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Old 12-23-2005, 10:27 PM
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Default ODDs math question

I'm trying to get my mind around poker odds. Let's take an example.

What are the chances of getting 3 of a kind on the flop, if we have any pocket pair?

Now, on the first flop card we have this chance:

2/50 = .04

Since we have 2 "outs" that would complete our trips, and there are 50 cards left in the deck after our hole cards are dealt to us.

And for the 2nd flop card we have: 2/49
And for the 3rd flop card we have: 2/48

Now, here's where I'm having a problem. As I understand it, if any of 3 probabilities will get the desired result we ADD these 3 probablilties to get the probability that the needed event will occur within the 3 events.

So, this would mean we'd add:

2/50 + 2/49 + 2/48
or .04+.041+.042 (last 2 rounded)

or .123 or 12.3 %

According to this web site:
http://www.homepokergames.com/odds.php

The odds are 10.9% to flop 3 of a kind when we have any pocket pair.

Where am I going wrong in my calculations?

Thanks all.

Eric
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