Ibeatyouraces
Joined: Jan 12, 2010
• Posts: 11933
May 19th, 2015 at 8:35:40 AM permalink
Here's a tough Omaha beat. And fittingly against Phil Hellmuth.

https://youtu.be/KHqLGXu63jU
DUHHIIIIIIIII HEARD THAT!
BTLWI
Joined: Nov 6, 2013
• Posts: 393
May 19th, 2015 at 7:32:21 PM permalink
If you both hold a pair and don't block each others cards then it's 1.2%

PLAYER_1 AA47
PLAYER_2 JJ23
800000 trials (randomized)

How often do(es)( PLAYER_1 flop hand category is set AND PLAYER_2 flop hand category is set)
1.2085%
andysif
Joined: Aug 8, 2011
• Posts: 430
May 19th, 2015 at 7:36:57 PM permalink
Quote: ThatDonGuy

("Doesn't that include times when either or both of you have a full house?" Not from the flop, as all three cards are different, so in order to have a full house, you would need to use three cards from your hand, which is not allowed in Omaha.)
Of course, this assumes heads-up; the more players at the table, the more likely it is that somebody besides you is dealt a pair.

As usual, (A)C(B) = ACB = the number of combinations of A things taken B at a time.

There are (52)C(4) = 270,725 possible Player 1 hands.
If the hand is a pair (and not two pair or 3/4OAK), there are 13 possible values (e.g. Aces) for the pair, 6 possible sets of suits (e.g. Ah & As) for the pair, 48 possible cards for the first single, and 44 possible cards for the second single, but divide that by 2 as, e.g., it counts both (2s, 3h) and (3h, 2s); there are 82,368 4-card hands that include one pair.

Ignore suits, and assume the hand is AA23. (Also ignore the fact that your pair of aces is going to be higher than the other player's pair. We'll take that into account later.)
The possible Player 2 hands are:

4456 (none of your cards match any of his)
There are 10 possible values for the rank of his pair (4-K), and 6 pairs of suits for each rank
For each of the 60 pairs, there are 36 possible cards for the first single, and 32 for the second, but again divide by 2 as you are counting, e.g., both (5s, 6h) and (6h, 5s).
The flop contains one of the 2 remaining cards to give you a set, and one of the 2 remaining cards to give him a set.
The third card can be:
(a) one of the 28 cards with a rank not in either of your hands;
(b) one of the 12 cards (three 2s, three 3s, three 5s, and three 6s) with a rank in one of your hands.
There are 10 x 6 x (36 x 32 / 2) x 2 x 2 x (28 + 12) = 5,529,600 different hand/flop combinations.

4425 (one of your singles matches one of his):
10 x 6 x 2 (the value of the matching single - in this case, 2 or 3) x 3 (the number of remaining cards of that value) x 36 (the number of cards that can be the fourth card in this hand) x 2 x 2 x (8 x 4 (cards not matching either hand) + 1 x 2 (cards matching the single in both hands) + 2 x 3 (cards matching the single in one hand)) = 2,073,600

4423 (both of your singles match both of his):
10 x 6 x 3 (remaining cards of the lower single) x 3 (remaining cards of the higher single) x 2 x 2 x (9 x 4 + 2 x 2) = 86,400

44A5 (one of his singles matches your pair; the other is not in your hand)
10 x 6 x 2 (remaining cards of your pair) x 36 (cards not in your hand or his pair) x 2 x 1 (there's only one card left in the deck that can give you a set) x (8 x 4 + 3 x 3) = 354,240

44A2 (one of his singles matches your pair; the other matches one of your singles)
10 x 6 x 2 (remaining cards of your pair) x 6 (remaining cards in either of your singles) x 2 x 1 x (9 x 4 + 1 x 2 + 1 x 3) = 59,040

2245 (his pair matches one of your singles; the singles are not in your hand)
2 (possible values for the pair - in this case, 2 and 3) x 3 (number of pairs of that value still in the deck) x (40 x 36 / 2) (number of sets of 2 different cards that don't match any your hand or his pair) x 2 (number of cards that make your set) x 1 (number that make his) x (8 x 4 + 3 x 3) = 354,240

