PLO Math...

Both Brackchips and I have been diving into PLO recently, I think partly due to some boredom with NLHE, partly due to the NLHE games getting worse by the day, and the PLO games still being very good. If you're a fish and you want to gamble, PLO is the game for you. Look how often you make a straight or a flush! Every frop you'll get at least a pair or something, how could you not stay in?

While it doesn't take a mastery of the game to pwn your average PLO game, I've been trying to do some more thinking about the game. Loyal spritpot readers might by now have become adept at the following types of NLHE problems:

You have AA, your opponent calls your pre-flop raise. The frop comes T63. How many combinations of 66 are possible? If your opponent calls with any two cards pre-flop, what are the odds he now has a set of sixes? What are the odds he has any of the three possible sets? What if he preflop calls with 30% of hands, and that 30% includes TT, 66, and 33?

Ok, that was a warmup. In NLHE it's not too difficult to work out those kinds of problems. In PLO it gets a little trickier since everybody gets four cards. But try the same problem:

You have AAJ9, your opponent calls your pre-flop raise. The frop comes T63. How many combinations of 66xx are possible? If your opponent calls with any four cards pre-flop, what are the odds he now has a set of sixes? What are the odds he flopped one or more sets? What if he calls preflop with 30% of hands, and that 30% includes all TTxx, 66xx, and 33xx?

Answers to come later...

-BRUECHIPS