PLO preflop suited stats

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Sohmurr

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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.
 
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Sohmurr

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Fixed!

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 :p ):

-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.)
 
slgalt

slgalt

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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?
 
Nickmond

Nickmond

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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
 
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