The effect of advantage players on bj hold percentage

Posted by Green Baize Vampire on 8 Dec 1998, 3:06 am

Blackjack is not a zero-sum game. The game of cat and mouse between industry and professional player is unneccessary and self-defeating: their relationship is symbiotic. Conditions could easily be fostered to the mutual benefit of both.

Take the following example: You are a pit boss whose sole aim is to maximise the win rate of your casino. You are watching a high roller flat bet the table maximum of £1000 on a four-deck game. You have been casing the deck and know there is an excess of high cards remaining. Suddenly a player jumps in and starts betting £100 a hand. You know this player is a professional backcounter-you have seen this man in the files kept by a detective agency who catch cheats and advantage players. What would you do?

If you answered "I would bar the player before he could make another bet", then you were incorrect, although I believe this is what 95% of executives would answer. In this instance, to bar the backcounter is to lose money. The backcounter is effectively shorting the deck of good cards. He, personally, is winning, but the high-roller suffers because of the extra hands that have been taken away from him in a good deck. Because the high-roller bets ten times what the backcounter is wagering, overall the effect is to increase the win rate of the casino.
By how much? Over 100 hands the backcounters win rate will be £20 (he is only playing a small number of these hands, though his advantage is quite large when he does play). Over 100 hands the high-roller, following basic strategy ( a high quality of play is associated with high-rollers) loses about £550. With the backcounter lurking this rises to £650, an increase of £100. Overall the casino gains £80 per 100 hands because of the backcounter.

This phenomena is linear with the number of decks, the casino always gains if the average bet of the backcounter is half of that table, yet the effect is stronger the fewer the decks used.

If you add additional ordinary basic strategists the effect of the backcounter on the win rate of the table is the same: however, for each individual player the effect is diluted. If their were two high-rollers in our above example each would lose $50 an hour because of the good cards that were sacrificed.

Note that in actual play the backcounter is even more likely to benefit the casino. The above figures assume the counter plays perfectly. Clearly this is not possible. The mental drudge of playing like an automaton day after day leads to inevitable errors. In the words of the legendary Ken Uston "An analogy might be made with tennis players-All players make mistakes: good players make very few". Therefore the expected win rate of the counter will be smaller than the above figure. By how much? Well, professional players regularly report that their actual earnings are no more than half of their expected earnings. Some card-counters do not vary the play of their hands with basic strategy, or use a limited range of indices. In this case their average expectation will be less. Also, the play of high-rollers, while generally above that of low stakes players, is generally worse than basic strategy. Certain errors are typical:- they take insurance, they stand with stiff hands Vs a 10 etc. These plays are erroneous with a full deck, yet they become correct when an excess of tens remain. If the backcounter is taking cards away in these ten-rich situations then the effect of these bad plays is exacerbated.

Now, the perceptive casino executive might say, "But there are other considerations besides the raw amount of money won, I do not wish my high-rollers game to be ruined by an undesirable player. I value their patronage more than the small extra gain produced for this comparatively short period of play.", which is fair enough, except that I specified the executive's sole aim was to maximise win rate. By all means, use this information as you see fit, but be aware of it.

*The above figures are based on my native English game, which has government-imposed restrictions on insurance and splitting decisions. In the absence of these restrictions in the US the player would win at a marginally higher rate.

Note that the difference between the amounts being bet does not have to be nearly as drastic in my example for the casino to benefit from the backcounter's intervention.

To illustrate the phenomena further I have conducted a range of simulations which are more typical of the games offered in US casinos.

To begin with I ran a simulation on a game with the following rules:- 6 decks, dealer stands on any 17, double-down allowed on soft hands, pairs split only once, double on splits and no surrender. 75% of the cards were dealt out. This is typical of the rules in Atlantic City. A simulation of 50 million hands gives the $10 basic strategists advantage as follows:-

Win rate per hour = -$4.62 % Disadvantage = 0.409% Action=$1032

The standard error on 50 million hands is .025.