2234 (his pair matches one of your singles, and one of his singles matches the other one)
2 x 3 x 3 (number of cards that can match the other single) x 40 (number that don't match anything) x 2 x 1 x (9 x 4 + 1 x 3 + 1 x 2) = 59,040

22A4 (his pair matches one of your singles; one of his singles matches your pair, and the other does not match anything)
2 x 3 x 2 (number of cards that match your pair) x 40 (number of cards that don't match anything) x 1 x 1 (there is only one card of each pair still in the deck) x (9 x 4 + 2 x 3) = 20,160

22A3 (his pair matches one of your singles; one of his singles matches your pair, and the other matches your other single)
2 x 3 x 2 x 3 (number of cards that match your other single) x (10 x 4 + 1 x 2) = 1512

The total number of second hand/flop combinations where both sets are made = 8,537,832
There are (48)C(4) x (44)C(3) = 2,577,017,520 second hand/flop combinations

Now, remember what I said about your pair always being higher? Every deal can be divided into pairs of two, where the flops are the same but the hands are switched; in each case, in one hand, your pair is higher, and in the other, his is. We are only interested in hands where his is higher, so divide the total by two.

The probability of this happening = 1/2 x 82,368 / 270,725 x 8,537,832 / 2,577,017,520 = 1 / 1984.1276

thank you very much. thats one hell of a job. it will take me some time to go over it.
andysif
Joined: Aug 8, 2011
• Posts: 430
May 19th, 2015 at 8:30:09 PM permalink
Quote: BTLWI

If you both hold a pair and don't block each others cards then it's 1.2%

PLAYER_1 AA47
PLAYER_2 JJ23
800000 trials (randomized)

How often do(es)( PLAYER_1 flop hand category is set AND PLAYER_2 flop hand category is set)
1.2085%

thanks. is this some program that you write yourself or is it available online
BTLWI
Joined: Nov 6, 2013
• Posts: 393
May 22nd, 2015 at 11:31:27 AM permalink
It's from Odds Oracle which costs about \$90 from www.propokertools.com That website has a Simulator tab which allows you to run hand vs. hand matchups for all forms of poker but to do english like queries you need to download Odds Oracle. I think it has a 7-day free trial. Pretty high learning curve for all of it's capabilities but I've had it for 2 years now and am fairly proficient.
Romes
Joined: Jul 22, 2014
• Posts: 5303
May 28th, 2015 at 8:32:42 AM permalink
Quote: andysif

true. LOL

thats why i want to know the odds of that happening.

Board is dry, not likely flush or straight draw. Only thing that could beat me is another set. How likely is that?

No math required... When I've taught a couple different people how to play Omaha, I give them the golden rule: If it's possible, someone probably has it.
Playing it correctly means you've already won.
ThatDonGuy
Joined: Jun 22, 2011
• Posts: 3560
May 28th, 2015 at 9:29:51 AM permalink
Quote: andysif

thanks. is this some program that you write yourself or is it available online

Actually, you don't need to simulate it under those conditions; it can be calculated.

BTLWI assumes that both players have different pairs, none of the cards in either player's hand are in the other's, and is calculating the probability that the flop will not have two cards from either pair but the third card can be anything, including a card that pairs another card in either player's hand. (My number (1 / 1984) is the probability without already knowing that both players have pairs, and taking the possibility of "overlap" of the hole cards into account.)

In this case, of the 44 cards still in the deck, 2 are Aces, 2 are Jacks, and 40 are others, so there are 2 x 2 x 40 = 160 possible flops that make both sets, out of a total of (44)C(3) = 13,244 flops, so the probability = 160 / 13,244 = about 1.2081%
beachbumbabs
Joined: May 21, 2013
• Posts: 12574
May 28th, 2015 at 9:34:36 AM permalink
Quote: Romes

No math required... When I've taught a couple different people how to play Omaha, I give them the golden rule: If it's possible, someone probably has it.

That is so, so true, Romes. I kept getting beat up on Omaha 8 (online) until I realized that my 4OAK's were always going to get rivered by a SF, and the FH I folded would have beaten the 2pair that won, but the FH I shoved on was going to lose. Etc. ad nauseum. Frustrating game. I still like it, but geez.... and if you didn't have a perfect low, it was deadly to stay. Very counter-intuitive, at least for me.
"Man Babes" #AxelFabulous
Romes
Joined: Jul 22, 2014