The Triton poker series has popularized short deck hold-em. I am sure that everyone knows by now that Short Deck is played with a 36-card deck since all the 2's, 3's, 4's, and 5's have been removed (of course, this is why Short Deck is also called Six-Plus poker).

It is a wildly fast-moving game with frequent large pots and tons of action. Pre-flop equities run much tighter than in Long Deck (regular) hold-em. Similar to PLO, the in-hand swings are wild it being common for each card (flop, turn, river) to greatly change who is ahead in the hand.

In previous threads, I looked at how often does a Flush occur in Short Deck vs Long Deck, how often do Quads occur in Short Deck vs Long Deck, and how often does a Full House occur in Short Deck vs Long Deck.

Here I want to do the same thing for Straights. Since there are fewer ranks in each suit, we would expect that straights are more common in Short Deck than in Long Deck. Of course, in Short Deck an Ace can also be used at the bottom end of the deck so that 9876A is a straight (just like 5432A is a straight in Long Deck).

I want to look into the differential frequency of straights in Short Deck vs Long Deck. To keep the comparison "apples-to-apples", I will focus exclusively on straights (including straight flushes) and ignore what other better hands might also be made on the same deal.

In particular, I will look at how often a straight is made by at least one player at a six-max table if each hand goes to showdown on each deal.

First a couple of preliminary results. I did a brute force exploration of each variant with only one player and found that one player makes a straight in Short Deck in 1,213,440 out of 8,347,680 possible deals (including straight flushes but ignoring any other better hands), which is 14.536%.

One player makes a straight in Long Deck in 6,454,272 out of 133,784,560 possible deals, which is 4.824%. Thus, these brute force calculations show that straights are inherently three times more likely in one-player Short Deck than in one-player Long Deck.

For these brute force explorations no distinction was made between board cards and hole cards since with only one player that distinction is irrelevant. I would welcome anyone who can confirm/deny either of those one-player results.

On to the 6-max results.


Long Deck (regular 52-card hold-em):

The combinatoric approach appears a bit daunting, so I resorted to our old friend the simulation. I simulated 100,000,000 deals of 6-max Long Deck NLHE where every player goes to showdown on every deal.

The simulation found that the percent of deals with at least one player making a straight was:

PERCENT = 20.045%


Short Deck (36-card Six Plus hold-em):

As above, the combinatoric approach appears a bit daunting, so I resorted to our old friend the simulation. I simulated 100,000,000 deals of 6-max Short Deck NLHE where every player goes to showdown on every deal.

The simulation found that the percent of deals with at least one player making a straight was:

PERCENT = 48.116%


Summary

We see that straights are inherently much more common in 6-max Short Deck than in 6-max Long Deck (48.116% vs 20.045%) when all hands go to showdown on all deals, and ignoring any other better hands (though we include straight flushes in our tallies).