When an advantage player looks at opportunities, two competing factors pull him in opposite directions. The first is the profitability of the opportunity, also known as expected value (EV). The greater the profitability, the more the AP wants to play the game.  In the other direction is volatility, also known as the standard deviation (SD). The AP would like to earn his profit with as little volatility to his bankroll as possible. In other words, the AP wants the value of SD to be as small as possible. The fraction EV/SD captures both of these values in one number.  As EV gets larger, the fraction EV/SD gets larger. As SD gets smaller, the fraction EV/SD gets larger. The AP wants this fraction to be as large as possible.

This fraction is exactly what the “Desirability Index” or DI captures. Here is Donald Schlesinger’s definition of DI from his book “Blackjack Attack” (page 186):

I have christened this ratio the “Desirability Index” (DI) and have defined it, for the play all game, to be equal to one thousand times (for convenience of expression) the ratio of that game’s per-hand win rate to the per-hand standard deviation. Similarly, for the back-counted game, DI = 100 times the ratio of that game’s win rate per 100 hands to the s.d. per 100.

For a game where the AP is back counting and only makes a wager when he has the edge, the value of DI in Schlesinger’s definition is given by:

DI = 100*(win rate per 100 hands) / (standard deviation per 100 hands)

The numerator is the EV per 100 hands. The denominator is the SD per 100 hands. In other words,

DI = 100x(EV-per-100/SD-per-100)

The larger the value of DI, the more likely it is that the AP will consider playing the game.

For a baseline, recall that when considering the world’s greatest blackjack player, we get the following DI’s for ordinary blackjack card counting:

  • For two decks, with the cut card placed at 75 cards (29 from the end): DI = 9.9.
  • For six decks, with the cut card placed at 260 cards (52 from the end): DI = 5.4.

As written in the glossary at bj21.com, the ordinary blackjack card counter,

would look for a desirability index of 6.6 or higher to find game which would be considered to be playable to most counters.”

In other words, the benchmark value of DI is 6.6. Above that, the game is considered playable. Below that, the blackjack card counter should look for something better.

There is a third factor that is important to understand when considering the likelihood of advantage play. This is the amount of money the AP can actually get down on the table. The higher the DI, the more the AP would like to wager. However, many side bets have austere limitations on the maximum wagers that can be placed. A high DI does nothing if the AP can’t get make large enough wagers to make it worthwhile.

For example, consider a highly bankrolled AP who can afford a $2000 maximum wager as an ordinary blackjack card counter on a double-deck game with a DI of 9.9. This AP will earn about $1300 per 100 hands. Compare this to the same AP wagering a table maximum $25 on the blackjack side bet Field Gold 21 with a DI of 22.9. This AP will earn about $60 per 100 hands off of the side bet. There is simply no question that this AP would choose ordinary blackjack card counting. However, for an AP with a limited bankroll, blackjack side bets become a much stronger play. In other words, only the extremely profitable blackjack side bets will attract top-level APs. The weekend-warrior AP is much more likely to be satisfied playing against blackjack side bets than the pro.

Baccarat is a whole different universe.

What makes baccarat side bets especially appealing to APs are the high table limits that often accompany them. It is not unusual to find EZ Baccarat tables with a $300 (or higher) maximum wager on the Dragon 7 and Panda 8. A team can play all the spots on the table, getting in excess of $2500 in play on a single hand. There are many casinos in Asia that allow Pair bets in excess of $10,000. The Tie bet can sometimes be played up to the table limit. Because the AP can get the money on the table in baccarat, side bets with equivalent values of DI in blackjack and baccarat are not at all equivalent. For top-level  APs, it’s all about being able to wager enough to make it worthwhile. Baccarat side bets are worthwhile.

The following table gives DI’s for all of the baccarat side bets I have considered. In each case, I use the best practical card counting system available.

baccarat side bets: desirability index

There are three side bets in this list that are computed in a slightly modified way. These side bets allow two opportunities per hand to make the same bet, once on the Player hand and again on the Banker hand. The card counting system for both is the same. The trigger true count is the same. When the count indicates, the AP then makes the same wager on both the Player and Banker hand. These three side bets are:

  • Natural 9
  • Natural 8
  • Pairs bet

For these side bets, the EV per 100 hands is twice as high, because the player can make 200 wagers in 100 hands. The standard deviation is also slightly higher, being multiplied by √2 (the square root of 2). The values in the table already reflect these modifications.

There are also several side bets in this table that allow concurrent wagering opportunities. Each sub-wager has its own counting system, EV, SD and DI. For these side bets, a team can keep track of the various wagers the side bet allows, using a separate card counting system for each. When any team member makes a wager on the side bet he is counting, the other team members follow suit, also making that wager. The “team” side bets are:

  • Dragon 7 and Panda 8
  • Lucky Win Player, Lucky Win Banker
  • Natural 8, Natural 9
  • Super Pay Egalite
  • UR Way Egalite

There is no obvious way to compute DI’s for team side bets with multiple betting opportunities. Each side bet has its own EV, SD and DI. Each member of the team gets the full benefit of the DI.  I am going to compute the total DI assuming "independence" of these bets. That is,

  • Total EV = sum of the EV's (per 100 hands) for each individual wager.
  • Total SD = square root of the sum of the squares of the SD's (per 100 hands) for each individual wager.
  • Total DI = 100x(Total EV)/(Total SD)

Before I give the overall results, I want to review my “risk” categorizations:

  • minimal: no meaningful risk to advantage play.
  • low: very low risk, card counting is highly unlikely.
  • medium: risk is roughly equivalent to ordinary blackjack card counting, take equivalent measures.
  • high: substantial risk to high-level advantage play, game should be carefully monitored.
  • extreme: imminent risk of significant loss to advantage play, take immediate steps to safeguard game.

The following table summarizes the Total DI’s, along with a risk assessment for each side bet.

baccarat side bets, total DI and Risk

Unlike blackjack, where the risk is usually constrained by low maximum wagers, in baccarat the risk of high-level AP play is significant. Only the Tie bet and the Dragon Bonus are truly low risk to the casino. Starting with the Dragon 7 / Panda 8 combination, there are dedicated high-level AP teams that are actively seeking out and beating these side bets.

Watch your games!

Received his Ph.D. in Mathematics from the University of Arizona in 1983. Eliot has been a Professor of both Mathematics and Computer Science. Eliot retired from academia in 2009. Eliot Jacobson