Texas Holdem is the iconic community card poker game and considered to be the most widely-played variant of poker.

Each deal has 4 betting rounds. First, each player is dealt two cards face down called the 'hole' or 'pocket' cards. This is followed by a round of betting. Most Hold'em games get the betting started with one or two 'blind bets' to the left of the dealer. These are forced bets which must be made before seeing one's cards. Play proceeds clockwise from the blinds, with each player free to fold, call the blind bet, or raise. Usually the blinds are 'live', meaning that they may raise themselves when the action gets back around to them.

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Once all bets have been made three cards are placed face up on the table for all to see (called 'the Flop') and use in order to improve their two 'hole' cards.

In this article, we'll explore a novel way to analyze PLO hands.

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The method we’ll use is a bit of a departure from standard PLO study; in fact, we’re going to start by doing some NLHE analysis. This can be useful because game trees in PLO are very large, and the structure of PLO ranges can be hard to visualize. By beginning with NLHE analysis, we can take a bird’s-eye view, and often find insights which generalize to other various hands and boards from either format.

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Example Hand

The PLO hand we'd like to analyze is a heads-up scenario. where the button raise/calls a 3-bet from the big blind, and the flop comes K♠️7♥️3♣️.

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NLHE Analysis

First, let’s take a look at what PioSOLVER thinks about this situation from a NLHE perspective. For our pre-flop ranges we'll use standard MonkerSolver ranges.

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In order to make the tendencies of various portions of our range easier to classify and visualize, we'll limit PioSOLVER's options to either a check or a 75% pot-sized continuation bet, for now.

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Figure 1 shows the PioSOLVER output for our K♠️7♥️3♣️ scenario. The first thing to notice is that PioSOLVER has the out-of-position player, who was the pre-flop 3-bettor, c-betting at a ~36% total frequency.

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A useful way to think about this total betting frequency is to think of it as a baseline frequency for a particular range. If a hand within that range is being bet much more often than this baseline, we can consider it to be betting at a high frequency, while a hand being bet much less than the baseline is one we can consider to be betting at a low frequency. A hand being bet at or around the baseline is being bet at an average frequency.

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Let's take a look at how some of our weakest equity value hands perform, since these are some of the more difficult hands to play. Specifically: weak top pairs (KT-K8, K6), and under-pairs to top pair (QQ-88).

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(Note that for the purposes of this lesson, we’ll only concern ourselves with the value portions of our range, and ignore our bluffing combos).

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PioSOLVER has these hands betting a wide range of frequencies, from ~1-43% of the time. There's a lot of spread there, but compared to the baseline frequency of 36%, we can think of these frequencies as tending low-to-average.

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If we look closer at the specific hands within this portion of our range, we can see an important pattern emerge: vulnerability seems to be driving betting frequencies as much as equity. As the pairs get weaker, the betting frequency rises dramatically - QQ is betting only 1% of the time, while 88 is betting ~43% of the time. This is because the lower pairs are vulnerable to many more potential over-cards on later streets; a hand like QQ isn't giving up as much by waiting.

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In other words, we don't always want to bet just because of our hand's winning chances; sometimes we want to bet to deny equity to parts of our opponent's range so that we win more often.

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Pro Analysis

For our PLO analysis, we'll use Run It Once's PLO Vision and choose the same flop of K♠️7♥️3♣️.

Run It Once Poker Training

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Figure 2 shows what PLO Vision has to say. Using PLO ranges on this flop, with a 50% pot-sized c-bet, the out-of-position player's baseline c-betting frequency is now ~67%.

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Again we want to look at some of our lowest equity value hands. With PLO ranges, these are going to be similar top pair and under-pair type hands, with uncoordinated side cards (AK22, QQxx, 88xx).

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Although betting patterns and sizes are different for PLO, if we examine how these hands are performing, we see a similar pattern to what we saw in our NLHE example. In this case, the spread of betting frequencies is ~49-88% betting frequency.

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This is a higher variation than in the NLHE, due to the complexities of how PLO ranges interact. But if we look closely at the specific hands within this group, and compare betting frequencies to the PLO Visions baseline frequency of 67%, we see again that the most vulnerable hands trend towards betting more often: QQxx is being bet at a ~52% frequency, while 88xx hands are being bet at an average of 64%. Similarly, a weak, uncoordinated top pair hand like AK22 is bet at a below-average frequency of about 57% frequency - but if the A were changed to a Q instead, to make the hand KQ22, the frequency jumps up to just about the baseline of 67%, due to the extra vulnerability.

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Nl Health

Things to Remember

In closing, here are some things to takeaway from today's lesson:

• Analyzing PLO from a NLHE perspective can make range tendencies easier to visualize.
  
• When using solvers, larger bet-sizings can help give definition to structures within a range.
• It's helpful to think about the betting frequency of a range as a range average or baseline.
• PLO betting frequencies are strongly equity-driven, but equity denial is still important.

Plo Preflop Ranges

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