6 card hi lo - odds pls!

[jipster]

could someone work out the odds for this coup please.... and explain roughly how one would calculate it (its the split that gets me!)

player A holding 6 8 10 J Q A
player B Holding 2 2 3 3 4 5

Flop 882

The reason i ask is i was player A, and very luckily scooped.... i called B's reraise without really thinking about the hand properly...

thanks

[bigpooch]

I suppose you are playing "6-card Omaha high-low" with an
eight qualifier for low. There are 15 seen cards or only
37 unseen cards and altogether C(37,2)=666 combinations of
turn and river cards (where it doesn't matter which card
shows up first).

If you make quads, you can only scoop if there is no low
(since your A6 won't beat any 34/35/45 for low) and there
are (2*4)+(3*3)+1=18 cards that don't give a low (four for
each of the nine's and king's, three for each of the other
honour cards, and the case deuce) so there are only 18
combinations of scooping with quads.

You can also make a boat by running tens/jacks/queens (but
not AA/66 as that would give low) for another 3*3 = 9
combinations. You also make a boat by hitting two of the
T/J/Q on another C(3,2)*3*3=27 combinations and by hitting
only a T/J/Q and then a 9/K on another 3*3*2*4 = 72
combinations. Altogether, you make a higher boat on 108
combinations without allowing a low to get there.

You scoop on 18+108=126 out of 666 combinations so you only
scoop with probability 126/666 = 7/37 or about 18.9189189%
of the time.

[jipster]

thanks bigpooch... can u also help me to work out the odds of a split? and my opponent scooping pls?