Short Deck Poker Math 102: Pocket Pairs as Straight Blockers

Short Deck Poker is a game which revolves around straights. With 36% of all boards offering the possibility of at least one straight on the flop, and 72% of all boards offering that same possibility by the turn, straights are a consistent presence in Triton Holdem. By way of comparison, in the Full Deck games of No Limit Holdem, 4 Card PLO, and 5 Card PLO, only 19% of flops offer the possibility of a straight, and 48% of boards permit a straight by the turn.

In fact, 95% of boards permit a straight if the board has not paired by the turn in the Short Deck game! That number overwhelms the 61% frequency in the Full Deck cases. The only possible unpaired boards that don’t contain a straight by the turn are those headed by exactly KQ, KJ or QJ.

In contrast with PLO, where a player must use both hole cards in order to make a hand, the Short Deck Poker rules follow those in No Limit which permit a player to use any or none of his hole cards to make a hand. As a consequence, 3-connector boards such as T♠9♣7♥A♠ assume a large significance in play since the pivot 8-rank offers an open-ended straight draw in addition to whatever flush draw or pairing cards are already present in a player’s holding.

It is at this juncture that I can give some hope to my beleaguered PLO readers, since playing straight blockers aggressively is something that they are very familiar with! They will be pleased to learn that the pocket pairs which block the made straights on this flop are even more powerful than they are in PLO, since they offer the additional possibility of drawing against the non-straight made hands in our opponent’s range.

This makes the accurate play of blocker pairs on boards that contain made straights an essential part of a strong Short Deck Poker Strategy.

If you hold the 8♠8♣ blockers here facing a completely random hand, then you cut the possibility of him holding a straight in half compared with when you hold, say K♠K♣. The absolute frequency that he will hold a straight on this flop drops from 7.3% to 3.6%. In practice on such board textures one must carefully consider the number of combinations of the actual straights available to each player. Would your opponent be playing all 16 combos of 86, only the 4 suited combinations, or none of them? What about the J8 combinations? Remember…

The context in which the hand is played will have a profound influence on the relevance of the blockers in practical play.

Before we get stuck into an example I’m going to take a moment to define labels for the seat positions in a game of Short Deck Poker. You may have watched some Triton Holdem videos on YouTube and seen references to UTG/CO/HJ but I’m not going to use those familiar terms as seat labels because they are intrinsically misleading.

The essential difference between ante structure games and blind structure games is that in an ante structure game no raise first-in can ever lead to you playing post-flop in position. This means that any reference to a position other than the button is going to lead you to make miscalibrated associations with the value of that position post-flop.

Instead, I’m going to coin an entirely new (and unashamedly formal) set of labels which proceed logically from the structure of the game. We retain the ‘Button’ label, and then work back from seats #5 to seat #1, as shown in the diagram below:

I have chosen the labels #1-#5 because Short Deck Poker games are usually spread 6-handed. If you are playing at a 5-handed table you simply drop the #1 seat; this approach ensures consistency when we are comparing ranges, a ‘#4 overlimping range’ is now a meaningful class for a pre-flop range. In case you are wondering what happens in those rare situations where the game is spread more than 6-handed, we simply continue to subtract one number per seat: #0, #-1, #-2 etc.

I doubt that I will need to make many references to Seat #-3 in my articles but, if I do, you will know what it means. Now on with our example!

A player opens with a raise first-in from seat #5 with a linear 20% range which we can decompose into:

99+, AxTx+, AxJy+, KxTx+, KxQy, QxTx+, JxTx

We hold 9♠9♦ on the button and elect to call and see a flop:

Our hand’s equity against his entire range is close to 48%, and we do not expect him to hold any exceptionally strong hands here, with the obvious rare exception of top set. Our opponent continuation bets half-pot on the flop and we have a decision to make. Let’s take a look at the equity breakdown for our hand against our opponent’s entire range is shown below:

Aside from our gut-shot and set outs, we can expect both the J and the T to set up an open-ended straight draw for our hand on the turn. We already have pair blockers to the nuts, and the new straights that the J and T complete are also blocked by our hand.

