Playing the Percentages in PLO: Two equity surprises

This is the first post in an aperiodic series of short articles whose goal is to present some interesting numbers and their immediate implications. These posts are meant to provide a change of pace from our more cogent analyses and are left deliberately open-ended. The reader is encouraged to share any insights that he develops as a result in the comment box below.

1) KQJT is a poor 3bet hand against a tight range

So are QQJT and KKQT; what is the justification for this counter-intuitive claim?

Card removal.

In a vacuum, a player opening with a 15% range has Aces around 17% of the time. When we hold four cards ranked between T and K (let’s call them brodway)

1 our opponent will have Aces 25% of the time. Furthermore, when he does flat our 3bet he will have KK 15% of the time (21% when our hand contains 4 cards ranked T to Q) against which we are a 70-30 dog. Lastly, the “standard” continuation bet on A high boards will fare worse since his tight range will hold an Ace 60% of the time when it flats2 (assuming he 4bets his AA). The combination of frequently facing a 4-bet, lack of equity edge when called and the need to frequently fire 2+ barrels to move our opponent off of a strong range makes for common -EV spots. The numbers are against 3betting a competent TAG with these types of hands.

The good news is that A-high 4-broadway cards make for good hands to 3-bet against tight ranges. Card removal now means that our opponent will only have AA 15% of the time3. The exception to this is if there are weak stack-off -happy players behind whom we do not wish to force out of the pot (especially when we have a suited Ace).

2) Calling 4bets with mediocre Kings is really, really bad4

I still see tons of regulars do this so feel free to continue if you don’t like my numbers (but if you do carry on can you please stop flopping top set against me?). Assuming your opponent always has AA, a hand as pretty as KK97ss is losing 3BB per call even when his opponent’s hand is face up and always all-in. This number assumes you 3bet from the BT to 9BB facing an opponent who pot pre-flop and pot 4bet (you lose 12BB/hand on the overall sequence). By comparison 9843ss is a +1.3BB gain per call face-up. If you don’t think you can call the 4-bet profitably with 9843 then don’t do it with KK5!

I have at least another two equity surprises in the tank for next week, so do check back if you enjoyed this short PLO article. Any feedback on whether you prefer longer or shorter articles is welcome either on my contact page or below. Please subscribe in the sidebar to the right (if you haven’t already) and enjoy your day.

Show 5 footnotes

  1. This is not a typo, I wanted a term for broadway cards excluding the A.
  2. For reference without the 4 brodway cards this drops to 50%
  3. An Ace with three non-broadway cards beside it will only run into AA 11% of the time.
  4. This applies against ranges which you will treat as AA 100BB or shallower. It doesn’t matter if you think he 4-bets wider if in practice you play him post-flop as if he has AA. Many poor 4-bet calls with Kings get justified on this logical disconnection.
  5. This argument does not imply that 9843 is a better 3-bet than KK97, although it can be in a different context (deliberate teaser for future post).
By | 2017-04-10T13:23:27+00:00 May 23rd, 2012|


  1. D July 9, 2013 at 8:01 am - Reply

    Seeing as Ahi with the 3 non-broadway cards has so many things going for it, wouldn’t that make it a prime, more practical replacement in a 3betting range (versus 9843), since it doesn’t have any of the disadvantages of QQJT, and will likely be breakeven against a 4bet?

    • Phil Rocquemore July 9, 2013 at 8:48 am - Reply

      Hi D,

      Thanks for your comment. There are close to zero A-high hands that can call a 4-bet pre-flop 100BB deep until your opponent has a very wide 4-betting range. Especially in games where many players add AKK/AQQ/AKQJ-type hands to their 4-betting range. There are plenty of A high hands that can be 3bet/folded pre-flop. Just make sure you are balanced on K/Q high flops; this can be a challenge when 3-betting against a tight open.


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