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-   -   Odds of overcards on flop (http://archives1.twoplustwo.com/showthread.php?t=531874)

Vertical Taco 10-26-2007 11:57 AM

Odds of overcards on flop
 
According to this Chart the chances of an overcard appearing on the flop when you hold TT is 70%.

Could someone show me how they arrived at these numbers? Show work plz.

rufus 10-26-2007 12:46 PM

Re: Odds of overcards on flop
 
It's a bit easier to work out no overcards, and subtract that from 1.

Of the remaining cards, there are 34 cards that are not over cards (2 tens, and 4 each of 2 through 9).

That means that there are 34 choose 3 flops that don't feature an overcard, and 50 choose 3 flops in total.

So the chance of no overcard is ((34*33*32)/6)/((50*49*48)/6)=(34*33*32)/(50*49*48)=35904/117600 - 30.5%.
So the chance of an overcard is 1-30.5%=69.5%.


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