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 02-20-2017, 06:20 PM #1 Acryl2 centurion   Join Date: Jun 2005 Posts: 197 quick probability question Hello! We know villains range consists of 70% value hands and 30% trash. Villain now bets, we assume that he bets his value hands all the time and bets his trash hands half the time: How is the ratio of valuebets/bluffs now?
 02-20-2017, 09:39 PM #2 whosnext Pooh-Bah     Join Date: Mar 2009 Location: California Posts: 3,787 Re: quick probability question If I am understanding correctly, this is straightforward. If you want, you can think of this as a direct application of Bayes Rule. Notation: - V is a value hand - T is a trash hand - B is bet - P is probability Then at a certain point in the hand we know the following: P(V)=.70 P(T)=.30 P(B|V)=1.00 P(B|T)=.50 We seek P(V|B) and P(T|B). Bayes rule tells us: P(V|B) = [P(B|V)*P(V)] / [P(B|V)*P(V) + P(B|T)*P(T)] = [(1.00)*(.70)] / [(1.00)*(.70) + (.50)*(.30)]] = .70/(.70+.15) = .70/.85 = 70/85 Similarly, it is easy to see that P(T|B) = 15/85. Thus, the ratio of value hands to trash hands given that he bets is 70/15.
 02-20-2017, 09:59 PM #3 Acryl2 centurion   Join Date: Jun 2005 Posts: 197 Re: quick probability question TY for the detailed explanation. I was actually looking for how the probability changed. I didnt know ratio was a different thing. So its 70/85, or in other words when he bets its a value hand in 82% and a bluff 18% of the time?
02-24-2017, 10:42 PM   #4
aner0
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Join Date: Oct 2013
Posts: 75
Re: quick probability question

Quote:
 Originally Posted by Acryl2 TY for the detailed explanation. I was actually looking for how the probability changed. I didnt know ratio was a different thing. So its 70/85, or in other words when he bets its a value hand in 82% and a bluff 18% of the time?
ye

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