The Wizard Ace/Five Count

Last update: Apr 19, 2007

Basic strategy blackjack players sometimes ask me for a simple way to overcome the small house edge in blackjack with little worry over being recognized as a card counter. This is often done with the motive of milking the casinos for comps and free tournaments. Most players with the goal of just breaking even use a traditional card counting strategy but with a very small bet spread. However, I offer the following alternative, which is easier to use, and I doubt will arouse any suspicions. The simple rules are as follows.

1. Establish what your minimum bet will be. This is called one unit.
2. At the beginning of each shoe, start a running count at zero.
3. For each 5 observed, add one to the running count.
4. For each ace observed, subtract one from the running count.
5. If the running count is zero or less then bet one unit, otherwise bet 2×(unit size)×(running count).
6. Use basic strategy for all playing decisions.

This strategy is designed to be most effective on six-deck games. To get past the break even point the dealer will need to stand on a soft 17. If surrender or resplitting aces is allowed then that is all the better, but not required to get a postive expected value. Most of the finer Las Vegas Strip casinos have liberal six-deck games, with the dealer standing on soft 17, late surrender, resplitting aces allowed, with 75% penetration the norm. These rules result in a player edge of 0.22%. As of August 2006, casinos with this game include the Bellagio, Caesars Palace, Golden Nugget, Hard Rock, Luxor, Mandalay Bay, MGM Grand, Monte Carlo, New York New York, Palms, Mirage, Treasure Island, Venetian, and the Wynn. For current blackjack conditions visit my Las Vegas blackjack survey. I ran simulations at different deck penetration levels. Unlike traditional card counting strategies, which require a true count conversion, penetration doesn't make much difference in the Wizard Count. The following table shows the player advantage based on penetration and rules.

The average bet size will be 2.85 times one unit. The standard deviation of the bet size is high at 3.2 units. The bet size is 10 or more units 6.58% of the time, and 20 or more 0.13% of the time. In simulations the bet size got as high as 38 units. So this not a strategy for those with a weak stomach. If you want something with a smaller bet spread you will have to play a more traditional card counting strategy, which requires tracking more cards and usually a true count conversion (dividing the running count by the number of remaining decks), and strategy adjustments based on the count. A strategy based on counting just aces and fives is discussed in some blackjack books, including Million Dollar Blackjack by Ken Uston. Using the hi/lo count, to get above break-even you will need to spread up to 4 or 5 units, depending on rules and penetration. To add marginally to your advantage stand on 16 against a 10 on any positive running count.

After the original publication of this page two people said that a 1 to 38 spread was too much to ask. First, let me say that I simulated 4 billion hands and the number of times a 38 unit bet was made was 6. However for those with a weak stomach I redid the simulation with a maximum bet of 10 units. The following table shows those results.

So with a 1 to 10 spread at the usual 75% penetration you will need the fully liberal rules with surrender and resplitting aces. With a 1 to 10 spread the average bet drops to 2.4 units and the standard deviation is concidentally also 2.4.

After publishing this section somebody accused me stealing the idea from Edward Thorp. Upon looking into the accusation, Thorp does indeed discuss a similar straegy in his fourth chapter titled "A Winning Strategy", in his book 'Beat the Dealer.' The difference is that Thorp's stratgy tracks fives remaining against total cards remaining. However I would still like to give proper respect to Thorp for thinking about counting fives at least 24 years before I did.