Friday, March 4, 2011

You can be a Three Card Poker expert too!

            This past week, I posted something on the Facebook page for Three Card Poker.  Shuffle Master asked people to relate their best story about Three Card Poker.  So, to get the ball rolling, I posted the following true story:

I'll get the ball rolling: A few years ago, my wife and I sat down at a Three Card Poker table (I think we were at Sunset Station). It was the first time my wife ever sat a casino table game. We had covered the basics of how to play the game (strategy-wise), but after the Dealer gave her her chips, she looked at me and said "now what do I do" - meaning just where to put the wagers. The woman to her right struck up a conversation by telling my wife exactly where to put the chips and how to play. She told my wife that you "'usually play with Queen or better, but sometimes you 'Play' with a Jack and can beat the Dealer." It took all my wife's strength to not respond to the woman, "Do you have any idea who my husband is? He WROTE THE BOOK on Three Card Poker!" (literally). This is an absolutely true story, and unless someone recognizes me - I don't tell anyone who I am in the casino so that's why my wife didn't say anything.


            In response, another reader, posted the following:

‎^^^ little cocky huh? 

By the way Q-6-4 is a great strategy - if you work for Shuffle Master.

Q-J, Q-10 isn't even a good one. King high only, but you did write a book on it so you must know what you're talking about.

            I couldn’t really argue with the ‘cocky’ part.  When it comes to gaming math, I am one of the experts.  Nearly every successful proprietary table game in the casino has had either my father’s work or my work behind it.  The rest of this person’s response had me a bit befuddled.  Queen – Six – Four is not a great strategy if you work for Shuffle Master.  It’s a great strategy (and the best strategy) if you play Three Card Poker.  In fact, it really is ALL you need to know to be an expert at the game.

            This poster seems to have it backwards.  It is not because I wrote a book about Three Card Poker that I know what I’m talking about.  It is because I know what I’m talking about that I wrote the book Expert Strategy for Three Card Poker.  My father worked with the inventor of Three Card Poker.  Several years ago, when Shuffle Master had a Three Card Poker tournament, they came to me to write a strategy booklet on the best way to play for Tournament Play.  But, it’s not because of all this that I know what I’m talking about.  It is because I can prove mathematically that Q-6-4 is the best strategy that I know what I’m talking about.

            How does one go about proving this?  In the case of Three Card Poker, it is very simple.  There are 22,100 unique 3-card hands you can receive from a 52-card deck.  For each of these, there are 18,424 possible Dealer hands.  Using a computer program, I run every one of these hands (just over 400 MILLION hands) and determine for each of the 22,100 Player hands whether the Player is better of Playing or Folding.  If the Player wins back at least the 18,424 units he would wager playing against each of the Dealer’s 18,424 possible hands, then he should Play.  If not, he will lose less by Folding than he would by making an additional wager.  When you analyze the results of this program, you find that the decision point is at Q-6-4.

            At Q-6-4, the Player will wager 18,424 additional units, but win back 18,546.  His net loss will be 18,302 which is still a bit better than Folding and losing 18,424.  At Q-6-3, he will win back only 18,377 creating a net loss of 18,471 which is a bit more than he would if he just Folded.

            So, the poster, seemingly attempting to mock my answer, suggests three other possible strategies – QJ, Q10 and even King High.  How do these stack up?  Well, QJ will get you a payback of 97.61%.  Q10 will get you a payback of 97.28%.  If you want simplicity and go with King High then the payback falls to 96.84%.  The payback for Q-6-4 is 97.98%.  So, there is a clear difference, but it may not seem so big to some of you.  So, let’s flip this around to look at the house advantage (100%-payback).  For Q-6-4, we give up 2.02% to the house.  For QJ it become 2.39% or nearly a 20% increase.  For Q10 it goes up to 2.72% for a 35% increase.  Last but not least, for King High, the house advantage goes to 3.16% or a 55% increase. 

            There are times when you may want to simplify the strategy to reduce errors with a tradeoff of some payback.  However, I really don’t think remembering Q-6-4 should push anyone’s brain to the limit.  It’s your money, you can lose 20-55% more by picking a different strategy or you can become an expert and remember Q-6-4.  Not because I wrote the book and not because I ‘must know what I’m talking about’, but because it IS the BEST strategy.

4 comments:

KW and Charlie Brown said...

Win or lose, I like the idea of reducing the house edge...always! I'll play Q-6-4 in this weekend's tournament. Thanks...

Alana Shaikh said...
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