Recently I’ve been hearing about a new game called short deck. It’s played just like normal Texas hold’em, except it’s played with a short deck—all the cards deuce through five are removed from the deck. Aces play as the low end of a nine-high straight. Some variants reorder the hand rankings, most notably changing it so that flushes beat a full house.
When I first heard about it, it sounded to me like the new math would break a lot of players’ intuition they’ve built playing regular no-limit hold’em. So the first thing I wanted to do was go through how some of the math changes.
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Let’s say you get dealt 10h 9h. Let’s go through the math of how often you flop straight and/or flush draws both for normal hold’em and then for short deck.
Full Deck Draws
Once you have your two cards, 50 cards remain in the deck. Three of these will appear on the flop, so there are 50 choose 3 total possible flops. (You can type 50 choose 3 into Google and it will give you the answer.) In this case, that’s 19,600 possible flops.
To flop a flush draw, you need two of the 11 remaining hearts on the flop, as well as an unrelated third card. So that’s 11 choose 2 times 39 (the number of non-hearts remaining in the deck). Since 11 choose 2 is 55, the total number of flush draw flops is 2,145. Divide that by the total number of flops, and you get about 11 percent, which is how often you will flop a flush draw.
To flop an open-ended straight draw you need either Q-J, J-8, or 8-7 on the flop—in each case also with an unrelated card. There are 16 ways to have Q-J (four queens times four jacks), and 16 ways each for the other two for 48 total ways.
If we specify that the unrelated card can’t be one that completes the straight, there are 40 possible unrelated cards for each of the 48 total ways to flop a straight draw. That makes 1,920 total straight draw flops. Divide that by the total number of flops, and you get about 10 percent, which is how often you will flop a straight draw.
Short Deck Draws
In short deck, there are 34 remaining cards after you get your two, so 34 choose 3 or 5,984 possible flops.
There are only 7 remaining hearts, so to flop a flush draw you have 7 choose 2 times 27 possible flops. That’s 567 flops or about 9.5 percent of flops. The full deck chance was 11 percent so flush draws are somewhat less common in short deck.
To flop a straight draw you still have your 48 ways to get Q-J, J-8, or 8-7 on the flop, but now there are only 24 unrelated third cards. That’s 1,152 total straight draw flops or about 19 percent. The chance of flopping a straight draw in short deck is much higher than it is with a full deck.
Making The Draw
Everyone knows the chance to make flush and straight draws in normal hold’em are nine and eight outs respectively. You can use the rule of two and four to estimate the chance of making the draws. But the exact way to figure it out is to do something similar to what we did on the flop. The only twist is you calculate the chance of missing the draw and then subtract that from one.
There are 47 choose 2 possible turn and river cards. That’s 1,081. If you have a flush draw (nine outs) then there are 38 cards that brick your draw, so you have 38 choose 2 ways to miss. That’s 703 total misses out of 1,081, or 65 percent. That leaves a 35 percent chance you hit your flush draw.
Straights work the same, except you have 39 cards that brick your draw. That’s 741 total misses, or 68.5 percent. That leaves a 31.5 percent chance of hitting the draw.
In short deck, there are 31 choose 2 possible turn and river cards. That’s 465. A flush draw has only five outs in this game. So there are 26 cards that brick your draw, and you have 26 choose 2 ways to miss, or 325. That’s about a 70 percent chance to miss, so it’s about a 30 percent chance to make a flush.
Open-ended straights still have 8 outs though. So there are only 23 cards that brick your draw, giving you 23 choose 2 ways to miss, or 253. That’s about a 54.5 percent miss percentage, so you hit your straight about 45.5 percent of the time.
That’s pretty close to 50-50! And you flop a straight draw to your connector nearly 20 percent of the time. Flushes are a bit harder to make in this game, but straights are much easier.
