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Re: I'm trying! Is it true flopping a straight with one gapper
So for any particular flop, you can calculate the chance of getting it in a few ways. Let's say that you're looking for a flop of type ABC where A B and C are all different cards. In our situation there are 4 of each card available, and 50 cards left in the deck.
So, consider 468. For the "first" card on the flop, there are 12 cards in the deck that could be the "start" of 468 (4 each of 4, 6 and 8). So the chance of the first card being a match is 12/50. Now there are 49 cards left in the deck.
For the 2nd card, there are 8 cards in the deck that could continue what we're looking for. If the first card we drew was a 4, then we need a 6 or an 8. If the first card was a 6, we need a 4 or an 8, and so forth. There are 8/49 ways that the 2nd card could be a match.
And for the 3rd card, we need which ever card we didn't already get, and there will be 4/48 of those left.
So, the odds of getting 468 (or any other unpaired flop that doesn't contain a card in our hand) is
12/50 * 8/49 * 4/48 = 384 / 117600
There are 3 such hands you're looking for, so you multiply that by 3 and you get
1152 / 117600
and we can pretty much instantly see that it's "about" 1/100. It's actually pretty close to 1/102
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