Suppose the world’s greatest blackjack card counter heads out to a casino to pursue his chosen vocation of beating the house. Our hero sits down and starts to count. After a few hands, he realizes that the casino doesn’t care: he is free to count the day away, playing and spreading his bets however he likes. He righteously believes that this is just how he believes it should be: if a player is playing by the rules, then he should be allowed to play. There is no more injustice in the world for our hero. He no longer has to play the game within the game. It's all about winning. He hungrily starts pushing chips into the betting circle. At the end of a long day he looks down at his winnings and can hardly believe the result.
This post answers the question left hanging -- what is his result? To get there, we need to set some parameters for this player. I will assume this counter uses the well-known high-low count. Because he is the world’s greatest card counter, he knows every strategy index (there are well over 100 of them). He left the so-called "illustrious-18" in the dust years ago. This counter plays these strategy deviations without error. The only other decision he has to make is the size of his bet, which will be based on the true count.
The counter knows that when the true count is +1 or higher, he will have the edge, otherwise the house has the edge. He decides that when the true count is +1 or higher, he will wager $100, otherwise he will just sit out the hand and wager nothing at all. He doesn’t care about the Kelly criterion, risk aversion, or betting ramps. He simply wants to maximize his profit. By betting his maximum wager whenever he has the edge and otherwise betting nothing at all, he will squeeze every drop of profit that is possible from the game.
We are witnessing the world’s greatest card counter in the world's best casino. He counts perfectly. He plays perfectly. He wagers perfectly. And the casino doesn't care about this card counter, not one bit.
Question: With a maximum wager of $100, how much does the world’s greatest card counter expect to win per 100 hands?
Try and come up with an answer to this question for yourself. Then, take whatever number you’ve come up with and divide it in half. Once you have come up with that number, read on.
This counter’s win-rate is as good it gets. No counter who uses the high-low system and has a maximum bet of $100 can win more than this counter. By determining this counter's earning potential, we will have an absolute upper bound on the win-rate for all blackjack card counters.
To answer the question posed above, I contacted Norm Wattenberger, the world’s greatest blackjack card counting analyst. Norm wrote the Casino Verite software, which has been the standard-bearer for analytic tools used by card counters for over 15 years. I asked Norm to analyze both a two-deck and a six-deck game. Norm very generously performed these simulations for me back in December, 2012.
First I will consider the two-deck game. The specific blackjack rules I considered were:
-
Two decks, cut card placed 29 cards from the end.
-
Dealer hits soft 17.
-
Player can double on any first two cards.
-
Player can double after split.
-
Splits aces receive one card each.
-
Blackjack pays 3:2.
The house edge for this game using basic strategy is 0.392%
Norm ran a simulation of 718,194,064 two-deck shoes for me. Based on this simulation, here are the results for the perfect card counter playing the two-deck game above:
-
Percent of hands with edge: 33.67%
-
Average edge: 1.97%
-
Win-rate per 100 hands: $66.30
These results show that the true count will be +1 or higher on 33.67% of the hands, so this is the frequency of the counter’s $100 wagers. The rest of the time the counter will just sit there counting but not betting. When he does make a wager, on average, the counter’s edge will be 1.97% over the house.
If we assume that this card counter is using just a little bit of cover, by betting $10 whenever the house has the edge and $100 when he has the edge (in other words, a bet spread of $10 to $100), then this counter’s win-rate goes down to $57.97 per 100 hands. Other factors will bring down the counter’s win rate even more, most notably shallower cut-card placement. Any counter less gifted than the world's best card counter, in any casino other than the world's best casino, will find it tough to win more than $50 per 100 hands playing a two-deck game.
Next, I consider card counting a six-deck shoe game. It is commonly believed that six-deck games yield less profit for the counter than two-deck games. The numbers for our perfect card counter demonstrate this truth.
Suppose our perfect counter is playing a six-deck shoe game with the following rules:
-
Six decks, cut card placed 52 cards (1 deck) from the end.
-
Dealer hits soft 17.
-
Player can double on any first two cards.
-
Player can double after split.
-
Splits aces receive one card each.
-
Blackjack pays 3:2.
The house edge for this game using basic strategy is 0.618%.
Again, assume our perfect card counter makes a $100 wager whenever he has the edge (true count of +1 or higher), otherwise he just sits at the table. Norm Wattenberger ran a simulation of 210,108,096 six-deck shoes for me. Based on Norm’s simulation, here are the results for the perfect card counter:
-
Percent of hands with edge: 28.99%
-
Average edge: 1.16%
-
Win-rate per 100 hands: $33.58
On a six-deck shoe game, our perfect card counter is earning under $34 per 100 hands.
If we assume that our perfect card counter uses just a little bit of cover, betting $5 whenever the house has the edge and $100 when he has the edge (in other words, a bet spread of $5 to $100), then his win-rate goes down to $29.37 per 100 hands. Any counter less gifted than the world's best card counter, in any casino other than the world's best casino, will find it tough to win more than $25 per 100 hands playing a six-deck shoe game.
To summarize, with a $100 wager whenever the count is +1 or higher, and a $0 wager otherwise:
-
For a two-deck game with rules (H17, DOA, DAS), the maximum win-rate is $66.30 per 100 hands. The practical maximum win-rate is about $50 per 100 hands.
-
For a six-deck game with rules (H17, DOA, DAS), the maximum win-rate is $33.58 per 100 hands. The practical maximum win-rate is about $25 per 100 hands.
The blackjack card counter is making a high frequency of wagers with a very small edge. This creates huge volatility with very little profit potential. With the vast variety of advantage play opportunities offering win-rates significantly higher than ordinary blackjack, the question becomes, why count cards at all? The answer is that there are very few professional card counters.
Indeed, most advanced advantage players view ordinary blackjack card counting with professional disdain. Some are actively hostile towards the proposition that they would even consider blackjack card counting. Blackjack card counting is to advantage play as a can of cat food is to a grocery store.
Nevertheless, there are two main reasons that ordinary blackjack card counting continues to be viable as a method of high-level advantage play:
-
The maximum wager for an ordinary blackjack card counter is bounded by the table maximum, which is typically much higher than $100. For example, with a $5000 table maximum, the card counter can win up to 50 x $66.30 = $3314 per 100 hands.
-
Other incentives and advantage play opportunities often accompany high-limit blackjack play.
The card counter cannot, under any circumstances, win at a higher rate than the win-rates given in this article. There are many on both sides of the tables who believe, in the face of extraordinary evidence to the contrary, that card counters can squeeze vast quantities of water from rocks. The world’s greatest card counter can do no better than a few precious drops. What was the result for our hero? Not nearly enough to make it worthwhile.
Advanced advantage players know that ordinary blackjack card counting is a waste of time. They may be hole-carding blackjack, or possibly counting a highly vulnerable side bet. They may be playing a lucrative loss rebate incentive. They may be crushing the carnival game on the adjacent table using any number of powerful methods. They may be edge sorting baccarat for millions, or beating the pairs bet using a smart-phone app. But, advanced advantage players are not card counting blackjack all by itself. They have better things to do.
