CASINO-OLOGY: The Myth of Offsetting Betting

The message of this month’s behind-the-scenes breakdown of casino play from game extraordinaire Bill Zender (l.) is cut and dry: offsetting betting is a myth, and actually falls in the house’s favor.

CASINO-OLOGY: The Myth of Offsetting Betting

I need to put this casino “myth” to bed for the last time. I thought I had done it several years ago but just recently it has reared its ugly head one more time.

The myth you ask?: The false belief that offsetting bets placed for the same or similar amounts wagered on bets that appear to be in opposition of each other. Here is the honest truth on the offsetting situation whether it is done in Baccarat with the Player/Banker wagers, in Craps with the Pass-line/Don’t Pass-line, or in Roulette on opposite even money bets (example: Red/Black):

Offsetting bets do NOT change, alter or eliminate the casino’s mathematical advantage! End of story!

Just recently I was involved in explaining why offsetting bets in the game of Baccarat does not pose a problem for the casino. In fact, offsetting wagering is greatly in the casinos favor. It guarantees that the casino will have a winning outcome, and it eliminates any degree of outcome volatility.

Here’s the basic explanation using Baccarat as an example:

Any wager made on the Player and on the Banker during the same hand is still subject to the wager’s mathematical advantage regardless of whether both wagers are of equal or similar amounts. If a customer places $100 on the Player and at the same time places $100 on the Banker, the Player wager is still subject to a house advantage of 1.24 percent and the Banker is still subject to a house advantage of 1.06 percent.

Based on these mathematical advantages, the customer placing the $100 on two separate wagers (a total of $200), is subject to a casino theoretical win (T-win) of $1.24 plus $1.06 for a total T-win of $2.30 for the $200 total wager.

Another method for calculating this is to combine the two mathematical advantages and estimate an average of the two. This calculates to 1.24 percent + 1.06 percent = 2.30 percent. By dividing this percentage by 2, the average is 1.15 percent. Since the customer in the previous example wagered a total of $200, the actual T-win is $200 X 1.15% = $2.30, the same dollar outcome as the example in the previous paragraph.

There is a third method for calculating the T-win for this situation and that is by multiplying each bet by the probability of both a positive and negative outcome (see Table 1). The dollar outcome is still the same even though there is a slight difference because of net payout rounding.

Table 1 – Win/lose Probability Model

Presented in this article are three different methods for supporting the fact that offsetting betting does not change the theoretical win of the casino using the Baccarat Player/Banker model.

These previous examples should be enough to prove the point, but unfortunately, I still get push back from casino people who are on the casino floor and watching Baccarat on a regular basis. They rationalize on what they observe and tend to doubt anything that needs to be proven based on theoretical events. In other words, if they do not see it happen, they don’t trust the theoretical outcome.

At this point I reached out to mathematics expert and past advantage player Dr. Eliot Jacobson. Eliot has in his possession a game simulator that he uses to determine different outcomes in Baccarat. I asked Eliot if he could run some Baccarat game simulations where a customer wagered the same amount of money, preferably $100 and $100, on the Player bet and Banker bet at the same time. I asked him to run ten separate simulations representing an eight-deck Baccarat shoe where 75 hands are dealt and wagered. I wanted a sample of ten shoes, simulated randomly, as an example of what actually happens when a customer offsets betting. Always the mathematician, Eliot pointed out that 10 shoes were not enough to take in a full spectrum of possible outcomes, that to be more accurate he would have to run more than ten shoes, much more than ten. I explained that for this example, ten random shoes were enough.

Eliot suggested that I use three examples of play: (1) the Player only outcome, (2) the Banker only outcome, and (3) the offsetting outcome. He explained that the three examples would help show the readers that Offsetting Betting would always return a positive outcome to the casino, as well as eliminate any outcome volatility. The results are as follows.

The Player example (Graph 1) shows the various outcomes of the ten randomly dealt eight-deck shoe over 75 hand decisions. The green line indicates the T-win for 75 decisions of $172.50 while the red line indicates the amount of comp dollars earned (customer reinvestment) based on a reinvestment percentage of 20 percent of T-win. Note that the variance in shoe outcomes is quite extreme with a Player losing of -$3800 during Shoe 2 and winning $1800 during Shoe 4.

