Its impact on post-flop hand valuations
This is an edited excerpt from Jeff’s book, Advanced Pot-Limit Omaha: Small Ball and Short-Handed Play.

One of the unique features of Omaha that hasn’t been discussed much in poker literature thus far is the pivot card. The pivot card is the boardcard that fills a gap in your hand to give you multiple backdoor-wrap possibilities. For example, if you hold Q-J-9-8 and the flop comes 10-3-2, you hit the pivot card, which in this case is the 10. Now, a 7, 8, 9, jack, queen, or king can come on the turn to give you either a 13-card or 17-card wrap.

While the pivot card hasn’t been discussed much (probably due in part to the stigma associated with backdoor draws), it actually has a fairly material impact on post-flop hand valuations at times.

One thing to be noted is that you have to have a hand with a 13-card wrap possibility in it, with or without a gap. This includes hands such as J-10-9-X, J-10-8-X, or J-9-8-X, or a four-card rundown with or without a single gap. That said, there are two basic applications of the pivot card:

1. When we are thinking about shoving all in while playing in low SPR [stack-to-pot ratio] situations
2. As part of a float

All-In Confrontations
I was playing in a $1-$2 blinds, $5 bring-in game in St. Louis when the following hand occurred. I had just bought in for the $500 maximum, and was dealt the 9Club Suit 8Club Suit 7Spade Suit 5Diamond Suit in early position. I thought I’d mix things up, and opened with a raise to $15. It was folded to my buddy Al, who reraised to $50. Everybody folded back to me, and I called.

The flop came AClub Suit 6Spade Suit 2Club Suit, giving me a flush draw; plus, I hit my pivot card to give me some backdoor-wrap possibilities. I checked to Al, who bet $100. It was now my turn to act, and Al had me covered.

At this point, I thought, “Well, maybe Al doesn’t have aces here, in which case I might be able to make him fold if I raise. He probably doesn’t have a bigger flush draw (unless he has an ace to go with it); otherwise, he probably (but not necessarily) would have checked behind. And even if I am wrong, I hit my pivot card, which has to be worth a couple of outs.”

So, I thought, “Let’s try it.” I raised to $400, and Al called instantly with a dry set of aces. I made the flush, and won.

Now, I must be honest: I actually kind of knew that Al had the aces, because I had played a lot of PLO [pot-limit Omaha] with him, and I don’t remember him ever three-betting me without them. I just figured that I’d shove it in and see if the play worked, and then figure out how close the play was later. And against Al’s hand, I was actually only about a 37 percent to 63 percent dog, so it was a relatively small mistake to put in about 44 percent of the money. And if there is any chance that Al doesn’t have aces and will fold to a raise, I think check-raising here figures to be a pretty close play in aggregate.

As it turns out, the pivot card on this flop is actually worth about three outs; according to Mike Cappelletti in Best of Cappelletti on Omaha, I will make a straight 13.5 percent of the time in this situation. This compares to a four-out gutshot making the straight 17.2 percent of the time.

That said, the implication here is that the value of the pivot card should be accounted for in low SPR situations. In another example, note that on an A-7-3 flop, a 9-8-6-5 for a gutshot plus a backdoor wrap is only a 31.2 percent to 68.8 percent dog against A-K-Q-J, ignoring suits. At a little worse than 2-1 against, you probably shouldn’t fold this hand in an ultra-low SPR situation, whereas you might be inclined to fold if you counted only the gutshot as your outs.

What follows is a table that summarizes the completion percentages of various rundowns when their respective pivot cards hit the flop. The completion percentages are taken from Cappelletti’s Best of Cappelletti on Omaha (Cappelletti refers to it as an “eye-card holding” when you hit the pivot card). It is worth noting that a four-card rundown has a higher completion rate than a three-card rundown when the pivot cards hits the flop.

The Pivot Card: Straight Completion Percentages
Hand Type Flop Completion *
Q-J-9-8 Rundown With Middle Gap 10-3-2 14.3
Q-J-10-8 Rundown With Bottom Gap 9-3-2 13.5%
Q-J-10-9 Four-Card Rundown 8-3-2 9.9%
J-10-8-X Three-Card Rundown With Gap 9-3-2 8.9%
J-10-9-X Three-Card Rundown 8-3-2 8.1%
*Source: Best of Cappelletti on Omaha by Mike Cappelletti

The Float
The other practical application of the pivot card is in regard to the float, as the backdoor-wrap possibilities when you hit a pivot card add real draw value to the float. Let’s say that you are heads up with position after the flop. You hold Q-J-10-8, the flop comes 9-3-2, and your opponent bets into you. Now, in addition to whatever float equity you have (based on the probability that your opponent will check and fold to a bet on the turn), you also have four sevens, three eights, three tens, three jacks, three queens, and maybe even four kings — 20 cards total, or nearly half the deck — that will give you enough draws to call if your opponent bets again on the turn.

And that’s just if you flop the pivot card; if you also flop a gutshot or a flush draw, hitting the pivot card adds considerable value to your draw. Moreover, you also will have some implied odds if you hit your backdoor draw, as it will be disguised.

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