[Buzz]

Manku - Interesting. (Wacky too).

Roughly half the time the final five card board on the river will have a pair (or two pairs or trips or a full house - but most of the almost half is simply one pair). When the board is paired, you want to either have quads or an overboat (pair in your hand matching a board card higher than the board pair).

Thus this is a game where you want your starting hand to have some big pairs.

But if the board is paired half the time, it's also unpaired half the time. It's possible trips will be the nuts on the river, but trips is relatively rare.

When the board is unpaired, there's a fair chance a flush will be possible.

I'm going to ignore straight flushes.

4*C(13,5)+4*C(13,4)(39-12)+4*C(13,3)(39)(36)/2 = 885456 (that's the total number of five card boards than enable a flush) <font color="green">Wrong. See edit.</font>

That's out of 52*48*44*40*36/120 = 1317888 possible non-paired boards.

Then 885456/1317888 = 0.671875 <font color="green">Wrong. See edit.</font>


Wow! Seems too high. Two thirds of the time, when the board has no pair, there are either 3, 4, or 5 cards of the same suit on the board? Whatever. At least when the board is not paired, it is flushed a good deal of the time. Two thirds though? Intuitively it seems too high. Whatever. Maybe someone who knows how to do the correct math will either correct me or affirm the result I got. (But I've checked it over a few times and that's what I keep getting). <font color="green">It is too high. See edit.</font>


If true, roughly five times out of six, the five card board will either have a pair (enabling quads or a full house) or the five card board will enable a flush (or straight flush. Could also be a straight flush possible if the board is paired). <font color="green">Wrong. See edit.</font>


So after high pairs, I think suited aces rule.

That's what I'd look for in starting hands, high pairs (for quads or overboats) and suited aces (for flushes).

That's very crudely figured. I left out consideration of three of a kind on the board and some other stuff that's relatively uncommon.

This thread probably belongs in the other games forum, but I'll leave it here where it will gradually fade into the archives. <font color="green">Wrong. See edit.</font>


Buzz

edit:
Found my mistake! (I divided the last term by 2 instead of 12).
545688 is the number of unpaired five card boards that enable a flush.

545688/1317888 = 0.4140625

That seems more reasonable. Roughly 2 out of every 5 unpaired boards enable a flush.

5/10 boards have pairs.
2/10 boards are unpaired and enable flushes.
3/10 boards are unpaired and don’t enable flushes.

Doesn't change my conclusions about what to want in a starting hand:
Look for starting hands with high pairs (for quads or overboats) and with suited aces (for flushes). High cards, even if unpaired are better than low cards in this game. Avoid small pairs, lest you make under-boats.

I agree with Iggy that threads about 14 card (or whatever) Omaha-high belong in this forum.

With 14 cards, it's hard to imagine a hand not being "coordinated" to some extent.

Buzz