The Baccarat “Scam” You Shouldn’t Ban

Sam the “scambler” (he likes to scam as well as gamble) plops down next to you. “I’ve got a good one this time,” he says. “Let’s say the table minimum on baccarat is $25, but I only want to play $5 a hand. Since you are basically betting on a coin flip, I put $30 on banker and $25 on player. Voila! When player wins, banker loses, and vice versa. It nets out to just a $5 bet on banker, and I have the added advantage of getting rated at $55 per hand.”

What do you say?
I’ve heard Sam’s argument numerous times, and it sounds so intuitively ingenious that I’ve known executives who have wanted to ban the practice. But, in fact, we should highly encourage bettors to follow this exact scenario. The more money Sam puts on the table, no matter how he divvies it up, the more money the casino makes.

Baccarat Basics
Let’s review the basic facts of baccarat:

• Player Bet
• House advantage = 1.24 percent
• Wins 44.625 percent of the hands
• Pays even money

• Banker Bet
• House advantage = 1.06 percent
• Wins 45.860% of the hands
• 5 percent commission on wins

• Tie Bet
• House advantage = 14.36 percent
• Wins 9.516 percent of the hands
• Pays 8:1

To simplify the following calculations, I won’t be including the columns for tie bets, as they are a push for either banker or player. Just remember that they account for the remaining 9.516 percent of hands that are won by neither banker nor player. For this analysis, I’ll assume that nobody is foolishly betting on the tie bet, and if they are, well, just enjoy that 14.36 percent house advantage and don’t worry about the details!

Is Sam Smart?
Now let’s see how betting $5 on banker really compares to betting $30 on banker and $25 on player.
Figure 1 shows the breakdown when Sam bets $5 on banker.

Figure 1
$5 Player Bet Payoff When Banker Wins Payoff When Player Wins
$0 Player (45.860% of the hands) (44.625% of the hands)
Banker Bet: $5 $5 x .95 = $4.75 $5
Player Bet: $0 – –
Total: $5 $4.75 $5

When banker wins, Sam wins $4.75, and when player wins, Sam loses $5.

The expected loss for Sam on each hand is:

Expected Loss = (Probability that Banker Wins x Payoff when Banker Wins)
+ (Probability that Player Wins x Payoff when Player Wins)
Expected Loss = (.45860 x $4.75) + (.44625 x -$5)
Expected Loss = -$0.053

Thus, from the casino’s point of view, we have a theoretical win of 5.3 cents per hand.

House Advantage = Theoretical Win / Total Amount Wagered
House Advantage = $0.053 / $5
House Advantage = 1.06%

We can see that our calculations check out because we wound up at the expected house advantage of 1.06 percent.

Compare this to Figure 2, which shows the results when Sam plays $30 on banker and $25 on player.

Figure 2
$30 Player Bet Payoff When Banker Wins Payoff When Player Wins
$25 Player (45.860% of the hands) (44.625% of the hands)
Banker Bet: $30 $30 x .95 = $28.50 $30
Player Bet: $25 $25 $25
Total: $55 $3.50 $5

In this scenario, Sam still loses $5 whenever player wins; however, now he only wins a mere $3.50 when banker wins instead of the original $4.75.
Following the same calculations as above we get:

Expected Loss = (Probability that Banker Wins x Payoff when Banker Wins)
+ (Probability that Player Wins x Payoff when Player Wins)
Expected Loss = (.45860 x $3.50) + (.44625 x -$5)
Expected Loss = -$0.626

Thus, from the casino’s point of view, we have a theoretical win of 62.6 cents per hand.

House Advantage = Theoretical Win / Total Amount Wagered
House Advantage = $0.626 / $55
House Advantage = 1.14%

Note that the house advantage has now increased from 1.06 percent to 1.14 percent. Recall that the house advantage on the banker bet is 1.06 percent, while the advantage on the player bet is 1.24 percent. As Sam shifts more money to the player, he will be nudging the house advantage up closer to that 1.24 percent mark.

Finally, are we rating Sam correctly? He has 11 times more money on the table ($55 instead of $5). If we were using a house advantage of 1.06 percent for rating purposes, we would now be rating him as losing $55 x 1.06% = 58.3 cents per hand rather than 5.3 cents per hand. Yet, because the house advantage is now 1.14 percent, he is theoretically losing 62.6 cents on each hand. Thus, if anything, we would be slightly underrating him in this situation.

Now, let’s look at the other side. How does betting $5 on player compare to betting $25 on banker and $30 on player?

Figure 3 shows the results if Sam bets $5 on player.