Graph 1 – Customer Betting $200 on the Player Wager

The Banker example (Graph 2), run simultaneously to that of the Player example, also shows the various outcomes of the ten randomly dealt eight-deck shoe over 75 hand decisions. As in the previous example, the green line indicates the T-win for 75 decisions of $172.50 and the red line indicates the amount of comp dollars earned. Please note that the Banker example is the corresponding opposite to that of the Player. For every time the Banker lost, the Player would win and vice versa. Graph 2 indicates that the customer betting on the Banker wager also shows a huge outcome variance from a -$2000 loser during Shoe 4 and a $3400 winner during Shoe 2.

Graph 2 – Customer Betting $200 on the Banker Wager

In both examples, there is evidence that the outcomes of the shoes vary greatly with some shoes equaling or surpassing T-win while some shoes losing or not coming close to the calculated T-win, or for that matter, enough to cover the amount of customer reinvestment. This is not the case in Graph 3 when subject to offsetting betting.

Graph 3 – Customer Offsetting; Betting $100 on the Player Wager and $100 on the Banker Wager

In Graph 3, one can see the effect of limited outcome variance. In this example the customer is never subject to a winning shoe. In each of the ten eight-deck shoes simulated, the customer loses between $145 and $205. These outcomes always are greater than the 20 percent comp dollars (red line) used as reinvestment based on the calculated T-win. Also note that the different outcomes are either slightly higher or slightly lower than calculated T-win illustrated by the green line. Note: Graph 3’s range is much smaller due to the limited result volatility due to the offsetting bet structure. Graph 3’s range is between $0 and a customer loss of $250. Graphs 1 & 2 reflect a much greater range of approximately customer loss of $4K to a customer win of $4K.

As the reader can see, whenever a customer decides to offset betting on two opposing wagers, the outcome will always be in the house’s favor, earning more than enough to cover the customer’s reinvestment costs, while providing the casino with practically zero outcome volatility.

At this point, someone is sure to ask about offsetting betting and coupon or promotional chip/token play. The same principles still apply when the customer uses the offsetting theory with coupon or free bet play. The cost of the coupon/free bet does not change; however, the issue of limited volatility needs to be the focus. In this situation, the customer is exhibiting a desire to limit volatility and “wash” through the coupons with no intention of gambling. During a previous situation, I watched as customers earning “free play” tokens through their slots played, elected to play them on Roulette, spreading the coupons straight-up across all thirty-eight possibilities. Although not truly “offsetting”, the eventual outcome is the same. The players earned the free play on a 12% slot machine but washed them all on a 5.26% game.

Any time customers show evidence that they are reluctant to gamble, management needs to consider their value as a future casino player. I have witnessed bus promotion customers who were handed promotional coupons upon departing the bus, wash the coupons by wagering them offsetting on Player-Banker in Baccarat. What this told me was that the bus customers were reluctant to gamble and were only there to take the financial benefits from the promotion. I never again invited that bus company back to the casino.

A good friend, Gary Saul, sent me a link to an article on offsetting betting that I would like to pass along to the readers. The article, written by Alan Krigman, gives you his point of view about offsetting betting in craps and in baccarat. I think it will be appealing to read by those who still have interests in this topic.

Articles by Author: Bill Zender

As former Nevada Gaming Control Agent, casino operator, professional card counter and casino consultant, Bill Zender has been involved in various areas of gaming and hospitality since 1976. In the past, Zender has instructed courses on game protection, card counting, advantage play and gaming operations at various colleges and institutions throughout the country. As a member of JMJ, Inc., Zender was an owner and operator of the Aladdin Hotel and Casino and has additional operational experience in card room casinos in California and is considered an expert in Asian gaming. Besides his practical gaming experience, Zender holds a bachelors in hotel administration and a masters in business. As a gaming author Zender has penned seven non-fiction books on gaming including Card Counting for the Casino Executive, and the Casino-ology series. Owner/consultant of Bill Zender and Associates, Zender spent was general manager at a major California cardroom casino from 2018-2019. For more information, visit