and he has 15 clean outs im trying to figure out where this translates into over 50%

47 unknown cards minus 15 winning cards = 32 bad cards
46 unknown cards minus 15 winning cards equals 31 bad cards
if every combination of 2 cards is dealt doesnt the losing number far exceed the winning ones?
only reason im asking is cause it was an all in bet and odds on the turn make no difference.

btw not saying he was right or wrong on calling as all sorts of factors come into play but look at it this way if someone said we are playing a game and ill pay you a dollar if you win and you pay me a dollar if i win, which side of the coin do you want to be on?
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Re: HELP! math thinking, PairTheBoard, 16. Oct 2003 10:11
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It's a big difference between making the All In call on the flop vs on the turn. If he makes it on the turn he is about a 2-1 underdog, ie about 30 misses vs 15 hits. However if he makes it on the flop he has two shots at hitting his draw. That translates to roughly 1/3 + 1/3 - (1/3 * 1/3) = 5/9 making him about a 5-4 favorite. Note: you must subtract the 1/3 * 1/3 to avoid double counting the times you hit on both cards. You may hit on both cards but it's only one win for you.
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Re: HELP! math thinking, Mark Barnett II, 16. Oct 2003 10:18
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wow too much brain workage today
on the turn you win 15 times immediatly and 32 undecided
on the river you win 15 times and i win 31 times
boy am i confusing myself seriously hehe
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Re: HELP! math thinking, Mark Barnett II, 16. Oct 2003 10:35
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nm going brain dead hehe
you win 15 immediatly 15/47 of the time
of the 32 times you dont win immediatly you win 15/46 of the times
so *roughly* you win immediatly 1/3 of the time and then win 1/3 the time on the river

using *fake numbers*
you have a pool of 27 *3X3X3*
you win 1/3 immediatly so thats 27/3 or 9
27 minus 9 equals 18
of the 18 remining you win 1/3 of that or 18/3 or 6
you win 15 bets and lose 12 *27-15*

even though i went momentarily brain dead hopefully the posts show a simple version of how odds are figured
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Re: HELP! math thinking, TrippH, 16. Oct 2003 15:42
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this is much easier if you think about it in reverse, i.e. the odds of not making one of your outs: (32/47)(31/46) = 992/2162 = 45.9%, so the chance of making a hand is then 54.1%
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Re: HELP! math thinking, Mark Barnett II, 17. Oct 2003 10:29
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my problem is i was ignoring that you win a % of the time on the turn and then win a percent of the time on the flop that you dont win on the turn
i was looking at it as (15/47)(15/46) which is horrible odds.

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Re: HELP! math thinking, stock53, 20. Oct 2003 11:15
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If, after the flop, you have 47 cards of which 15 win for you:

Chances of not hitting a winning card=47C2*(32/47)*(32/47)=46.36%
Chances of hitting a winning card=1-.4636=53.64%

(C stands for Combination)
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