Now adding a backcounter who enters the game at a true count of +1 and leaves at a count of 0, again betting $10

Win rate per hour=-$6.02 Disadvantage = 0.533% Action=$1032

The backcounter himself has these results

Win rate per hour=$2.32 Advantage =0.995% Action=$234

These statistics may have limited application because backcounters at the 6-deck will not generally be satisfied with flat betting. By spreading their bets to a mild extent they can greatly increase their profits and maintain the same risk of ruin. As long as the backcounters play one hand only this will have no effect on the basic strategist at the same table. A backcounter who spreads from 1-4 units will have the following expectation:-

Win rate=$5.74 Advantage=1.25% Action= $458

Note that in Atlantic City, virtually no counters will play through all counts no matter how negative. The bankroll requirements are just too high for that style of play in the shoe game.
In the more and more frequently used eight-deck game a card-counter must spread his bet from 1-32 units before he can get a reasonable edge with a play-all style! To successfully play in Atlantic City a professional must avoid most negative counts. I suspect that because of this the majority of advantage players located in AC have made as much money for the casinos as they have done for themselves. The no-barring rule in effect in AC has worked to the industry's advantage.

AC has probably the worst conditions for advantage or regular blackjack players in the world. By contrast Reno, Las Vegas has the best, with the single-deck game still prevalent.
Two rules that typify are that the dealer hits soft 17 and doubling is only permitted on hard hands of 10 or 11. Again a simulation of 50 million hands gives us the basic strategists expectation:-

Win rate per hour=-$5.76 Disadvantage = 0.530% Action=$1090

With a backcounter adopting the same strategy as before (A TC of +1 does not give the backcounter an advantage but by leaving all negative counts in the single-deck game he still has a very good edge):-

Win rate per hour=-$8.74 Disadvantage= 0.803% Action=$1090

Note that the effect of a backcounter is twice as devastating to the basic strategist as in the AC game. The downside from the casinos point of view is the win rate of the backcounter:-

Win rate per hour=$8.16 Advantage =2.47% Action=$330

These figures suggest that if the backcounter's bets are large relative to the basic strategist he poses some threat to the casino in this very favourable game, assuming he is a sufficently competent player. However, if the reverse is true the backcounter could save the casino a fortune!

In either case, there is less practical relevance to this study currently, as the single-deck game is watched very closely making backcounting difficult to pull off undetected. Many counters are happy to play every hand at single-deck because a small spread will give them quite a big edge. Nevertheless, because the phenomena we are studying is strongest and most easily observed I have provided data of the expectations of the basic strategists advantage with and without the backcounter at the conclusion of this report.

Moving to downtown Vegas we find that typically the dealer hits soft 17, and that doubling-down is permitted on any two cards, though not after splits. Two-deck games are popular here. The basic strategist plays at the following disadvantage:-

Win rate per hour=-$6.42 Disadvantage=0.574% Action=$1118

Adding a backcounter, who now enters at a TC of +2 and leaves at -1, because a TC of +1 (worth 0.5%) does not give him the edge, and he can no longer rely on gain from play variation and deck fluctuation as much as in single-deck:-

Win rate per hour=-$7.36 Disadvantage=0.658% Action=$1118

While the backcounter performs like this

Win rate per hour=$3.64 Advantage=2.530% Action=$144

Note the drastic difference made by adding the single-deck and the fewer hands played. Despite the dramatically reduced expectation many card-counters prefer double-deck over other forms of blackjack. Double-deck is not watched as closely as single-deck, yet provides superior returns over six or eight decks.
Because the backcounter is now waiting for a higher TC than before he is no longer playing the marginally favourable but frequent TC's between 0-1. This means he has a much less effect on the basic strategist, even than in the 6-deck game.

There are two other implications of this study with respect to backcounters: firstly, in jurisdictions where blackjack shills are permitted, a casino could employ shills to backcount and cheat high-rollers. I wouldn't recommend this: the more traditional tactic of preferential shuffling is far more effective, and both are very dubious legally grey practices likely to damage the casinos reputation and lose money in the long-term. To illustrate, the basic strategist loses roughly twice as fast in shoe games when any count of +2 is shuffled, and an amazing twelve times as fast in a single-deck game! In our first example the high-roller would lose an extra $600 an hour with such a shuffle. This is six times more effective than employing a shill to enter the game at all plus counts.

