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GameMasters Secret's Page
The GameMaster's Secrets
Milking the Single-Deck Game

Most of the Blackjack games available at Internet casinos shuffle the deck(s) after every hand, so card-counting techniques are virtually (no pun intended; well, maybe a little) useless. But, with the technology of multi-player tables becoming more and more common, that's changing a bit and change always means opportunity. You may not be familiar with all this, but some Internet casinos are trying to replicate the 'real' casino experience and that includes games where more than one player can take part so, at least as it applies to Blackjack, the card-counter can see quite a few cards before the deck(s) are shuffled. (Remember that, at an Internet casino, all the cards are dealt face up; it won't typically happen at a 'real' casino.) While that slight amount of penetration is basically useless in multi-deck games, in a single-deck scenario there's something to be gained.

The reader who asked for my help found a casino that offered a single-deck game where the dealer stands on A-6, the player may double on any first two cards, double after split is permitted, insurance is available, etc. Pairs may be split, but not resplit (for example if you split a pair of 8s and the first 8 gets hit with another 8, you may not resplit that into a third hand) and that's usually done to save room for the computerized graphics, not because the casino doesn't want you to split more. Anyway, such a game offers the basic strategy player a very slight edge over the house; it's really the double after split which puts this game into positive expectation territory and that's typically not available in 'real' games. But it is online (at more that one casino, too) and, when one figures in the cost of not being able to resplit, the player starts with an edge of 0.08%. That's very small, of course, but we may be able to make it bigger. The key here is that this casino allows a customer to play up to 3 hands and, at the multi-game tables, two or more players can bet on five spots, which means they may play 5 hands between them. Because it's one round and shuffle, those 5 hands would all be played with an average edge over the casino of 0.08%, so if two partners were to bet $100 on each spot, their long term return would be $500 X .0008 = $.40 or forty cents per round (not per hand, per round) and, at a rate of 60 rounds per hour, that's worth $24/hour. The catch here is that the swings in their bankroll would be breathtaking. To get that $24 an hour, they'd be betting 60 X $500 = $30,000 each hour , so it's not difficult to imagine that there would be times when they were up $5000 or down $5000 in the same hour! A total bankroll of about a million bucks will do for this little scheme. Not very practical is it? Hell, for $1,000,000 you could buy your own Internet casino and toss out rascals like me.

Okay, better idea. Card counting will help in two areas of this game, the insurance bet and for changing the play of the hand. Betting doesn't matter of course, since it's one round and shuffle. Peter Griffin, in his book "The Theory of Blackjack" calculated what perfect betting, play and insurance was worth, according to the penetration of a single-deck game. At the 10-card level, perfect insurance decisions are worth .07%. If you and a friend get a table together and he plays 3 hands and you play 2, you'll see 11 cards before you make an insurance decision (the dealer's up card and the two cards in your 5 hands) and, if you use a count which gives you perfect insurance decisions (it exists; see my Blackjack column "Single-level Counts"), your edge is now 0.08 for the basic game, plus 0.07 for the insurance = 0.15%. It gets better. Griffin's calculations for the gain from perfect strategy shows that at the 11-card level, perfect playing adds 0.24%. Now, no counting system has a Playing Efficiency of 100%; the best 'mental' system is about 70% efficient. (But, what could one do with a computer??) Anyway, the strategy gain goes up as more cards come out and, at the 15-card level, it's about 0.40%. By the time you play the 5th hand, you'll be at about that level, since each of the 4 preceding hands will average about 1 card in hits. So, let's say you use a counting system with a 64% Playing Efficiency (like Snyder's "Zen" count), then you'll get a chart that looks like this:

Spot
Number		 Cards
seen		 Perfect
Strategy 		Gain x P.E.
of .64		 Net Strategy
Gain
1 11 .24% .24 X .64 .14
2 12 .26% .26 X .64 .15
3 13 .30%. .30 X .64. .19
4 14 .35% .35 X .64 .22
5 15 .40% .40 X .64 .25

Still with me? Okay, so we've established that altering the basic strategy according to the count gives us a bigger and bigger edge as we see more cards. And, in case you're wondering, this applies whether the count is positive or negative!! To those strategy gains, we need to add the 'basic' edge (0.08%) and the 'insurance' edge (0.07%), since those apply to all hands. So, our average edge on hand #1 is 0.14 + 0.08 + 0.07 = 0.29; for 2 it's 0.30; for 3 it's 0.34, for 4 it's 0.37 and for 5 it's 0.40.

If you were to bet $10 on hands 1 to 3, $20 on hand 4 and $40 on hand 5, your long term expectation is $10 X .0029 = 2.9 cents on hand #1, 3.0 cents on #2, 3.4 cents on hand #3, .0037 X $20 = 7.4 cents on hand #4 and .0040 X $40 = 16 cents on #5. Add those up and your long term expectation is 32.7 cents per ROUND. You'd be betting $90 per round so the average edge on this play is 0.3633%. Your income at the rate of 60 rounds per hour would be about $19.00/hour. The catch is that your bankroll fluctuations will be considerable since that's a very small edge. $15,000 is needed and even that carries a 14% risk of total loss.

An alternative is to find a public table and sit at spot 5 ("third base"), find a friend to keep the insurance count for you and play with an average 0.40% edge, if the table is always full. With just one hand, a $10 bet will produce an average long-term return of 4.0 cents per hand and the bankroll requirement is about $3500 with a 10% 'risk of ruin'. Obviously, this is not the road to riches, but it is an edge.

How can we do better? Well, if some of you bright engineer-types out there were to develop a program which calculated the exact value of each remaining card in the deck as it related to the hand being played, you could up the Playing Efficiency to 85% or so, maybe more. Then, that hand #5 would be played with an edge of almost 0.50%. The bankroll needed is still pretty large, but what if you found a game with a dollar minimum and just put in the time and built it up?

This will, of course, also work in 'real' casinos, but the big problem you'll have there is seeing all the cards. Single-deck games are almost invariably dealt face down and players are admonished to not 'flash' their cards to other players. Even if you were to play all 5 or 6 spots at a table yourself, they require you to finish the play on the first hand before looking at the cards for the second and subsequent hands. The only exception to this is if the dealer is showing an Ace; you may then look at all your hands to see if you'd like to insure any. That allows you to fully exploit the insurance bet, if you're using a count with 100% Insurance Efficiency. There are a variety of team strategies to get the information regarding the other cards to the 5th or 6th spot player ("third base"), but the use of a computer is typically illegal, so your Playing Efficiency is going to be in the 60-65% range, at best. However, at a 'real' casino, you'll probably get two rounds before the shuffle, so you may ultimately see more cards than at an Internet casino. According to Dr. Griffin's book, the strategy gain where the player has seen 27 cards is 0.97% (for perfect play) and the insurance gain is 0.21%. The big kicker is the betting gain, since that would apply in a two-rounds-dealt game. If a player could see 15 cards before making a bet on the second round, the betting gain would be about 0.80% and there are many, many counting systems with Betting Efficiencies in the 95% area. Now you know why the casinos are afraid to offer really good single-deck games. They're chicken.

See you here next time.

  

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