First of all, I don't have an iPhone, as they do not support Verizon (yet?). Hopefully eventually they will, but until then I suppose I will be shopping around for an acceptable Blackberry when my contract is up for an equipment upgrade in March.

One of my favorite things to do this summer has been going to AC. I've gone to the clubs, stayed in many casinos, learned craps, and played blackjack.

The reason for these 2 seemingly uncorrelated thoughts is that I recently came across this blog about a new iPhone app, regarding perfect blackjack strategy.

http://perfectplayblackjack.blogspot.com/

with the actual app found at http://www.iphoneappindex.com/2009/07/18/perfect-play-blackjack-card-counter/

Every single card counting system with indices aims to model this by lumping together certain cards as +1 (such as 10's, A's), some at -2 (such as 2's, 3's), etc. Then, if the total count is above +3 (such as 3 "10"'s, 2 "A"'s, and 1 "3"), or some number (referred to as an index), then you change whether or not you hit on a 15 vs. a King, for example.

I have thought about this for a while, and realized that depending on how many of each cards left there are, there is an actual correct strategy (or deviation from Basic Strategy, if you like). This iPhone app basically deals with a Rainman-like situation, in which you could actually have 14 separate side-counts (actually it would be 10 side counts, as face cards are the same as a 10). This means that instead of knowing that the count is +3, you would know that there are 8 Kings left, 2 Queens, 4 Jacks, etc. left in the shoe. This feat is near-impossible for most people without some sort of computing tool to help (note I said near-impossible, not impossible). The idea is that knowing these exact side counts would allow one to know the exact mathematically correct thing to do in any situation.

This iPhone app also indicates the counts of several popular card counting systems (such as Hi-Lo, featured in the movie 21), which is presumably used to see how well the indices given by these systems (the approximately correct thing to do) actually lives up to the theoretically correct thing to do.

This app does not, however, indicate the correct betting strategy. The way card counting betting strategy works is based on the Kelly criteria (http://en.wikipedia.org/wiki/Kelly_criterion or http://www.bjmath.com/bjmath/proport/riskpaper1.pdf) which means that if you have a 1% advantage, bet 1% of your money (this is a crude example). This assumes that you know the advantage. Currently card counting aims to approximate this advantage, again by lumping together cards. There are many card counting systems currently in use (many seen at http://www.qfit.com/card-counting.htm), but if we knew the exact distribution of cards remaining (i.e. 10 side counts), there would also be an exact calculation of the advantage. The math involved in this is beyond me, and based on advanced combinitorial analysis.

In my opinion, however, I'm not sure how useful that would be. The current blackjack card counting systems do a damn good job of estimating the advantage, and are easy to use. In fact, the more advanced counting systems have been shown to barely increase the advantage. And regarding this iPhone app, the current method of using indices seems to be pretty good (see http://www.blackjackinfo.com/bb/showpost.php?p=91289&postcount=7).

But hey, from a mathematical perspective, I fully support this quite impressive app, and believe that a rigorous evaluation of index play is nothing to scoff at, if only to check how well one's index system is performing compared to the theoretically correct thing to do. In conclusion, it probably won't be used in any sort of casino environment (as it's actually illegal to use a device in a casino, not just frowned upon), but I think it will be a good evaluation and fun learning tool for people interested in the theory behind card counting index play.

FYI check out www.blackjackinfo.com for descriptions of a lot of things I've talked about, such as card counting or index play. Gotta love gambling!

-Rob Toth

[edit] P.S. I almost forgot, on a COMPLETELY unrelated note, my dear friend Katt wanted me to include this in my blog: "Good girls are the bad girls that don't get caught.". Happy, Katt? :)