The Pair vs Pair Paradox

#2 17th April 2009, 11:17 PM

Why is this a paradox? It's just the probability of an event occurring given that another event has occurred. Seems like simple statistics to me.

If this is the common conception, this is a good informative post

#3 18th April 2009, 1:12 PM

Play it just like any other hand. Watch the other players and their raises. If you flop a set then bet it. I cracked aces with pocket 3s in our live game tonight. If you have a small pair and feel you're beat then you gotta give it up. I'm not sure about a paradox, maybe you are just thinking too much into it.

#4 19th April 2009, 3:43 PM

Its not a paradox, and its not independent property, as you seem to assume.
In the coinflip example its a binominal distribution, but in the pair example it as hypogeometrical distribution, so you need to take that into calculation.
So calculating the chance that any of your nine opponents have a pair differs from calculating the chance that any of your nine opponents have a pair provided you have one.
In the first example: P(x=anyone of the nine players has a pair)=42.05%
In the second example: P(x=anyone of the nine players has a pair|you have a pair)=40.86%

#5 19th April 2009, 4:15 PM

Interesting post.

I have to admit, I do sometimes feel a bit cheated when I get QQ and someone has either KK or AA.

It is very hard to handle, but it is understandable why people feel aggrieved, especially if they were card dead for a long period before getting a strong hand.

#6 19th April 2009, 6:06 PM

[ ] paradox
[x] pretty good thread

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