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#11
01-12-2006, 07:22 PM
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Re: $215 - aggressive against field with draw (Level II)
I dunno, isn't it 1 - (chance of not hitting 1st card * chance of not hitting second card)
1 - (34/47 * 33/46) = 48.1% Doesn't work like chance of rain. Within 35 cards an out HAS to fall, but rain doesn't. 
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#12
01-12-2006, 07:36 PM
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Re: $215 - aggressive against field with draw (Level II)
[ QUOTE ]
I dunno, isn't it 1 - (chance of not hitting 1st card * chance of not hitting second card) 1 - (34/47 * 33/46) = 48.1% Doesn't work like chance of rain. Within 35 cards an out HAS to fall, but rain doesn't. [/ QUOTE ] But either "rain" or "not rain" has to fall. It's exactly the same with cards. Your math is right, 1- ((chance of not hitting turn)*(chance of not hitting river)) is the chance of hitting on the turn OR the river. However, (chance of hitting on turn) + (chance of hitting on river) is not equal to the above calculation, because you double count the times that you hit on both the turn and the river. However, 1-((chance of not hitting turn)*(chance of not hitting river)) is equal to (chance of hitting turn) + (chance of hitting river) - (chance of hitting both turn and river). Substitute "hitting" with raining and it's the same analysis.
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#13
01-12-2006, 07:41 PM
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Re: $215 - aggressive against field with draw (Level II)
Both formulas are equivalent (somebody better not have beaten me to this).
1 - (34/47 * 33/46) = 1 - (a/b * c/d) = 1 - ( (b-x)/b * (c-y)/d ) (x = 13, y = 13) = 1 - ( (1-x/b)* (1-y/d) ) = 1 - (1 - (x/b + y/d) + xy/bd) = x/b + y/d - xy/bd = x/b + y/d - (x/b * y/d) = 13/47 + 13/46 - (13/47 * 13/46) (doens't matter if it outs have to eventually fall or not, all we care about is the probability they fall on this street)
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#14
01-12-2006, 07:42 PM
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Re: $215 - aggressive against field with draw (Level II)
Yeah, you guys are both correct. You used different roads to get to the same place, and both work. I was just off on my probability. I did the math wrong, but the percentages I showed were roughly correct when checking with twodimes.net. So the odds and correct calls I showed originally still stand.
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#16
01-12-2006, 08:12 PM
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Re: $215 - aggressive against field with draw (Level II)
Very nice, both of you. Using algebra and everything.
I checked the result and got thrown by rounding differences. oops. The rain is a bit different because the chance of it raining today doesn't necessarily affect the chance of it raining tomorrow, but if you set the problem up like it did it's the same equation. Sorry.
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