Six Plus Hold’em/Short Deck Poker Odds and Probabilities

One of the games that have seen a flurry of interest over the last few months is Six Plus Hold’em, also referred to as Short Deck Poker.

Six Plus Hold’em is an exciting and fun poker variant based on Texas Hold’em where the game is played with a deck of 36 cards as opposed to the usual 52 cards in traditional hold’em. Deuces through fives are removed from the deck giving the game its name Six Plus Hold’em/6+ or Short Deck Poker.

Aces are played both low and high, making both a low-end straight A6789 and the high JQKTA. Also, with a shortened deck, the game changes a bit in terms of hand rankings and rules. A Flush beats a Full House and in most places where Six Plus is offered, a Set or a Three-of-a-Kind beats a Straight.

Because the low cards are removed, there are more playable hands compared with traditional Hold’em, and so it is more of an action-orientated game. Not only are the hand rankings modified but so are the mathematics and odds/probabilities of the majority of hands.

Before we talk about the odds and probabilities of some of the hands, let’s have a look at the hand rankings offered in Six Plus Hold’em (ranked from the highest hand to the lowest):

Six Plus Hold’em Hand Rankings Comparison

One may wonder why a Flush is ranked higher than a Full House or why Three-of-a-Kind is ranked above a Straight. That’s because in Six Plus Hold’em, a Flush is harder to make since there are only nine cards in each suit instead of thirteen. Similarly, the stripped-deck also means that the remaining 36 cards are much closer in rank and so there will be smaller gaps between the cards in the hand and those on the board. This increases the probability of a hand becoming a Straight and hence Straights are ranked higher than a Three-of-a-Kind.

However, it is worth noting that the rules vary from game to game. For example, in the Short Deck variant offered in the Triton Poker Series, a Straight is ranked higher than a Three-of-a-Kind like in traditional hold’em even though mathematically a player would hit a Straight more.

One of the reasons why an operator would rank a Straight higher than Three-of-a-Kind is because it would generate more action. If Trips were ranked higher, a player with a Straight draw would have no reason to continue the hand as he or she would be drawing dead.

Let’s take a look at the odds/probabilities of hitting some of the hands:

Six Plus Hold’em vs Traditional Hold’em (Odds and Probabilities comparison)

As you can see in the table above, the odds of being dealt pocket Aces are doubled as you now get the powerful starting hand dealt once in every 105 hands, as opposed to once in every 221 hands with a full 52-card deck. However, the probability of winning a hand with aces vs a random hand decreases from 85% in traditional hold’em to 77% in Six Plus Hold’em.

The probability of hitting a Set with pocket pairs increases to 18% from 11.8%, and the probability of hitting an open-ended Straight by the River also increases to 48% in 6+ Hold’em compared with 31.5% in traditional Hold’em.

Let’s now have a look at some of the pre-flop all-in hand situations:

Six Plus Hold’em vs Traditional Hold’em (Hands Comparison)

As mentioned earlier, the equities run very close to each other with the shortened deck and so a hand like Ace-King versus Jack-Ten is almost a coin-flip, whereas the former is a favorite in Texas Hold’em. Again, a hand like Ace-King versus a pocket pair like Tens is a coin-flip in 6+, whereas a pocket pair is a slight favorite in normal Hold’em.

Now, let’s take a look at the probabilities when a connected or wet Flop is dealt:

Player 1: Ac Ks
Player 2: Td 9h

Flop: Kh 8c 7d

In traditional Hold’em, Ace-King is a favorite with 66% and Player 2 is chasing the Straight draw with a close to 34% chance of hitting it. However, the probability significantly changes in both variants of 6+ Hold’em. In a variant where Trips beat a Straight, Player 1 is only a slight favorite with just 52% (more like a coin-flip). However, in a Short Deck game where a Straight beat Trips, Player 2 is now slightly favorite with 52% chance of hitting a Straight by the river.

Another hand:

Player 1: As Ah
Player 2: Qd Jh

Flop: Ad Th 9s

It’s pretty clear when it comes to normal Hold’em, but in a Short Deck variant where Trips beat a Straight, Player 2 is drawing dead as opposed to the other variant where Player 2 still has a 32% of chance of completing a Straight by the River.