Secondly, it is possible for teams of advantage players to use the opposite tactic :- a minimum bettor will sit at first base, and spread to multiple hands in negative decks. A high-roller will sit in third base and play basic strategy or flat bet and vary the play of his hands using a count system optimized for playing efficiency. The high-roller's gains will far outweigh the small player's losses, yet neither exhibits play of the traditional card-counting variety. Only the sharpest of pit bosses will pick up on this. Norm Wattenberger conducted a study on the subject. Taking a double-deck game with typical rules, player A using the High-low system and player B using the Advanced Omega II system, he determined that if player A played two hands in negative counts and one hand in positive counts and bet $15 per hand, then B betting $250 on a single hand would win $80 an hour. The total win for the two players would be $70 an hour.Wattenberger reports that the methodology is ultra-sensitive to penetration.

This effect is even stronger in single-deck, though it is not possible to use this method if a fixed number of rounds are dealt. A gain of 1.2% is possible under typical conditions.

Such a team can enhance their earnings further if the small bettors play their hands in order to "preserve" a high count or use up cards in a negative count for the benefit of the high-roller. They can then appear to be playing very badly by making plays contrary to common sense when in fact they are boosting the win rate of the team.

A yet more subtle refinement of this method involves the minimum bettor spreading to multiple hands off the top of the shoe, then dropping back to one hand later in the deck, regardless of the count. This allows the big player to play more hands deeper into the deck, when the gains from play and bet variation are largest. A gain of 0.5% can be achieved with a minimum bettor spreading to three hands in the first two rounds, cutting back to one thereafter.

Of course, while most advantage players do not play every negative hand many do not fit into the strict backcounting variety either.

How does a more common variety of card-counter affect the game? Well, it depends greatly on his style of play, not only how often he leaves negative decks but how many hands he plays in both positive and negative decks. The issue is complex: some card-counters play several hands in negative decks and play only one in positive situations. This is style of play, known as "card-eating", was pioneered by Ken Uston in "Million Dollar Blackjack". It increases the expectation of the card-counter by using up more cards in negative decks leading to less money wagered in those situations. Conversely, many players do the exact opposite of this and play one hand in negative decks, spreading to multiple hands in positive decks. Why do they do this?

The reason is that although they play more hands in negative decks and slightly lower their win rate, spreading to multiple hands reduces fluctuation. Fluctuation is greatest when the card-counter has his large bets out, therefore spreading to multiple hands allows the card-counter to lessen the wild streaks a full-time player must endure. This strategy has recently been popularised by Don Schlesinger in "Blackjack Attack". Some players will also play multiple hands in order to exceed the table maximum.

Card-eaters tend to prefer single or double-deck. Card-eating can noticeably increase expectation in these games, and has the reverse effect on the win rate of the table that backcounters do- ie the other players lose at a much slower rate, or if they play something close to basic strategy may have a positive expectation!

Players who follow the Schlesinger strategy tend to play six or eight-deck games. This is because the bankroll requirements to play in these games are high and the counter needs to reduce fluctuation by any means available, also the loss of extra cards in favourable situations is much less significant, which means that the effect on other players is not of great importance. Schlesinger recommends not spreading to multiple hands till a true count of +5 is reached. This happens very rarely in six-deck games.

The card-eater has a beneficial effect on the expectations of each individual player at the same table. The player who spreads to multiple hands in positive decks has a negative effect . In both cases the effect on another individual player will not be as large as the advantage gained by the card-counter, but the effect on the whole table may well be more significant than the expectation of the card-counter, especially if more money is wagered by the players.

Note that card-counters tend to follow quite conservative betting strategies. A professional following an optimal betting strategy will bet 1/1500 of his bank for every TC point. A backcounter will bet 1/350 of his bankroll for every TC point.

It may well be that card-counters bet significantly less of their total bankroll than the average player because they fully understand the risks involved. The average player, by definition does not understand the risk involved, which is certain and inevitable ruin if they play for long enough with a negative expectation.
Of course, there are other methods to advantage play at blackjack The bulk of these involve some method of hole-card play. The advice given concerning hole-card play in the standard reference works contains almost all of what an executive needs to know. Hole-card play in itself has no effect on the expectation of other players at the same table, though the hole-card player, particularly one who exploits front-loaders, represents a sizeable threat to the casino by himself with a win rate of 6-7%. Without exception the casino should exclude hole-card players, though the danger has become incidental since many casinos switched to no hole-card.