Figure 3
$0 Banker Bet Payoff When Banker Wins Payoff When Player Wins
$5 Player (45.860% of the hands) (44.625% of the hands)
Banker Bet: $0 – –
Player Bet: $5 $5 $5
Total: $5 $5 $5

Expected Loss = (Probability that Banker Wins x Payoff when Banker Wins)
+ (Probability that Player Wins x Payoff when Player Wins)
Expected Loss = (.45860 x -$5) + (.44625 x $5)
Expected Loss = -$0.062

Thus, from the casino’s point of view, we have a theoretical win of 6.2 cents per hand.

House Advantage = Theoretical Win / Total Amount Wagered
House Advantage = $0.062 / $5
House Advantage = 1.24%

Once again, our calculations check out because they match the established 1.24 percent house advantage on the player bet.

Compare this to when Sam bets $25 on banker and $30 on player, as shown in Figure 4.

Figure 4
$25 Banker Bet Payoff When Banker Wins Payoff When Player Wins
$30 Player (45.860% of the hands) (44.625% of the hands)
Banker Bet: $25 $25 x .95 = $23.75 $25
Player Bet: $30 $30 $30
Total: $55 $6.25 $5

Expected Loss = (Probability that Banker Wins x Payoff when Banker Wins)
+ (Probability that Player Wins x Payoff when Player Wins)
Expected Loss = (.45860 x -$6.26) + (.44625 x $5)
Expected Loss = -$0.635

Thus, from the casino’s point of view, we have a theoretical win of 63.5 cents per hand.

House Advantage = Theoretical Win / Total Amount Wagered
House Advantage = $0.635 / $55
House Advantage = 1.15%

Now, in either scenario Sam wins the same $5 whenever the player wins. However, when banker wins, he is now losing $6.25 instead of $5. He has obtained a slightly lower house advantage (1.15 percent instead of 1.24 percent) by spreading some of his money to banker, but because there is more money on the table, he now loses 63.5 cents instead of just 6.2 cents on every bet.

As for his player rating, similarly to above, we are now rating him at 1.06% x $55 = 58.3 cents per hand. However, we have established that he is theoretically losing 63.5 cents per hand. Thus, we are still slightly underrating him. [Note that if we use 1.06 percent for rating purposes, any bets on player will always be underrated, as the house advantage is actually 1.24 percent.]

The Exact House Advantage
As Sam apportions his bet between banker and player, he can vary the house advantage from the low of 1.06 percent (all of it bet on banker) to a high of 1.24 percent (all of it bet on player). However, he cannot reduce it any lower than the 1.06 percent he’d get by betting it all on banker; nor can he increase it beyond the 1.24 percent he would get from betting it all on player. Figure 5 shows the impact on house advantage as Sam spreads his bet across banker and player.

Figure 5
% on Banker % on Player House Advantage
100% 0% 1.06%
75% 25% 1.10%
50% 50% 1.15%
25% 75% 1.19%
0% 100% 1.24%

If, for some strange reason, you wanted to calculate the exact theoretical house advantage for a given betting pattern, the formula is:

House Advantage = [(P-.95 x B) x .45860] + [(B-P) x .44625] where:

B = % of Total Bet that is bet on Banker
P = % of Total Bet that is bet on Player
.45860 = the probability that Banker will win a given hand
.44625 = the probability that Player will win a given hand

For example, if Sam bets $150 on banker and $50 on player:
B = $150 / ($150 + 50)
B = $150 / $200
B = 75% or .75
P = $50 / ($150 + $50)
P = $50 / $200
P = 25% or .25

House Advantage = [(P-.95 x B) x .45860] + [(B-P) x .44625]
House Advantage = [(.25 – .95 x .75) x .45860] + [(.75 – .25) x .44625]
House Advantage = [(.25 – .7125) x .45860] + [.5 x .44625]
House Advantage = [-.2121] + [.2231]
House Advantage = .011
House Advantage = 1.10%

Final Thoughts
Baccarat is more than a coin toss, or else we wouldn’t make money. If we ignore ties, the banker wins 50.7 percent of the time and the player wins 49.3 percent of the time. Since the banker wins more than 50 percent of the resolved bets, the commission is where we make the money. And since the player wins less than 50 percent of the resolved bets, yet pays even money, we make money on that bet as well. If Sam decides to spread his money across both player and banker bets at the same time, the house advantage will vary between 1.06 percent and 1.24 percent. If we use 1.06 percent for rating purposes, as Sam bets more money on player, we will actually be slightly underrating him. Thus, as Sam puts more money on the table, the casino makes more money and he is rated correctly.

So next time you meet a Sam in your casino, you might pause for a moment to ponder, and then reply, “Well, Sam, you sure got me on that one! I can’t stop you from betting $30 on banker and $25 on player. And you are absolutely correct that I’ll rate you at $55 a hand. Whatever will you think of next, you sly weasel?”

Then slap him on the back, and smile all the way to the bank.

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