“A very small cause that we fail to notice determines a very significant effect that we cannot fail to see, and then we say that the effect is due to chance.”
– Henri Poincaré

Short Deck Poker Strategy is one of the newest domains in which I currently conduct research at the Cardquant Institute. During the course of my research I have identified some essential concepts that enable a player new to Triton Holdem to familiarize himself with the structure of the game.

This article is the first in a series that demonstrates how the new probability structures inherent to Short Deck dictate sound strategy. Before continuing, I recommend that you read my key article on Short Deck Poker Strategy Fundamentals if you haven’t already.

When you transition from No-Limit Hold’em to PLO the hand probabilities change but the board probabilities stay the same. The only thing that changes as regards your in-game evaluation of board probabilities is that in PLO you hold two extra cards which gives you additional information. However, when you transition from either game to Short Deck Hold’em the hand probabilities change AND the board probabilities change. This means that, when you start to learn Short Deck, you should largely disregard any intuition you have about relative hand value and treat it as the entirely new game that it is.

By way of illustration consider this: when you see a flop in a Triton Holdem game you can count 5 cards, leaving 31 cards between your hand and your opponents’ hands. In the same scenario in No Limit Holdem there would still be 47 cards remaining. As a result of this difference, any one card is more likely to hit in Short Deck than in No Limit, for both you and your opponents. This has led some writers to hastily invent a ‘Rule of 6 and 3’ as a way of simplifying in-game calculation. We shall see the folly of this rule shortly! (pun intended)

Let us continue our analysis below with some important practical examples, starting with an exposition of the impact of back-door draws.

A Strong Short Deck Poker Strategy Values Back-door Draws

As we discussed in the introduction, the short deck makes any one category of ‘outs’ worth more in equity. The key challenge, common to other poker games where multi-way pots are common, is being able to recognize when a particular hand type qualifies as an ‘out’ in a given context.

Consider the following example: we call a raise from seat #3 as the button and join a heads-up pot holding the T9 on this flop:

Were we playing NLHE, then the T9 would have only 23% equity against A♠K♣. If you attempt to naively use “The rule of 6 and 3” that has been lazily rolled out as the new Short Deck dogma on mainstream poker blogs, then you will focus excessively on the gut-shot draw here. This would lead to a quick calculation of 6×4= 24% as your in-game estimate of the strength of the T9 on this flop in Short Deck.

In fact, the Cardquant Short Deck Calculator shows that T9 has 35% equity against A♠K♣. Good thing we don’t play by mainstream rules!

A deeper examination of the Equity Breakdown by turn transition will show you where this extra equity comes from.

Short Deck AJ7 Turn Equity

Whilst there are several turn cards which are a near-lock for one of the two players, there are 8 cards which keep the equity of T9 at or above 33%. The K transition brings both additional straight and flush draws, as does the Q, and all of the tens and nines bring additional trip or two pair outs. This demonstrates an essential feature of heads-up pots in Short Deck, namely that your hand is often more likely to win by hitting any one of its back-door draws than by hitting a flopped gut-shot straight draw.

The significance of this in practical play cannot be overstated. In case you thought I was being uncharitable in my criticism of “The Rule of 6 and 3”, consider the equities for two other gut-shot hands facing A♠K♣:

Short Deck AJ7 Straight Draws

What accounts for the large gap between the equities of these hands facing A♠K♣ and the equity of the T9?

It is obvious that the King blocker in our opponent’s hand hurts the QT, but the large drop in equity when we hold KQ is counter-intuitive for the NLHE player. The reason for this drop is that our opponent’s King also prevents runner-runner two pair or trip draws which involve the King from promoting our hand. In NLHE the KQ has 20% equity against A♠K♣, significantly closer to the strength of the T9.

It’s not just subtle features like back-door draws that are affected by the change in board probabilities. The relative hand strength on the flop changes dramatically in Short Deck Holdem, lending a false familiarity to many No Limit players that leads to catastrophic failures in judgement. We will take a look at one of the more pronounced examples in the next section.

In Triton Holdem Flopped Sets are Flipping versus Flopped Straights

In No Limit Holdem you have to be unlucky to run a flopped set into a flopped straight on the board below, but when you do you have only 30% equity.

Short Deck T87 Trichrome Flop

In Triton Holdem, pocket tens have just over 50% equity against J9