S
Sohmurr
Rock Star
Silver Level
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 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.