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View Full Version : probability of a bad beat hand

2ndGoat
07-17-2003, 12:27 AM
Ok here's one I've worked on for about... 5 minutes, and figured this might go faster in parallel with the rest of you.

A poker site's hold'em bad beat jackpot has the following requirements:
1) both the winning hand and losing hand must use both hole cards.
2) quads or better must be beaten.

at a ten-handed table where everyone plays to the river, how often does this come up?
while we're at it, how about a 5-handed table, or a heads-up one?

2ndGoat

asdf1234
07-17-2003, 03:13 AM
How often does this come up? Not too damn often. If two people have pocket pairs, there are precisely 44 boards that will give quads over quads out of a possible 1712304 boards. That's 35672:1 against. Add to that the fact that at least two pocket pairs need to be dealt with all their cards remaining live and you've got something that is incredibly rare. Not to mention that sometimes someone is left with an underpair on the flop and mucks it only to see the board come with their running pair (I've actually done this twice in the last two weeks).

If one person has a pocket pair and the other doesn't, the chances are very minute, slightly less than 2000000:1 against and maybe worse because you said both cards must play. 88 vs. 62 on 88666 wouldn't count, but would sting an awful lot.

So, in conclusion, don't count on it.

Copernicus
07-17-2003, 01:46 PM
You left out quads beaten by SF and SF beaten by higher SF..which in hold em may be more common than quads getting beaten at all, with a 3 straight flush on the board filled at both ends buy pockets.

Under any circumstances, I wouldnt be playing there for the bad beat pot!

asdf1234
07-17-2003, 11:39 PM
Oops. Yeah, I did leave that out didn't I? Well, something like 77 vs. 54s with the 77 not containing the same suit as the 54, given these two holdings, you have the terrific odds of 19457:1. 65s vs. 77 is a little better with 12971:1 against, given that two people have these hands.

Straight flush over straight flush is remarkably common compared to these. Ex. If somebody holds 45s and somebody else holds T9s of the same suit, a board of 678s gives two straight flushes and comes up about .057% of the time, or relatively good odds of 1728.6:1 against (again, given that people have these exact holdings before the flop).

In any case, the odds are pretty astronomical. Getting preflop holdings that have potential isn't that easy, then you have to get the correct board, while keeping the potential hands in for the whole way. I've never been beaten in a hand that would qualify for this type of jackpot (I've seen it a couple of times, but no jackpot was available).