Omaha Hi-Lo - Drawing to Half the Pot

Omaha Hi-Lo: Drawing to Half the Pot

In my Introduction to Split Pot Games and Omaha Hi-Lo Starting Hand Guide, I really try to emphasize the importance of choosing hands that have the potential to win the entire pot, not just half. In split pot games, pots are often quite large, because having a lo winner as well as a hi means more playable hands for everyone. As a result of these big pots, it often seems correct to play long shot draws. If you’re playing Hold’em and there’s 15 big bets in the pot, it’s correct to call a bet with a four or even three-out hand. However, in Omaha Hi-Lo, you will often need six outs in the same situation, because half of the pot will go to the lo winner. I say often because sometimes there is no lo, in which case the odds are the same as if it were Hold’em. The following example illustrates the adjustments you have to make in your pot odds and expected value (EV) calculations when you are only (or potentially only) drawing to half the pot.

Example

You’re playing a $5/$10 Omaha Hi-Lo game in an online poker room and you flop the nut flush draw. You call a small bet and miss on the turn. There’s another round of betting and you’re faced with a $10 bet. There is $50 in the pot. The flop was 742, so you can be sure that someone already has a lo. Ignore the possibility of an opponent hitting a full house on a card that makes your flush. Should you call?

If you call, your EV = (Potential winnings)(Probability of hitting your flush) + (Size of bet)(Probability of missing your flush)
 
We’ll go through it term by term. Your potential winnings in most EV calculations are simply the size of the pot (at the end of the hand). However, since there’s a lo, the potential winnings are only half the final pot size. There’s $50 in the pot now, and we’ll assume $10 more on the river (this is for simplification, you should actually factor in your additional bet and however many opponents you expect to call) if you hit, for a final pot size of $60. Half of that is $30. Your probability of hitting is based on your number of outs, 9 when you’re on a flush draw. 9 out of the 46 remaining cards help you, so your probability of winning is 9/46. The bet size is $10 and your chance of missing is 37/46. So,

EV = (30)(9/46) – 10 (37/46)
      = -2.17

That means you lose an average of $2.17 when you call, so you should fold. If you were getting 6:1 on your money instead of 3:1, as would be the case if there was no lo, it would be an easy call, your EV would be +$3.69.

What if there were only two lo cards on the board? Let’s imagine that 4 of our 9 flush would make someone a lo, but 5 of them would give you the entire pot. In that case,

EV = (Final pot size/2)(4/46)+(Final pot size)(5/46)-(Bet Size)(37/46)
      = (30)(4/46)+(60)(5/46)-(10)(37/46)
      = 1.09 or $1.09

A chance of winning the whole pot radically reverses our EV, and makes a fold a call.