PLO Tournament Strategy Part II: The Math

Gus Hansen

In Part I, we outlined three main factors for a re-steal: position, the opponent and your cards.

In Part II, we'll look more closely at factor three, your cards, plus the math of the matter.

Generally speaking, when you try to re-steal you play the situation more than your cards. If you've picked your spot well, your opponent will have a relatively modest hand and lay it down.

But if he happens to have a big hand, or makes a weak call, you want one of two things: the best hand, or a hand that, while not the best, is unlikely to be a large underdog.

To minimize the chances of getting your chips in as a big underdog, it's usually best to have a hand that's one of the following types:

1. Any four-suited (good) or double-suited (better) connected cards ten or lower

For example: 4-5-6-7ds (double-suited) is an ideal hand to try a re-steal with. Even if your opponent calls with an extremely strong hand such as A-A-T-9 or A-K-J-T, your hand will only be a slight underdog (47%-53%) against A-A-T-9. It will actually be a small favorite (51%-49%) against A-K-J-T.

Sammy Farha, PLO aficionado and still proponent of open shirt/chest hair advantage.

With the relatively rare exception of being up against a similar but slightly higher hand such as 6-7-8-9ds, there are very few hands you'd be in bad shape against with a hand such as 4-5-6-7ds. Even single-suited one-gappers, such as 5-7-8-9s, play reasonably well against a typical holding such as A-K-J-9 (45%-55%).

2. Suited, connected medium pocket pairs

These are surprisingly strong hands in Omaha. For example, 8-8-7-7s is a 51%-49% favorite against A-K-Q-Ts and only a 45%-55% underdog against a monster hand such as A-A-K-J.

3. Any four, suited (ideally) paint cards to the A-K or A-Q

These are good cards to re-steal with and are actually strong enough for a regular re-raise. If you're called by hands such as K-Q-J-9 or A-J-T-8 you'll generally be somewhere in the range of a 62-68% favorite.

Hands to Avoid: Medium-to-large pocket pairs with two rough cards, such as J-J-T-8, Q-Q-7-6, and Q-Q-J-8.

Those are all poor hands. You're unlikely to be very far ahead and could easily be way behind (you're a 25%-75% underdog against K-K-J-T, for example). Also, hands like K-Q-J-9 can be problematic as you may find you're up against something like A-K-Q-J.

The Math Behind the Move

Okay, now you're ready to attempt a re-steal. Let's suppose you have started the hand with $2,000 chips: what does the math look like?

In Pot-Limit Omaha at the $50/$100 blind level, a late position raiser would typically raise to $350. This allows you to re-raise to $1,200, leaving you with $800 chips.

If your opponent folds, which in my experience he will do at least 50% of the time, you gain $500 chips or roughly 25% of your stack.

When you're called, or more likely, re-raised all-in (note: if you do not get re-raised all-in and are first to act on the flop, you must push in the rest of your chips), you'll tend to win around 45% of the time.

There will be $4,150 chips in the pot, so your equity in the pot is approximately $1,870, or an expected loss of $130 chips. Therefore, on average, the re-steal shows a positive expectation of $185 chips (0.5 x$500 - 0.5x$130 = $185), or nearly 10% of your stack.

Bill Chen
Even the math guys like Bill Chen will tell you: It can do your head in.

Now imagine there is a limper and a late position raiser. This is an even better time to use the re-steal from the blind. Again, with blinds of $50/$100 and a limper, the late position raiser would likely raise to $450, rather than $350 (a pot-sized raise).

This would then let you re-raise to $1,600.

In this case if you get a fold (which you still will roughly 50% of the time), you pick up an uncontested $700 ($150 in the blinds, $100 from the limper, and $450 from the raiser). Note: the math if you get called is basically the same as above.

Notice you're able to put more pressure on the raiser in this scenario, as he's now forced to call $1,150 rather than the $850 in the previous example. This works out to a positive expectation of $306 chips, or roughly 15% of your stack.

Furthermore, if you think there's a higher than 50% chance your opponent will fold (as may well be the case on the bubble), this play is even more profitable.

Finally, if there's a late position raise and a call, you can try a squeeze play. Imagine the blinds are still at $50/$100 and a late position raiser raises to $350.

If the button calls the $350 and the action is to you in one of the blinds, you can re-raise to $1,550. The initial raiser is now caught in a squeeze play.

Generally speaking, the likelihood of the re-steal being successful is quite similar to the probability in the above example, and consequently so is the positive expectation.

Perhaps the next time you play an Omaha tournament, you'll give it a try. Good luck.

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Chris 2009-12-22 00:46:30

My apologies I misunderstood your question.
You are right, 4 suited cards is worse than two suited (and the other two preferably suited too of course).

Chris 2009-12-22 00:17:47

The reason 4 cards in a row is good, and you are not 'holding your own outs'. Is because you are not. You have a much higher chance of hitting the straight with for example 6789 than 45 89.
I don't know how to explain this but say for example you have 6789, you are much more likely to flop a straight or an open ended straight draw. The thing about omaha is your outs could actually be one of the cards you hold, but it doesnt need to be. The fact you hold 3 of the cards needed to make the straight, but you already have an open ended straight draw using only two of them. Means if you hit one of the two that give you the open ended straight draw, you can just sub in the other card and you have your straight.
For example you hold 6789 and the flop is 10 J 2. You have Q, 7, 8 and 9 as outs. You should not think of it as 'holding your outs' rather, giving you more outs.
having the remaining 3 9's as outs is better than having none of them as outs.
Sorry for the poor explanation.

Sean Lind 2009-06-24 23:10:00


you're correct in your thought process here; here's how it breaks down:

Ideally, you'd always want to be double suited (like you have in your example). If you're not double suited, it's second best to have two cards suited, after that any more of that suit you have in your hand are simply cannibalizing your own outs.

But, it's better to have four suited cards than no suited cards.

Also, AKQJ suited is definitely worth playing in PLO. It's not a hand to get into a raising war with, but it's strong enough to take a look at a flop.

Rray 2009-06-24 18:53:00

Thanks for the article.

Could someone kindly elucidate on the relative value of a double suited hand.

In the examples given of 4567d or 6789c, is it not better to be pushing with say 45c67d or 67h89c.

My thinking behind this has been that I'm holding my own outs. The same goes for AKQJc a hand I've often folded with the background though that I'm holding my own outs.

I'm new to Omaha so clarification would be appreciated. Thanks.

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