Poker enters the pit

Feb 13, 2006 10:40 PM

(Part 1 of a two-part series)

A few weeks ago, I wrote about Progressive Gaming’s Texas Hold’em Bonus Poker. This week, it’s time to review Ultimate Texas Hold’em, Shuffle Master’s entry into the Hold’em table game arena.

For proper disclosure, I did the mathematical analysis on Ultimate Texas Hold’em (UTH) for Shuffle Master, but I own no financial stake in the game whatsoever.

As in Progressive Gaming’s version, the goal of UTH is to be dealt a better hand than the dealer. To begin a hand, the player makes an ante wager and a Super Bonus (or blind) wager. Each player is dealt two ”˜pocket’ cards.

The dealer is also dealt two pocket cards face down. At this point, the player has two options. He may either bet four times his ante or he can ”˜check’ and do nothing.

The dealer will then turn over the first three community cards. If the player checked previously, he may now wager two times his ante or check again.

If he wagered before the flop, he is finished betting. The dealer will now turn over the final two community cards. If the player has checked all the way to this point, he must now either make a wager equal to his ante, or he must fold, forfeiting his ante and blind bets.

The dealer will turn over each player’s cards. If the dealer beats the player, the player loses all his wagers. If the hands tie, it is a push. If the player beats the dealer, he will be paid as follows.

The ante bet pays even money if the dealer has at least a pair. If not, it pushes. The play bet is paid even money. The blind bet will push if the player has three of a kind or less. If he has a straight or higher, the player will be paid according to the following paytable:

Hand                         Pays

Royal Flush              500

Straight Flush           50

Four of a Kind           10

Full House                   3

Flush                     3 to 2

Straight                         1

To the best of my knowledge, UTH is the only game that has this type of betting structure. That is, once you bet early, you cannot bet again. This created quite a challenge in determining the proper strategy.

Normally, the player should bet as much as he can when he has the advantage (i.e. he will win more than he will lose). However, in this case, for those hands that are very close to this decision point, it may pay for the player to wait it out and see if the hand turns for him or against him.

If it turns for him, he will only be able to wager half as much, but with a higher chance of winning. If it turns against him, he won’t be stuck having gone ”˜all in’ so early in the hand. The details behind this process, I’ll leave for another day (or my next book).

When I analyze a game, I have two things in mind with regard to the strategy. The first is to come as close to computer perfect strategy as possible for the purposes of creating a theoretical payback of the game. The second is a human playable strategy that comes very close to this theoretical payback. Sometimes, these are one and the same, and sometimes they differ by a little.

In the case of Four Card Poker, a simple strategy was developed that pays 98.41%. I created ”˜expert strategy’ that gets you to 98.6%. I’m sure some computer program could push it to 98.65% or so, but no human could play at this level, so it really has little practical use.

Because of the extreme complexity of UTH, my focus was on the human playable strategy, which is to say the least, complex to begin with. Again, I’m sure a computer could likely raise the payback another 0.1 to 0.2%, taking into account minor variations of the community cards make up or the equivalent of what ”˜Penalty Cards’ are in video poker. However, given that the payback of the human playable strategy is over 99%, I would say this it the right place to focus our energies.

Let’s get right to the point — the strategy. The first decision is whether to bet four times your ante before the flop. At first glance, you’d think that only the very best hands would be played this way. However, you have to throw away most of what you know about Texas Hold’em for this game.

The dealer is as likely to have an unsuited 2-3 as he is an unsuited A-K. At this point, 50% of your hands will wind up actually beating the dealer. But as stated earlier, it does not pay to bet 4x on all of these, because in the long run, you’ll be better off with a ”˜wait and see’ approach. In the end, the following are the rules you should use:

If you are dealt a pair of 3’s or higher, bet 4x.

If you are dealt an ace, bet 4x.

If you are dealt a suited K-X, where X is any card of the same suit, bet 4x.

If you are dealt a suited Q-X, where X is greater than a 4, bet 4x.

If you are dealt a suited J-X, where X is greater than a 7, bet 4x.

If you are dealt an unsuited K-X, where X is greater than a 4, bet 4x.

If you are dealt an unsuited Q-X, where X is greater than a 7, bet 4x.

If you are deal an unsuited J-10, bet 4x

These hands will account for 38% of your hands, so be prepared to bet four times your ante a fairly large number of hands. You will wind up winning these hands a little less than 60% of the time, so they are not sure winners. However, playing this wager too timidly will cost you money in the long run. As the first wager is the ”˜easy’ part of the strategy, the rest will have to wait for next week, when I’ll cover the final two wagers and some other key points to this new game. From what I’m told, there are now about 50 placements of Ultimate Texas Hold’em.