The other well-documented method of blackjack advantage play involves analysis of the shuffle. The most well-known shuffle-tracking method involves cutting segments of unfavourable cards out of play. By itself this gets the shuffle-tracker between 0.5-0.8%, and more importantly so does everyone at the table. This would seriously lead me to question the logic of the casino industry, which has slowly been abandoning single-deck games (which are easy to shuffle thoroughly and foil tracking) in favour of multiple-deck games (which are harder, and sometimes impossible to randomise without slowing down the game overmuch). Moreover the shuffle-tracker wins at a much higher rate than the regular card-counter. There is some compensation to the casino if the shuffle-tracker does not play negative slugs. The shuffle-tracker has a much better idea of when the deck is bad than a regular player, so this will ameliorate the effect of skilled cutting to a certain extent. The conclusions concerning spreading to multiple hands for card-counters are also valid here, though even more so.

Advanced trackers use a method known as ace location.This has a devastating effect on the other players at the table (though many ace-location teams prefer to monopolize the table) since ace locators effectively short the deck, causing the other players to lose at the rate of 1 -2% (depending on their skill and the number of riffles).

It is easy to see that, overall, the effect of the advantage player has on the casino hold percentage is not nearly as obvious as first thought. The countermeasures the casino use against such players are frequently, if not decisively, counterproductive. It is not difficult to see that measures such as "no mid-shoe entry" cost the casino greatly. Often the consequences of such measures are not properly considered. No mid-shoe entry for example may prohibit backcounters, who we have already established are not the threat they are thought to be,but it greatly assists play-all counters and shuffle-trackers. Play-all counters benefit because other players cannot enter during the course of the shoe, yet players already at the table can leave. This means that there are more likely to be other players at the start of the shoe and less likely to be any at the end. The counter gets more hands at the end of the shoe when play variation and bet variation are most valuable. Shuffle-trackers get to sit down and record the value of the various slugs dealt out without having to bet, greatly easing the considerable mental burden of shuffle-tracking.

It should be recognised that the elimination of advantage players, even if it were possible, is not particularly desirable.

There is the potential for an effective compromise between advantage players and the casino industry whereby advantage players can excersize their skill without harassment and the casino can realise greater profits. This can be achieved by for example permitting backcounters to play at the table minimum, or to a tenth of the table maximum. Regular card-counters could be encouraged to play multiple hands in positive counts. It is unlikely the advantage player will be making money for the house in each and every instance, but procedures should be considered so that the advantage player increases the hold percentage over the long haul. For example, a backcounter may enter a game with one other ordinary player betting $50. The backcounter may start betting $75. In this instance his presence is costing the house a small amount. Yet if there are high-rollers betting $500 at three other tables in the casino, it is better to let the backcounter play this shoe in the likelihood he will move into one of their games.

In most instances, the backcounter will be marginally taking or losing money from the house. However this may be deceptive. There is an asymmetry between what the backcounter can take from the house and what the backcounter can make for the house. Occassionally the backcounter will wander into a game with a whale and "make up" for any expected value they have taken from the house previously.

An obvious, yet important point to remember is that backcounters cannot play on their own!

A final consideration is that the amount of cards dealt can and should be increased when the advantage player is increasing the table win rate. For a long, long time paranoid casinos have been unnecessarily cutting large numbers of cards out of play to foil card-counters. Card-counters and some enlightened executives have argued this costs the casino far more in shuffle-time and fewer hands per hour than it saves in the pitiful losses to counters. Further to this consideration is that if an advantage player is increasing the table win rate dealing out more cards will increase the win rate of the table dramatically.

Neutral observers might point out that such a cosy arrangement hurts the interest of ordinary players. However, this is not necessarily the case, since ordinary players are already paying for the huge cost casino surveillance and game protection measures, which would cease to be of such importance, and are losing money to backcounters whether the casino knows it or not. Further, unskilled players are sometimes barred or badly treated mistakenly when their betting patterns accidentally coincide with those of a professional. One such experience can easily put a customer off gambling for life.

By all means do not be uncritical of these findings: do your own research and specify the particular game conditions you offer. It is in your own interest to do this. But the general conclusions here cannot be contradicted. They are not assertions or opinions: they are fact. If you run simulations and your methodology is sound you will come to identical conclusions.