Casino Control Committees believe that restrictions placed on card-counters make barring unnecessary. It is thought that by restricting players to certain rules and by varying the placement of the cut card, the threat from card-counters can be eliminated. This is not the case.

Before I present the argument in favour of barring card-counters, a little background information will not go astray.

How card-counters operate

We know that card-counters work to a strict strategy that varies according to a matrix of indices. We know that bet variation in proportion to the advantage is also essential. What is not so widely known is that all professionals work on a very strict bank-to-bet ratio, i.e. the size of the bet placed is a percentage of their bankroll at any given advantage.

There are several formulas available for calculating the bankroll required for any given degree of acceptable risk.

An aggressive strategy would recommend betting that proportion of your bankroll equal to the advantage. This is known as the Kelly Criterion. Most players would use the more conservative half Kelly or quarter Kelly. That is, simply doubling or quadrupling the bankroll requirement for a more acceptable element of risk. (1/4 Kelly gives a better than 95% chance of not going broke).

Each digit of 'true' count (running count divided by decks remaining) equates to a 0.5% advantage. In Australia, on average, the game is a 0.5% disadvantage when the player sits down at a table. So the following applies: -

a count of true 1 = 0% advantage (which brings the game to even)
a count of true 2 = 0.5% advantage
a count of true 3 = 1% advantage
a count of true 4 = 2% advantage
and so on

Therefore if a player had a $40 000 bankroll, it would be divided by 200 to give a betting unit size of $200. They would then bet $200 at true 2, $400 at true 3, $600 at true 4, $800 at true 5 and table maximum at anything above.

Successful professional players and teams operate off bankrolls large enough not to be concerned with bank-to-bet ratios. Their bet size is limited only by the table maximum - they would bet table maximum at any advantage.

For the purpose of this exercise we will assume a $200 000 bankroll and full Kelly. Playing off $200 000, subject to restrictions (one box only, must bet every hand), at a three-quarter full table with eight decks cut two, a professional would expect to earn $130/hour. He may experience huge fluctuations on this figure but will eventually get into the long run (say a year or more of 50-hour weeks).

Why casinos should be able to bar card-counters

As you can see the above player does not present a major threat to the casino's bottom line. The problem arises when he forms a team. You might expect that if he were to form a team of ten players off this same $200 000 bankroll, it would equate to ten players playing off ten $20 000 bankrolls, each with a unit size of $100 ($20 000 divided by 200).

This is not the case. Providing they play on different tables, they can all play at the same time off a $200 000 bankroll as though each were the only player. This situation does not increase the risk in any way, in fact it reduces the fluctuation (some will be winning, some will be losing) and allows a team to get into the long run almost on a month by month basis. In effect a ten-member team is simply compressing time.

Look at the following examples: -

Ten players working off a $200 000 bankroll will each have a unit size of $1000 and a return of $130/hour or $1300/hour for the team

Ten players working off 10 x $20 000 bankrolls will each have a unit size of $100 and will return $32/hour or $320/hour for the team.

Conclusion

It can now be seen that a single player with a $200 000 bankroll, working 50 hours a week for 45 weeks of the year, will have an expectation of approximately $300 000 and will experience significant fluctuations. On the other hand, the ten-member team working off the same $200 000 bankroll and putting in the same hours will have an expectation of around $3 000 000 with far less fluctuation from this figure.

On a lesser scale if you have a dozen or so competent players each with a few thousand dollars, their impact to the bottom line is insignificant and the return to the players not sufficient to warrant giving up their day jobs. However if they pool their resources you now have a dent in the bottom line, high turnover with low hold and players earning a tax-free wage.

It also seems unreasonable that a casino can't prevent a card-counter from playing when the following is taken into consideration: -

Whilst all casino bets put the player at a disadvantage he is not obliged to accept those bets. He may look at Keno and say "no way will I give away 40%." Conversely, the casino, when faced with a competent card counter, is forced to make a disadvantage bet.

This does not seem equitable.

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