Playing the Percentages in PLO: Dodging the nuts

This is a 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) Is 4betphobia justified?

You are happily on the grind in your regular 6max PLO game. Any downswing is in the distant past or at least you can’t see it around the corner. You are winning flips and your top set seems to actually be holding. A weak-tight opponent opens from UTG (100BB effective) with his 20% range and you look down at QJ85ds. You drag the bar and prepare to 3bet… wait. I haven’t told you what seat you are in; does it matter?

Before we go any further, click in the search box in your browser and type in how often as a percentage you think you will run into AAxx when you 3bet here MP v UTG. Don’t worry about calculating it (not to spoil the suspense, but I do that for you in the next paragraph) but get a figure down from your poker intuition.

In a 6max game, when you 3bet a 20% UTG opener from MP without an Ace in your hand, someone at the table will have AAxx 24% of the time. If you do it from the BB, your sole remaining opponent will only have AAxx 15% of the time. Since our opponent is going to have a +EV 4bet spot with his AA when we are 100BB deep or shallower in the majority of cases and since many hands we might like to 3bet cannot call a 4bet profitably our absolute position matters when we 3bet.

Peruse the table above to get an idea of the relative weight of the factors {remaining players, width of opening range, A blocker presence}. This chart is crucially important for PLO MTTs (or playing at a table with short stackers) since the light 3bet (or indeed any non-AA 3bet) that seems to pick up 1BB in EV with 30BB stacks could easily be negative EV once you take into account AA-frequency. In such a situation, unless your hand has awesome equity against AA (think double-suited low rundowns) then you should think twice about 3betting a tighter open from in position without an Ace in your hand.

2) When a set beats a straight

An aggressive opponent raises from MP with a 25% range and you call OTB. The flop comes down:

Q♠T♣9♠

Your opponent continuation bets near-pot and you decide to raise. Looking down at your cards would you prefer QQxx or the bare KJ (no redraw in either case)?

I prefer the QQ every time; here’s why:

If your opponent is willing to stick it in with {Add, QQ, KJ, TT} from his initial 25% range we are flipping (51% edge) with our KJ. Against the same range with QQ no redraw we are on an exact coin-flip. As is often the case in PLO, this situation is not a hand-issue but rather a range-issue. If we want to attack this board on a semi-bluff (some NFD variation) then we should have some value hands in our flop raising range. Since QQ and KJ give us virtually the same (null) equity edge against our opponent’s stack off range, it seems unlikely to matter which we choose if we just choose one of them.

However, it is of great benefit to our calling range to still have some very strong hands on bricks. On a blank (say 3♠) turn, KJ has 65% equity against the stack-off range described. If our opponent cannot find it in him to fold J8 against our line this becomes 70%. Conversely, QQ is still flipping against the flop stack-off range described and is actually a 45-55 dog if we now include J8. Our calling range is not going to have difficulty continuing on board pairs or flushing cards but without the made nuts in it we would have difficulty on bricks. Consequently, watch out for players who always shove the nut straight here, since they will have difficulty calling down 3 barrels when the turn-river brick off.