In fact, the situation that arises here when you hold 9♠9♦ is an example of a Postflop Pattern that you would do well to learn to recognize: The 3-connector plus gutter. On such flops your pair serves as blockers to the current nuts, a natural gut-shot, and has the potential to make a 4-connector on the turn (or 3-connector with double-gap) for an 8 out straight draw.

Here’s another example of the 3-connector plus gutter:

If you hold Q♠Q♦ on this flop then you block the KQ straight, have the K gutter outs to the nut straight, and can turn either a 9 or an 8 for additional straight outs against any made two pair or set.

My readers with a No Limit background may be thinking, “well this example is identical to the NL situation, so what’s the big deal?” and they would be right as regards the board structure. However with the change in board probabilities in Short Deck the chances of our Queens hitting any one of those key cards against, for example, A♠T♠ is just over 48%!

We can now see why continuing with pocket pairs with straight blockers is a critical component of a strong Short Deck Poker strategy. Their unique combination of blocker potential, draw equity, and nut potential makes these hands excellent candidates to bet or call multiple streets.

I will now continue my analysis with an exposition of the relative power of pocket pairs on boards with straight potential.

There are 5 possible combinations of cards which set up a 4-connector, where holding a single card of the pivot rank will give you an open-ended straight draw. These 4-connectors are, exhaustively:

6789
789T
89TJ
9TJQ
TJQK

You will notice that different ranks of card make 4-connectors with different frequencies; the 6 and K appear once, the 7 and Q appear twice, the 8 and J thrice, and the 9 and T four times. Already we have some indication that the pairs ranked 88-JJ are going to be significantly more valuable as potential blocker + draw hands than the other pairs.

We can go a step further in our efforts to differentiate between the value of these pocket pairs as part of a 4-connector. Notice that even when we do hold 66 as part of a 4-connector, we make it necessarily on a board which contains 3 possible made straights, and we do not block the nut straight at all. In contrast, KK also makes a 4-connector on a 3-straight board, yet it blocks the nut and second nut straights, as well as offering a draw that will beat the present second and third nuts.

All other pocket pairs make a 4-connector on at least one 2-straight board. In case the reader is finding it challenging to visualize this all in his head, I have tabulated the combinations for the most interesting pair, the TT, below:

From the table above you can see immediately that TT always blocks both the nut and the second nut straights, and that on three of the four board classes it does so when there are only two possible straights available.

In fact, the power of TT to make straights is so significant that it influences the hand’s strength even in all-in pre-flop confrontations against a very strong range:

No other pair is quite as significant a drawing hand/blocker as TT is on boards which contain a 3-connector. AA is an unusual hand because it is exceptional as a blocker and yet never offers any open-ended draws.  Of the remaining pairs, the JJ always block the nut straight when they complete a 3-connector, and the 99 block the nut straight on three of the four 4-connectors on which they make a straight (QJT being the exception). I invite the reader to work out for himself how often the 88 block nut straights when they form part of a 4-connector.

Boards which contain a potential 4-connector by the turn are extremely common in Short Deck Poker. As a consequence, 66 and 77 gain little in value preflop since they block only 1 nut straight between them. In contrast, the pairs 88-JJ are more profitable than their raw equity would suggest since, rather than purely set-mine into a multiway pot, they can apply pressure on several 3-connector boards.

In this analysis I have shown you how to recognize where your pocket pairs form part of a 3-connector or 4-connector and also demonstrated how an appreciation of the myriad potentialities of these hands post-flop helps you to build a stronger Short Deck Poker strategy.

Whenever you look at a flop texture and formulate a plan for the play of a hand you are examining it through a certain lens or perhaps, as an advanced player, a series of lenses. The overwhelming majority of poker players, even professionals, remain ignorant and believe the way that they look at the game already is the only correct way to look at it.

I apply the approaches that I am versed in from my studies in Natural Philosophy to design new lenses that enable the user to see the structure of a poker game more clearly. If you take the opportunity to look through these lenses then you will see new strategic opportunities that were blocked from your vision before.