Ultimate Texas Hold’em Hole-Card Play: Two Dealer Cards

Ultimate Texas Hold’em (UTH) must surely be the most widely available and profitable opportunity for hole-card play right now. Over the last few months, I finally took the game to task and wrote a series of articles about various hole-carding situations the player might encounter. I thought I had covered it all until an AP recently contacted me and asked about the edge when the AP sees both dealer hole-cards before acting. Wow! Is this stuff for real?

At any rate, the project was not tough at all. I already have the software written, it just takes a while to run a cycle. I quickly modified my code and it took 2 days to complete the run. After it was done and I was double checking the results, I noticed that my code double counted each hand. In practice that means that the results are correct, but it could have completed in 1 day. I suppose the same is true of the other analyses I’ve completed for UTH as well. This isn’t exactly a bug, it’s just sloppy programming.

Here is the spreadsheet that gives the output produced by my program:

Here is a summary of the results from using computer perfect play to hole-card UTH when the AP knows both dealer hole-cards:

• The player edge in UTH knowing both dealer hole-cards is 38.5816%.
• The player makes a 4x pre-Flop raise on 34.7368% of his hands.
• The player checks pre-Flop on 65.2632% of his hands.’

Computer perfect play isn’t feasible in this case.  Fortunately for the AP (or unfortunately for the casino), the world’s easiest strategy performs remarkably well.

Here it is:

• Raise 4x if you are ahead pre-Flop. Otherwise,
• Raise 2x if your five card poker hand outranks the dealer’s five card poker hand post-flop. Draws do not count in this ranking. It is just straight comparison of poker hands. Otherwise,
• Raise 1x if your best five-card poker hand beats the dealer’s best five-card poker hand after all 5 community cards are dealt. Otherwise,
• Fold.

The only subtlety to this strategy comes when comparing pre-flop hands. First, pairs outrank non-pairs. Otherwise, the top card of the two-card hand is used to compare the hands. If the top cards tie, then the lower card is used to compare the hands. If the two hands are tied, then suited hands are used as tie-breakers.

Here are some pre-flop examples:

• Raise 4x if you hold a pair of 5’s and the dealer holds a pair of 4’s or less.  Check if you hold a pair of 5’s and the dealer holds a pair of 5’s or better.
• Raise 4x if you hold 7-5 unsuited and the dealer holds 7-4 or worse (suited/unsuited doesn’t
• Check if you hold 7-5 unsuited and the dealer holds 7-5 or better.
• Raise 4x if you hold 7-5 suited and the dealer holds 7-5 offsuit.

I programmed this strategy into a Monte-Carlo simulation and let it run for one billion hands. The result:

• If the player knows both dealer hole-cards, then the world’s easiest strategy gives the player a  34.254% edge over the house.

It is worth noting that there are examples where the pre-flop strategy given above does not match computer-perfect play.  If the player’s starting hand is 7c,5c and the dealer’s starting hand is 6d,4d then:

• EV “Check” = 0.721132.
• EV “Raise 4x” = 0.721025
• Computer perfect strategy is to check 7c,5c against 6d,4d.

Likewise, the player should check with:

• 6c,4c against 5d,3d
• 5c,3c against 4d,2d

On the other hand, if the player holds 8c,6c against the dealer’s 7d,5d then correct strategy is to raise 4x.

Don’t ask me why. I don’t know.

If you are an AP who is lucky enough to find this opportunity, you would probably have used exactly this strategy. Intuitively, there are going to be improvements post-flop with flush draws, and possibly open-ended straights. But, is it really worth it to figure those out? I mean, 34.254%, really!

As for the casino side. If you have a dealer who is exposing both hole-cards, then you have bigger problems than incompetent dealers.