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Best of Donald Catlin

Gaming Guru

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Wild Six Card Draw Poker

6 March 2009

This past November I attended the Global Gaming Exposition (G2E) in Las Vegas. There was the usual array of new slot machines, video poker machines, and table games. One of the table games caught my eye because one of the co-owners is my good friend Stanley Ko. Stanley, like me, is a gaming analyst and in my opinion one of the best in the country. Stanley teamed up with a gent by the name of Mike Timpano and together they developed a game whose title is the title of this article.

Wild Six Card Draw Poker is played with a 54-card deck that contains the usual 52 cards plus two Jokers that are wild cards. The game is played on a Blackjack-type table. In front of each player are three betting spots entitled Poker, Jacks or Better, and Draw Bonus. These last two are optional wagers so I will treat them later and concentrate on the mandatory Poker Bet. There is also a rectangle marked Draw.

Play begins with the player and dealer each receiving five cards face down. The player now looks at his hand. If the five-card hand is a straight or better the player automatically wins even money. This feature avoids so called bad beats. Otherwise the player can either keep his five-card hand or can replace one of his cards. He does this by placing the card face down on the space marked Draw and the dealer gives him a new card from the deck. The dealer receives another card for a total of six cards. The dealer selects his best five card hand from his six cards and this hand is compared to the player's five-card hand. If the players hand is higher in rank than the dealer's hand the player wins even money. If the dealer's hand is higher in rank than the player's hand the player loses his wager. Ties are treated like pushes; no money changes hands.

The optional wager Jacks or better is simply a bet that the player's original five-card hand will contain Jacks or better. The wager is paid according to a pay table. The Draw Bonus is a wager that the player's final five-card hand (after possibly replacing one of his cards) will be two pair or better. You are probably wondering what happens in the case that the player's original five-card hand is a straight or better. In this situation the player wins the Poker bet but his hand is not collected. He keeps the hand and can draw a new card if he so desires. Just as in the case of the Jacks or Better wager the hand is paid according to a pay table. I am not going to reproduce the pay tables here since it is common in new games that pay tables are adjusted once the game hits the casino floor.

The mathematical analysis of this game is a daunting task. It turns out there are 9,508,150,956,704,400 player/dealer hand combinations. I did not calculate a house edge for this game. Stanley Ko, however, did. I do not report figures that I do not calculate myself and it is quite possible that the game's owners consider Ko's work proprietary. I will state, however, that the game's house edge is in line with other new table games.

Now you may wonder why this game has an edge at all. After all, don't the player and dealer form their hands from (possibly in the player's case) six cards? Not exactly. Let me illustrate the idea with a simple example. Suppose we have two four-card decks. Each deck consists of two red cards marked 1 and 2 and two blue cards marked 1 and 2. There are two players called A and B. Player A receives a two-card hand from one of the decks and has the option of replacing one of his cards from the remaining two-card deck. Player B is dealt three cards and picks the best two-card hand from the three.

Player B has four possible three card hands: (1R, 1B, 2R), (1R, 1B, 2B), (1R, 2R, 2B), (1R, 2R, 2B). Notice that player B ends up with a (1, 1) hand half the time and a (2, 2) hand half the time. Now if player A has a hand like (1R, 2R) he would replace the 1R card and end up with either a (1B, 2R) hand or a (2B, 2R) hand There are six starting hands, two of them made hands, and four mixed hands like my example. I'll let you write out the possibilities. The final probabilities look like this:

(1, 1)      1/6
(2, 2)      1/2
(1, 2)      1/3

There are six possible situations. For example A and B could both have (1, 1) hands and this would happen with probability 1/6 x 1/2 or 1/12. (This is why I used two separate decks so the A and B hands would be independent.). If A has a (1, 2) hand and B has a (1, 1) hand then B beats A and this happens with probability 1/3 x 1/2 or 1/6. I'll let you do the other four situations. All in all we have the following results:

EventProbability
Tie4/12
A beats B3/12
B beats A5/12

As you can see B definitely has the advantage over A.

Wild Six Card Poker is an interesting game and I wish Stanley and Mike well with it. I played the game at their booth at G2E and thought it was a lot of fun so it should attract players. See you next month.


Don Catlin can be reached at 711cat@comcast.net

Donald Catlin

Don Catlin is a retired professor of mathematics and statistics from the University of Massachusetts. His original research area was in Stochastic Estimation applied to submarine navigation problems but has spent the last several years doing gaming analysis for gaming developers and writing about gaming. He is the author of The Lottery Book, The Truth Behind the Numbers published by Bonus books.

Books by Donald Catlin:

Lottery Book: The Truth Behind the Numbers
Donald Catlin
Don Catlin is a retired professor of mathematics and statistics from the University of Massachusetts. His original research area was in Stochastic Estimation applied to submarine navigation problems but has spent the last several years doing gaming analysis for gaming developers and writing about gaming. He is the author of The Lottery Book, The Truth Behind the Numbers published by Bonus books.

Books by Donald Catlin:

Lottery Book: The Truth Behind the Numbers