My weekly 2-7 has been running since October and I've seen 3 chopped pots! I guess it's not as rare as I thought it'd be.

Home game?

3 is not a lot

I run it at a local club. Players really enjoy the game.

I imagine in triple draw 3 is not a lot but in Single Draw?! I was hoping some math savant would throw out some numbers! Lol!

I'm certainly not a math savant, but when Hero is dealt 75432, there are three cards of each of those ranks left.
3*3*3*3*3=243. That's the number of ways an opponent could also hold 75432. That's out of C(47,5) = 1533939 possible hands an opponent could have if Hero has 75432.

243/1533939=0.0001584 is the probability an opponent will also have been dealt 75432. That's small enough to multiply by the number of opponents to get the probability one of multiple opponents was also dealt it.

When you're dealt 75432 in a six handed game, the probability one of your six opponents will also be dealt 75432 is 0.0001584*6=0.0009504... about one time per 1052... call it about one time per thousand.

Is that what you wanted?

Buzz

I'm guessing you're using "the nuts" hand as an example?! After the draw I had 3 chopped pots in six months. I just thought that chopping a five card hand with a draw included after both show 108754 (example) was kinda rare. Your math pretty much proves it for me.

Yes. And that's a hand nobody would draw to.

I think both ending up with T8754 would be rarer than both ending up with the nuts. If both players were dealt that hand, they'd both have to decide not to draw to it.

Buzz

There is a draw though, so that has to increase the chances quite a bit?

If Hero is dealt 22347, discards a deuce, draws a five, then from Hero's perspective, there are 2*3*3*3*3 ways his opponent can also end up with the nut low. That's out of C(46,5) possibilities.

On the other hand, if Hero is dealt 2347K, discards the king, and draws a five, then from Hero's perspective, there are 3*3*3*3*3 ways his opponent can also end up with the nut low. That's out of C(46,5) possibilities.

Recall that when neither discarded, there were 3*3*3*3*3 ways his opponent can also have with the nut low, but that was out of C(47,5) possibilities.

So, yes, discarding changes the odds. And depending on the cards involved, from Hero's perspective, the odds can either be greater or less.

From the perspective of someone watching from the rail, someone who can only see the five cards in each of two hands at the showdown, when one player shows down any particular hand, say 75432, there are 3*3*3*3*3 ways his opponent can also have the same hand.

Odds are figured from some particular perspective, and depend on the cards that are seen from that perspective. (Depending on what one can see, the odds may differ).

Buzz

C(47,5)= 1533939
C(46,5)= 1370754