Flop A 5 6

Three players go all in - each player had 5 6 for a three way chop.

That got the table talking to see what is more rare, three players all having 5 6 and 5 6 coming out on the board, or a bad beat (quad 6's or better losing).

I am not a statistician so I have no way of knowing this, but it interests me. Can anyone chime in?

Was this a 1-2 or 1-3 game? How does everyone get all-in on that board? No one folds thinking A6 or A5 or a set is out there?

As for your real question, I have no idea. I'd have to think, when you put a qualifier like 6's or better in that bad beat scenario, three players all flopping the same hand is way more likely, but I'm not going to run the numbers.

One guy went all in preflop with very little (like 5 bucks).

When flop hit one one player went all in and the other called. It was 1/2.

It depends if you take into account the greater chance that players with unpaired cards are to fold preflop. The easiest solution is to assume players never fold. In that case, there are way more combinations of hands where three players all get the same two pair hand than combinations of hands where two players hit quads.

Have you ever played live poker ever?

+1

it doesn't have to be a 1/2 game, I've seen 3way all in's on the flop plenty of times in higher limits as well!

Welcome to live poker, Goud21

As for the odds, there is a formula and I think it might be something similar to this:

(6/52)*(5/51)*(4/50)*(3/49)*(2/48)*(1/47) = ?

If you play at a 10 handed table where no one ever folds then Quad 6s will lose a hand about every 140K hands according to a chart I found online. This obviously is not real life ... people fold.

At a 10 handed table where UTG, UTG+1 and UTG+2 get the 'XY' a quick calculation puts this probability at over 23 million hands between events with the remaining X & Y hitting the board also. The best case is when the first 2 players are dealt different cards.

This can be cut down drastically if you have the B, SB and BB receiving the XY combos @ about every 11.3 million hands AND you factor nothing in there for the cards 'not' being dealt to anyone else in between.

If you go the 'combo' route (9/1225 x 4/1128) it figures that 3 players will get the same hole cards (XY, not suited) about every 38 thousand hands dealt and then it's a less than 1% (2/32 x 1/30) expectation that the other 2 cards will hit the Flop. This comes out to about every 18.5 million hands .. which is between my 23m and 11m from above, so I must be onto something!

Obviously quite a large difference between the two but that should be expected since you are not 'picking' the hand that beats Quad 6s ... only that it 'does' get beat by something. And there are more 'somethings' to choose from rather than specific cards ending up in certain seats and the board.

I never know if I'm using the right math .. but it's fun to try. GL

Thanks!

That's pretty much all I've played. I can promise, depending upon stack sizes, I'm almost never going to be the third one getting all my money in with bottom 2 in this scenario.

Of course, if the other two players only have $15 left it seems inevitable. But, if everyone had 50+ BB, I'm probably folding bottom two facing two all-ins. I'd love to play with players who would risk their whole stack with bottom two in that scenario.