TABLE TALK: Theoretically speaking
by Elliot Jacobson
October 17, 2011
One of the most significant challenges for marketing is getting an accurate estimation of the theoretical win (theo) for proprietary table games players.
The mathematics is provocatively simple: theo is equal to (rounds played) x (average bet) x (house edge). With slots, the data gathered gives a spin-by-spin record of a player’s gaming activities so that his theo can be accurately computed. For table games, this computation is much more subjective. It’s not just that marketing can’t get close—the numbers for tables are often so unreliable that some players are given a fraction of what they’re due, while others are deluged with gratuities.
If a table games player is given too much reinvestment based on an erroneously high theo, then the casino can easily get upside down with the player making him a capital expense. If a player is given too little reinvestment based on an erroneously low theo, he will take his business to where he is more appreciated. Either way, it’s a loss for the casino. The obstacles to getting an accurate estimation of a table game player’s theo have only been compounded in recent years by the explosion of proprietary games and side bets.
For proprietary games, it’s usually not correct to look at one wagering spot to estimate the average bet. Some games have up to five wagering spots for the main game, as well as one or more side bets. In determining the average bet, the question of which bets should be averaged is fundamental.
The problem of determining the average bet is intertwined with the equally sticky issue of house edge. First consider proprietary side bets. If a player splits his bets evenly between the main game and a side bet, then the house edge is simply their average. But players rarely do this. They mix and match wagers among various opportunities in ever changing amounts. Some side bets have a house edge lower than the main game (e.g. a commonly used Pair Plus pay table in three card poker). The house edge for other side bets can be more than 20 times the house edge for the main game (e.g. the Fire Bet in craps and Lucky Ladies in blackjack). A $100 blackjack player who places a $5 wager on the Lucky Ladies bet is generating the same theo as a $200 blackjack player. How does the casino rate a craps player who plays the proposition bets and Fire Bet heavily? How does this compare to a player who is only playing the pass line and taking full odds?
Unlike blackjack and craps, very little is known about the practical house edge for the new breed of proprietary games. A game like Ultimate Texas Hold’ em has a house edge of 2.18 percent if the house is only counting the ante bet in determining average bet. However, player strategy is extremely complex and has never been fully quantified. Poor play can easily drive the house edge over 5 percent. On the other hand, this game has a house edge of 0.53 percent if all wagers are used in determining the average bet, making a 10-times error in theo a real possibility.
Game pace can also be a real head-scratcher. If a rating formula paces craps at 50 rounds per hour, is that 50 rolls of the dice or 50 pass line decisions? A complex side bet or rule change for blackjack can slow the game down well below the formulaic pace.
Several commercial products have been created to address the theo dilemma. Some of these systems rely on RFID chips. However, the cost of these chips is daunting. In addition, special tables have to be used with their own lease fees and training overhead.
The old fashion approach is to systematically audit the current systems, to reorganize rating procedures, to educate staff and to update technology. Those employees who engage in rating players should be well trained on each game. This includes training on which wagers are counted, how to estimate average bet when players split wagers among various options, and how to assess a player’s skill level. Game pace should be carefully tracked for all games. A modern table game data system should be used.
For the time being, rating table games is going to remain more art than science. However, if the worst rating offenses are repaired, staff is adequately trained, and the data systems are gradually improved, the result will be more accurate ratings for more players. By giving players the reinvestment they’ve earned, but no more, the bottom line has nowhere to go but up.
is president of Jacobson Gaming, based in Santa Barbara, Calif. He has held positions as professor of mathematics and professor of computer science, and with dozens of research articles, publications and media appearances to his credit, he is widely recognized for his expertise in casino table games and casino game mathematics.
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