Flopping A Set
The odds of flopping a set change also in short deck. You can figure it out the same way as the chance of making draws—count the flops where you miss the set and subtract from one. With a full deck, there are 48 choose 3 ways to miss your set, or 17,296. That’s about 88 percent of flops, leaving about a 12 percent chance to flop a set.
In short deck, there are 32 choose 3 ways to miss your set, or 4,960 flops. Divide that by the 5,984 total possible short deck flops, and there’s about an 83 percent chance to miss, leaving a 17 percent chance to flop a set.
Final Thoughts
I don’t know how many of us will be playing short deck soon. The game is popular in only a small number of places, mostly in ultra high-stakes cash games. I think one reason it’s become popular in those games is because it turns your ingrained intuitions against you.
When you’ve played hold’em long enough, you begin to internalize the probabilities to make certain hands. You end up getting to the correct answer in many situations through intuition honed over zillions of hands.
Short deck wrecks a lot of those intuitions. The probabilities to make the basic hands are just plain different. Therefore hand values are different. The hands to semi-bluff with and bluff catch with and so on are also different. Blockers mean more in some contexts.
The basic concepts of poker are all the same. But the details of how to resolve conflicts between competing concerns is turned on its head.
Shaking things up in this way always tends to reward the best poker players. The ones who can adjust more quickly than anyone else. The ones who can figure things out rather than rely solely on learned intuition.
Doing the math in this article is the beginning of this process. ♠
Ed’s newest book, The Course: Serious Hold ‘Em Strategy For Smart Players is available now at his website edmillerpoker.com. You can also find original articles and instructional videos by Ed at the training site redchippoker.com.
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.
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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
| Traditional Hold’em | 6+ Plus Hold’em (Trips beat Straight) | 6+ Plus Hold’em (Straight beat Trips) |
|---|---|---|
| Royal Flush | Royal Flush | Royal Flush |
| Straight Flush | Straight Flush | Straight Flush |
| Four of a Kind | Four of a Kind | Four of a Kind |
| Full House | Flush | Flush |
| Flush | Full House | Full House |
| Straight | Three-of-a-Kind | Straight |
| Three-of-a-Kind | Straight | Three-of-a-Kind |
| Two Pair | Two Pair | Two Pair |
| One Pair | One Pair | One Pair |
| High Card | High Card | High Card |
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)
| Traditional Hold’em | Six Plus Hold’em/Short Deck Poker | |
|---|---|---|
| Getting Dealt Aces | 1 in 221 (0.45%) | 1 in 105 (0.95%) |
| Aces Win % vs a Random Hand | 85% | 77% |
| Getting Dealt any Pocket Pair | 5.90% | 8.60% |
| Hitting a Set with a Pocket Pair | 11.80% | 18% |
| Hitting an Open-Ended Straight by the River | 31.50% | 48% |
| Possible Starting Hands | 1326 | 630 |
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)
| Hand All-in Pre-Flop | Traditional Hold’em | 6+ Hold’em (Trips beat Straight) | 6+ Hold’em (Straight beat Trips) |
|---|---|---|---|
| Ac Ks vs Th Td | 43% vs 57% | 47% vs 53% | 49% vs 51% |
| Ac Ks vs Jc Th | 63% vs 37% | 53% vs 47% | 52% vs 48% |
| As Ah vs 6s 6h | 81% vs 19% | 76% vs 24% | 76% vs 24% |
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
| Traditional Hold’em | 6+ Hold’em (Trips beat Straight) | 6+ Hold’em (Straight beat Trips) | |
|---|---|---|---|
| Player 1 vs Player 2 | 66% vs 34% | 52% vs 48% | 48% vs 52% |
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
Short Deck Holdem Ranges
| Traditional Hold’em | 6+ Hold’em (Trips Beat a Straight) | 6+ Hold’em (Straight beat Trips) | |
|---|---|---|---|
| Player 1 vs Player 2 | 74% vs 26% | 100% vs 0% | 68% vs 32% |
Short Deck Hold'em Starting Hands
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.