PLO preflop suited stats

The following are some quick percentages of how often your starting hand will be suited and what type of suited in Omaha Hi. There is a problem though. Try as I might, there is a 10% discrepency. I can't figure out where it goes. It can't be due to rounding errors. But until that 10% is accounted for, the stats are useless as they can't be trusted.

I did these calculations originally to help me find out how often I should expect a double-suited hand preflop in PLO. Obviously you can't just play any double-suited hand, but this may help find the right balance of what to play once the problem is corrected.

Since there are 4 suits in the deck, and since each suit is equal in value, we'll call the suits 1, 2, 3, and 4 (for later equations).

The first type of suited hand is a nonsuited hand (1 heart, 1 diamond, 1 spade, and 1 club). You will get this (52/52)(39/51)(26/50)(13/49)= 10.55% of your hands.

The next type is when you have same-suit (all spades, for example). You'll get this (52/52)(12/51)(11/50)(10/49)=1.06%

The next type is when you have 3-same suit (ex. 3 spades, 1 heart). This is a little trickier, but not too bad. The cards can come in 4 orders: 1112, 1121, 1211, or 2111. Therefore, you get this 4*(52*39*12*11)/(52*51*50*49)=16.48% (Note: I wrote the math as one equation to save time and space, but it is still correct)

Next is the single suited (ex. 2 spades, 1 heart, 1 club). This can come in one of 5 ways: 1123, 1213, 1231, 2131, or 2311 (Note: 2311=3211, 2131=3121, and so forth). You get this 5*(52*39*26*12)/(52*51*50*49)=48.69%.

Lastly, the big daddy, the double suited (ex. 2 spades, 2 diamonds). This comes in 3 ways: 1122, 1212, or 1221. 3*(52*39*12*12)/(52*51*50*49)=13.48%

As you can see 10.55%+1.06%+16.48%+48.69%+13.48%=90.26%. A full 9.74% is missing. I've looked it over, but I can't find where it goes. If you understand where I went wrong then please share.

Here is one last bit of Omaha trivia/math: there are 52*51*50*49=6,497,400 starting hands in Omaha! That's huge compared to the 52*51=2652 starting hands of Texas Hold'em.

I've figured out what the problem was so now you can use these stats with confidence. The error was in the single suited type hand (ex. 2 spades, 1 heart, 1 club). There are in fact 6 types of ways to be dealt this hand: 1123, 1213, 1231, 2311, 2131, and 2113. That makes up the difference. It ends up being 6*(52*39*26*12)/(52*51*50*49)= 58.43%.

So: 10.55+1.06+16.48+58.43+13.48=100. Yay!

So, to review post 1 without the calculations (for the math challenged ):

-all different suits = 10.55% or 1 every 9.48 hands
-all the same suit = 1.06% or 1 every 94.34 hands
-3 of one suit = 16.48% or 1 every 6.07 hands
-single suited = 58.43% or 1 every 1.71 hands
-double suited = 13.48% or 1 every 7.42 hands

These are true for any starting hand in a 4 card game. I stated these for Omaha, but having thought about it, the stats are probably more applicable for Badugi because a primary concern of that game is suitedness. Anyway, no matter how you use these stats, enjoy!

(I did some calculations a while back for Razz starting hands so I may post those at a later date.)

Thanks, I've been looking for some good math stuff for plo. Do you have any links to suggest where I can find some pot odds info for plo?

Good stuff, always a lot harder to fine this info than with nlhe. The complexity of the numbers in Omaha are why I like it so much