6 card plo : whats the maths

[77dave]

interesting hand came up on the flop of a DC game from 6 card plo

the 2 hands are

hand 1:

hands 2: 

They see a flop of :   

What equity does each player have on the flop and how do we work it out

[Rupert]

so there's 37 possible turns and 36 possible rivers 37*36=1332 different outcomes, see who wins on each possible outcome and total it then divide by 1332.

[Honeybadger]

You can do a simulation at propokertools. It only does 5 card PLO so I just made the Qs and Kh dead cards instead. It won't change the results too much. The wrap plus FD has almost 65% equity.

5-Card Omaha Hi Simulation ?
666 trials (Exhaustive)
board: Ts 7s 5d
dead cards: Qs Kh
Hand   Equity   Wins   Ties
3s 4s 6d 8c 9s   64.86%   432   0
Ac Ad Th 7h 5c   35.14%   234   0

[Rupert]

oh yeah I guess it's only 666 outcomes because the order doesn't matter

[SuuPRlim]

without even looking at the maths its IMPOSSIBLE for the wrap and FD to have less than 60%, would be higher still if they wrap had some SF outs cos as it stand they have zero kill outs so board pairing turn has it with 0%.

This should never be a flop all in though because hand 2) should never be in the pot pre-flop in a month of sundays and unless he has like 2/3 of a pot bet back this looks like a pretty easy flop c/f for hand 1)

[SuuPRlim]

obv got the last two mixed up, hand 1) should never be in the pot p/f and hand 2) should c/f the flop.

it is early

[Honeybadger]

Yeah completely agree with Lil'Dave: Hand 1 is a terrible hand and I would not put a penny into the pot with it preflop. Even on a miracle flop like this one it can still sometimes be in all sorts of trouble if a big pot gets played since even such a 'huge draw' is so easily dominated by the NFD and the upper wrap (J98). This is the reason you don't play these sort of complete junk hands at 6 card PLO - because even flopping a miracle is not guaranteed to be a good thing!

[77dave]

Not going to argue about the way the hands have been played, but thats why we make money playing mixed games as people just cant fold as they have 6 cards.

ok so if we know now that their are 666 possible combos for turn and river for the wrap f/d to be a 66% fav it must need circa 444 good combos. Apart from counting them 1 by 1 or running the numbers on a simulator which their isnt for 6 card games how do we know its 66%