Quad Dangt

[wiseheart]

Okay, if you read some of my posts last week
you may have noticed I kept running into backdoor
quads (that is 3 of the same rank on the board by
the river)

This week, variance has in some way boomeranged
back to me and I have picked up backdoor quads
numerous times, most notably in a Omaha 8 tourney
where in the course of the first 15 hands I got
backdoor Quad Aces twice. Though, that was with
two aces in my hand. Now, Ive done some counting
and tried to pinpoint how many times quads are
coming up whether they are 3 on a board and 1 in
a hand or 2 on board , 2 in hand and they seem to
come up more times than chance should allow. I would
figure if youve seen eight cards, 1 left to go, 1
to make quads, thats 43 to 1. Now, I also tried a
hand on two dimes of AA23 vs. A579 board = A955
and it showed the AA winning hi 39 to 1.

The point is, how many should quads come up? Has
someone run a simulation on what the realistic
expectation of seeing quads is, both 2 in hand,
and 3 on board? How does your results compare to 2dimes?

Thanks.

[Buzz]

[ QUOTE ]
Now, I also tried a hand on two dimes of AA23 vs. A579 board = A955
and it showed the AA winning hi 39 to 1.

[/ QUOTE ]

Wiseheart - The above doesn't make sense to me. (But no matter, unless I'm missing something).

[ QUOTE ]
The point is, how many should quads come up?

[/ QUOTE ]

Depends on what you mean. Do you mean getting quads yourself or anybody getting quads. (I'll answer both below).

[ QUOTE ]
Has someone run a simulation on what the realistic expectation of seeing quads is, both 2 in hand, and 3 on board?

[/ QUOTE ]

Sort of.

When the final board is 6c9c9dTdJc and Hero holds Ac2cJhJd, in a nine handed game (eight opponents), Hero loses 512 times out of 10000. Since Hero could only lose to quads, an opponent in a non-folding simulation must have quads 512 times out of 10000, or about five per cent of the time. The number would be a bit lower in a real game, because a real opponent might fold a hand that would have ended up as quads.

In other words, I ran 10000 trials of nine-handed simulations with the deck stacked to make the final board 6c9c9dTdJc each time, one of the hands Ac2cJhJd each time, and with the other eight hands dealt random cards each time. The only way Ac2cJhJd could lose would be to quad jacks held by an opponent. Ac2cJhJd lost five per cent of the time.

The above is how often (maximum expected) you'll run into quads when you have a full house. It's simulation data. I vaguely remember also calculating it at some time or other and also coming up with a result of about five per cent (or about one time out of twenty) with eight opponents.

As to how much you'll make quads yourself, when you have four different ranks, as with A234, if you stick it out to the end, that's fairly easy to calculate. You figure to end up with quads about one deal out of 432. That’s about the same as 23 quads per 10000 deals. And of course that's about what it turns out to average in simulations.

When you have one pair, you’ll end up with quads about 98 times per 10000 deals. Most of those are quads made with the pair in your hand and a pair on the board, but some of them are with one of the (two) unpaired cards in your hand. That’s purely from simulation data. I suppose we could also calculate it, if it matters. But about once every hundred deals is good enough for me.

When you have two pairs, you figure to end up with quads about 177 times per 10000 deals. Those are all quads made with the pair in your hand and a pair on the board. My simulated results are 173 times per 10000 deals. Close enough. (177 is a better answer than 173). Think of it as almost twice every hundred deals.

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How does your results compare to 2dimes?

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I don't see any way to run the needed simulations on twodimes.net because I don't know how to stiuplate random cards for opponents on two dimes net. It's fairly easy to run these sorts of simulations using Wilson's software (and that's the source of the simulation data indicated in this post).

Buzz

[wiseheart]

Thanks again for the info buzz, I
was seeing quads as miracles, but
they are much more likely than I
thought, Ill have to look into that
software.