In our previous blog post, we looked at the House Edge as a lever that a table games operator can influence, with an impact on revenue, profits, and guest experience.

We discussed modifications to game rules and/or side-bets in an effort to reach the sweet spot for both the patron and operator of the game. In other words, the house-edge where a game operator’s ‘willingness-to-sell’ optimally matches the patron’s ‘willingness-to-buy’. In this blog post, we present a counter intuitive strategy for modifying the house edge of a Baccarat game, that increased profitability, despite a lower house edge for a specific bet.

The data presented in this case study is actual data collected at a Baccarat operation I was involved with.

BASIC BACCARAT HOUSE EDGE

Disregarding any side-bets, basic Baccarat has three main betting propositions with the following House Edges:

The lower House Edge when betting on ‘Banker’ includes the commission the player has to pay on winning Banker bets.

What is notable here is the large distance in House Edge values between Tie and Banker/Player bets: almost 12 times greater. This makes intuitive sense due to the low frequency of a Tie outcome in Baccarat. Despite that, the Tie bet is popular with patrons and the excitement is often at a maximum when a tie hits on a busy game, due to the payout.

‘BLENDED’ BACCARAT HOUSE EDGE

In coming up with a single value for Baccarat House Edge, operators typically set a blended House Edge of 1.15%: the average of 1.06% (Banker) and 1.24% (Player) assuming an even distribution between Player and Banker. The blended House Edge, under the assumption that players will place bets on either side with a 50% occurrence, can also be displayed as follows:

In this Blended Baccarat House Edge calculation, the Tie Bet is excluded since the participation frequency on Tie is typically not accurately measured. This is the same challenge with the side-bets on other games, as discussed in our previous blog post.

ACTUAL HOUSE EDGE
Blending Non-Frequent Wagers into The House Edge

To come up with an Actual House Edge in the case of Baccarat, operators can measure the participation frequency of the wagers on the Tie bet, relative to the total wagers on Banker/Player.

At an operation that I managed, we manually sampled thousands of rounds played over the course of one month on eight Mass Gaming tables across different days of the week and times of the day. From the data collected, we found that on average, for every $100 wagered on Banker/Player, an additional $4.60 was wagered on the Tie bet. This meant that, when including the Tie bet participation, the distribution was 95.6% (for $100) on Banker/Player and 4.4% (for $4.60) on Tie, from the total of $104.60.

This measurement allowed us to include the Tie House Edge in our blended Baccarat House Edge calculation, as follows:

This value of 1.73% represented the Actual House Edge for this particular Baccarat operation. In other words, when taking into account the additional $4.60 placed on Tie for each $100 on Banker/Player, the Actual House Edge is 50% greater than the initial 1.15% considered.

THE COUNTER-INTUITIVE STRATEGY:
Lowering the house edge to incentivize participation

Armed with more accurate data on our Baccarat Actual House Edge (and on our Baccarat players’ behaviour), our hypothesis was that we could increase participation by incentivizing patrons with a better payout (and lower house edge) on the Tie bet. Is there a sweet spot that we could offer and increase the excitement of hitting the Tie while betting on the Tie action? Could we achieve this while increasing our Baccarat Win?

One option was to offer a payout of 9 to 1 instead of 8 to 1 for the Tie bet. This was risky as the approach would lower the House Edge for the Tie from 14.3% to 4.8%. This is a three-fold decrease, meaning a minimum of a three-fold increase in participation would be required to make up for the lower house edge. With the perception from a player’s point of view that it is only a difference of one unit (from 8 to 9), it was a fair assumption that our Tie Bet Participation would not increase by a factor of three times to break-even.

Instead, we resorted to offering only selected Tie outcomes to be paid 9 to 1, while continuing paying 8 to 1 for the other outcomes, as follows:

• All Ties with outcomes values of 9, 8 and 0 will pay 9 to 1
• All the other Tie outcomes will continue to be paid at 8 to 1

This modification of the pay-table decreased the House Edge for the Tie bet, from 14.3% to 11.6%. However, if this incentive would result in increased participation on the Tie proposition, the trade-off could improve the overall Baccarat Actual House Edge.

After this change was implemented on the gaming floor, it was visible that on the player excitement side of the equation, it was a success: players embraced the new pay-table and were very prompt to point to each other when they hit the premium Ties. Also, as it was a new procedure and at first some dealers were occasionally forgetting to pay according to the new rule, players were very prompt in pointing it out to them.

Next, we measured the results to test the hypothesis:

1. Did players place more than $4.60 on average for each $100 placed on Banker/Player, and by how much?
2. What impact did this have on the Actual House Edge for Baccarat after blending in the new values?

Using the same methodology and sample size, we established that the Baccarat players were now placing, on average, $7.20 on the Tie proposition for each $100 placed on Banker/Player, up from previous $4.60. This also meant that the distribution percentages changed to 93.28% (for $100) on Banker/Player and 6.72% (for $7.20) on Tie.

Calculating the Blended Actual House Edge for Baccarat, we were pleasantly surprised with a ~6.9% increase in the blended actual house edge, despite lowering the house edge of the Tie bet:

While the House Edge for the Tie alone decreased, the increase in the participation for this proposition determined an increase of the game’s Actual House Edge to 1.86%, an increase of 13 percentage points (6.9%) from our former Actual House Edge of 1.73% (Fig. 3).

Note: For comparison, switching from a traditional “Commission” to a “No-Commission” version of Baccarat will increase the Baccarat House Edge by 20 percentage points.

This evolution further indicated an expectation of an increase in Hold% by 1.4 percentage points for Baccarat, which was confirmed by the monthly results. In addition, as this change remained in place for following years at this operation, the Tie Bet became a very popular fixture on the property’s brand.

CLOSING REMARKS

It is worth noting that modifying rules as discussed in this blog could have had effects on other variables as discussed in our previous blog post:

1. Game Pace: did the new procedure affect the speed of the game? Were dealers taking longer to pay the Tie winnings?
2. Revenue cannibalization: were those extra $2.60 placed on the Tie cannibalizing the main bet Banker/Player, or were generated by extra Drop?

To answer these questions requires further measurements. We offered this example mostly to bring home the point that House Edge is an important lever to consider when it comes to a game’s profitability and appeal to players. There could be a significant difference between the Theoretical House Edge and the Actual House Edge for a game when various side-bets and the afferent participation are to be taken into consideration. Measuring the participation of a side-bet allows a better picture of the bets’ appeal with the players and its profitability.