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Analysis of 4-card poker

Mar 1, 2004 11:57 PM

A few weeks ago, Shuffle Master launched its latest table game in Nevada. Four Card Poker made its debut at the Sahara. I first found out about Four Card Poker (FCP) a few months ago. A reader of my Three Card Poker article sent me an e-mail asking what I thought of Four Card Poker. I had heard of FCP just a few hours earlier reading Shuffle Master’s quarterly report. What fortuitous timing!

I immediately set out to find out more about this new game. Based on its name, I was expecting a sort of copycat of Three Card Poker with an additional card. I was hopeful that there was something more to this new game, and I wasn’t disappointed.

There are some similarities between the two games. FCP is also broken down into two distinct games. The player has the option to play either one or both. The first game is called Aces Up and it resembles the Pair Plus portion of Three Card Poker. Basically you are betting that you will be dealt at least a pair of Aces. The second part, also called Ante-Play like Three Card Poker, allows you to see your cards and then decide if you want to play against the Dealer’s hand by making an additional bet.

Like Three Card Poker, there are bonus payouts, regardless if the player wins, for the top hands.

The similarities end there. First of all, despite its name, you’re actually dealt FIVE cards to make your best FOUR card hand. Secondly, the Dealer does not have to ”˜qualify’ in order for you to collect fully on a winning hand. The Dealer DOES, however, get dealt SIX cards to make the best possible FOUR card hand. It is from this extra card that the dealer derives his edge. The last major difference is that if you decide to ”˜Play’ against the dealer, you have the option to bet up to THREE times your original bet. This feature combined with the elimination of the need for the Dealer to qualify, can make strong hands VERY profitable.

Let’s take a closer look at each half of the game:

Aces Up

There is essentially no strategy for this half of the game. You place your bet. You get dealt five cards. You get paid if you have at least a Pair of Aces or better. The paytable in use for Aces Up is:

Aces Up Paytable

Four of a Kind 50
Straight Flush 40
Three of a Kind 8
Flush 6
Straight 4
Two Pairs 2
Pair of Aces 1

Calculating the overall payback of Aces Up is pretty easy. Being that you are dealt five cards, there are 2,598,960 possible hands that can be dealt to you. Using a simple computer program, we can figure out how many of each type of hand is dealt, multiply each by the payout of each and sum them up. Doing this we discover that the total payback of Aces Up is 95.76% This payback leaves a little something to be desired. Unfortunately, I believe this is a trend we’re going to see more of for games for which there is no strategy. In the long run, the casinos know that Aces Up will pay exactly 95.76%. The casinos don’t care about how an individual player does. To the casino, every single game of Aces Up for ALL players combined will over time approach 95.76% and stay very close to that number. As a result, the casinos want to make sure that their vig is large enough to meet their needs. Playing Aces Up, you can expect to have a winner about 18.56% of the time. Ironically, the most common winning hand will be Two Pair, followed by Flushes, Straights, Pair of Aces, Three of a Kinds, Straight Flushes and Four of a Kinds.

Ante/Play

Ante/Play is a good deal more complex. Essentially there are two decisions that have to be made for each hand: Will you Play or Fold?

If you Play, will you bet 1x or 3x your original bet.

The decision to Play or Fold is similar to the one in Three Card Poker. Many of the hands that you are betting on will lose more often than they will win, but it still is better than the alternative of Folding the hand and surrendering your bet. Because Three Card Poker only has three cards for the dealer and the player, finding this ”˜breakpoint’ is very easy because you can run every hand through a computer program. Four Card Poker presents a challenge in this regard. As stated earlier, there are 2,598,960 unique player hands. For each player hand, the Dealer can have any 1 of 10,737,573 unique hands. This presents a total of more nearly 28 TRILLION possible hand combinations. Instead a sort of trial and error approach was used. I picked a Player hand and ran all 10,737,573 unique Dealer Hands against it to determine an Expected Value (EV) for that hand. I was looking for the breakpoint at which the Expected Value of the hand dropped below 50%. Any hand below 50% should be folded and any above 50% should be ”˜Played’ (at 1x original bet). Fortunately, this breakpoint falls out in a nice clean spot. If your hand does not contain at least a Pair of Threes, it should be folded.

The other decision point is arrived at in a similar way. However, the breakpoint is not nearly as clear. First of all, hands that outrank one another do not necessarily have a higher EV. A Pair of Jacks with a Two, Three and Four does not necessarily have a higher EV than a Pair of Tens with an Ace, King and Jack. This is because the kicker cards act as penalty cards to the Dealer’s hand. Every card in your hand that is above the Ranking of the Pair you are holding, takes away chances of the Dealer’s hand beating your own. Secondly, in a similar way, the EV of a hand is affected by the suit make-up of the hand. There are a few other interesting twists that makes figuring out this breakpoint almost as much art as science!

The good news is that these problems are more my problem than necessarily yours. Shuffle Master, in its information card about FCP, gives you a ”˜Basic Strategy’ of betting 3x the original bet if you have a Pair of Tens or Better. I was a little suspicious at first as to how good this strategy was, as whoever heard of a gaming company giving out the strategy for it’s games?! As it turns out, kudos to Shuffle Master. While the strategy is not ”˜Expert Strategy’, it’s awfully close and it’s pretty easy to remember. Using their strategy, I ran 200 Million Hands. Before accounting for the Bonus Payouts, the payback of FCP using ”˜Basic Strategy’ results in a payback of 95.29%. Fortunately, there are Bonus Payouts for Four of a Kinds, Straight Flushes and Three of a Kinds. These are 25, 20 and 2, respectively. When these are added into the mix, the Overall Payback of FCP works out to be about 98.41%. This makes Four Card Poker a VERY competitive table game.

I’ve been analyzing all the hands around a Pair of Tens to determine if there are any better strategies. I’m still working on it, but so far, I’ve really only found one that is marginally better. I’m avoiding any strategies that are overly complex as you are more likely to make errors. If I were to sit down and play, I would use a strategy of betting 3x only when the hand contains a Pair of Tens PLUS at least a Jack or better. The overall payback stays the same, but the net result is that you bet a little less money over time. Given that the Expected Value is below 100%, in essence this will save you money. I’m still running through a variety of scenarios, but I don’t expect any that will increase the payback by anything more than .02%. For a table game that plays maybe 30 hands per hour, this is pretty negligible.

One last point about the strategy. It NEVER calls for betting twice your original bet. You’re either Folding, defending your position (betting 1x) or going All-In.

When I finish my evaluation, I’ll be putting together a new booklet, Expert Strategy for Four Card Poker. It will go over the finer points of the game and explain some of the more complex concepts in greater detail. It will also explain more of what to expect from the game. If you would like to know when the booklet is released (I expect at some point in March), feel free to drop me an e-mail at [email protected]