Four Card Poker – Finally

In Part One, I reviewed the Basic Strategy provided by Shuffle Master. In Part Two, I introduced the first half of a more precise Expert Strategy. This week, I will refine the Expert Strategy even further. As previously stated, this strategy will still not be 'Perfect' Strategy. As previously discussed, perfect strategy for Four Card Poker would require a strategy table, several pages long, that would require close scrutiny of ALL 5 cards dealt to the player. As each player card can act as a penalty card to the Dealer's hand, even the exact SUIT makeup of the player's hand can become relevant to the strategy.

The refined Expert Strategy for Four Card Poker is still a strategy that will account for the Dealer's Upcard and occasionally a single kicker in the Player's Hand. It will NOT look at the other cards in the player's hand (i.e. 'second' kickers) or at the suit makeup of the Player's Hand. Basic strategy will achieve a payback of about 98.41%. My first cut at Expert Strategy brought the payback to 98.50%. This final piece of the strategy brings the payback to 98.60%. While the nearly .2% increase in payback may not sound like a lot, it will reduce the House Edge ('vig') by better than 10%.

According to Basic Strategy, you should bet 3x anytime you have a Pair of 10's or Better. This ignores the Dealer's Upcard completely and is not taking advantage of this benefit. We should be betting 3x ANYTIME the EV of the hand goes positive, meaning we expect to win the hand more often than we will lose the hand. The strategy presented below is different than the one presented in Part Two. The strategy in Part Two was an improvement over Basic Strategy, but the following Strategy goes a little further. Through computer analysis, the following Expert Strategy has been devised:

• Bet 3x on all Pair of Aces or Better
  
• Bet 3x on all Pair of Kings, except bet 1x if facing an Ace and you don't have an Ace in your hand
  
• Bet 3x on a Pair of Queens looking into a 2-Q. Bet 3x if Dealer has a K or Ace up, and you have the Dealer's up-card in your hand
  
• Bet 3x on a Pair of Jacks looking into a 2-J. Bet 1x if Dealer has an Ace up. If the dealer has a Q or K up, Bet 3x if you have the Dealer's up-card in your hand.
  
• Bet 3x on a Pair of 10's looking into a 2-9, Bet 1x if Dealer has a J-Ace. If the Dealer has a 10 up, and you have a Jack or Better kicker, bet 3x, otherwise bet 1x.
  
• Bet 3x on a Pair of 9's looking into a 2. All other Pairs of 9's, bet 1x.

The strategy listed above is for the decision to bet 1x vs. 3x. The other decision that needs to be made is when to fold vs. bet 1x. According to Basic Strategy, you should bet 1x on all Pairs of 3's or better (except when you bet 3x), and fold all Pairs of 2's. Expert Strategy will alter this, as well, albeit only slightly. Again, through computer simulation, the following strategy has been developed:

• Bet 1x on a Pair of 2's looking into a 2

So, besides the payback difference, where do these changes leave us in terms of what to expect?

• We can expect to fold just a little over 47% of the time. This is essentially unchanged from Basic Strategy
  
• We can expect to bet 1x just a little less than 24% of the time. This compares to just under 22% of the time for Basic Strategy.
  
• We can expect to bet 3x just a little under 29% of the time. This compares to just under 31% of the time for Basic Strategy

The net result is to shift about 2% of our wagers from 3x betting to 1x betting. By doing this, we buy ourselves an additional .2% of payback. On average, we also bet about a nickel less per hand based on a $5 ante bet, which also helps to slow our loss rate over the long run.

With the analysis now complete, I should be able to focus on completing 'Expert Strategy for Four Card Poker' in the coming weeks. For those of you who already e-mailed me regarding this new book, I will be sending out the information shortly. For those who are interested, feel free to drop me a line at compuflyers@prodigy.net and I'll forward information to you as soon as the book is out. According to Shuffle Master, there are now nearly 100 Four Card Poker tables out there, so this game looks like it may be poised for a successful run.