If you could prepay commission in Baccarat, what would the House Advantage be?

So with a $100 Banker bet, you could add $5 to it. If it wins, you win $100, if it loses, you lose $105.

What would the HA be with counting?

Quote: Liwet

So with a $100 Banker bet, you could add $5 to it. If it wins, you win $100, if it loses, you lose $105.

What would the HA be with counting?
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Counting makes almost no difference: this bet is about a 1.0% house edge without counting, and still effectively unbeatable with counting.

Base house edge (8 decks, exact calculation, as a share of the $100 stake)

Version House edge
Standard Banker, 5% commission on wins 1.06%
Your version, $5 fee returned on a tie 1.00%
Your version, $5 fee kept on a tie 1.47%

Paying the $5 up front on every bet costs slightly less than 5% of wins, because the bet loses more often than you might expect. So the version where the fee is refunded on a tie is marginally better than standard commission. If the casino keeps the $5 on ties, which occur about 9.5% of the time, it is clearly worse.

Effects of removal

These show the change in house edge when one card of each rank is removed from the 8-deck shoe. Negative values favour the player.

Rank Effect Rank Effect
0 (10s/pictures) +0.002% 5 −0.009%
A +0.005% 6 −0.012%
2 +0.006% 7 −0.009%
3 +0.007% 8 −0.005%
4 +0.012% 9 −0.002%

The pattern is the familiar one: removing 4s helps Banker, and removing 6s helps Player. However, each effect is about one hundredth of a percent, against a base edge of 1%.

With perfect card tracking

I simulated 20,000 shoes, assuming you know every remaining card exactly and play down to 14 cards from the end:

The bet has a positive expected value on only about 0.3% of hands. In the fee-kept-on-tie version it is about 0.04%.
If you bet only on those hands, the average gain is about 0.0008% per hand dealt. That works out to roughly $0.0008 per $100 hand observed, or around one penny per shoe.
The best edge seen was about +2%. Those hands occur only in the last few cards of rare shoes, which a normal cut card usually prevents you from reaching.

Conclusion: The $5-ahead structure reduces the edge by about 0.06 percentage points compared with standard commission, but it does not change the countability. Like standard Banker, this bet cannot be counted at any useful level. The finding that the main Banker and Player bets cannot be counted profitably goes back to Thorp’s analysis. In baccarat, the "countable" opportunities remain the side bets, such as Dragon 7, Panda 8 and Tie, where removing particular ranks has a much larger effect.Even these produce very little profit.

One caveat: the effect-of-removal model is linear, so it is approximate deep into the shoe. That does not change the conclusion.

Dropping the commission from 5% to 4.762% isn't going to do much. 5%, or 19:20 pays, makes commission relatively easy to calculate.

Any theoretical benefit for the player would appear to quickly evaporate when the dealer tries to calculate the discounted vig.

What can the HA be with counting on 4% commission bacc? I've seen this irl albeit temporarily as a promotion to get people to come.

Quote: harris

What can the HA be with counting on 4% commission bacc? I've seen this irl albeit temporarily as a promotion to get people to come.
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Even at 4% commission, counting barely helps. The bet still has a 0.60% house edge off the top. On the rare hands where perfect card tracking shows a positive edge, that edge averages only about 0.1–0.2%.

4% commission Banker, 8 decks, exact

Base house edge: 0.60%, down from 1.06% at 5% commission
The effects of removal are essentially unchanged from 5% commission: removing 4s helps Banker most, removing 6s hurts Banker most, and each effect is about 0.01% per card.


This simulation assumes you know every card left in the shoe and bet only when the Banker bet has a positive edge. It covers 20,000 shoes for each cut-card depth.

Cards behind cut card Hands with player edge Average edge on those hands Value per hand dealt Best edge seen
14 (very deep) 1.3% +0.24% 0.003% +2.0%
52 (1 deck) 0.26% +0.11% 0.0003% +0.7%
104 (2 decks) 0.03% +0.07% ~0 +0.35%

To put the best case in money: dealt to 14 cards, at $100 a hand, that is about $0.25 of expected value per shoe. You would get roughly one bet per shoe, almost always in the last handful of hands. At a normal cut of about one deck, it is about 2 cents a shoe. A practical count system such as a simple 4s-versus-6s count would capture only part of even that.

A 4% commission halves the house edge, but Banker remains unbeatable by counting.

The problem is not with the house edge, it is with the weak effects of removal. Modulo 10 games by definition tend to have low volatility of advantage which is probably why the game became so popular with casinos.

Btw It is fairly easy for a high-roller to get away with not paying commission altogether after a long losing streak. This removes the house edge altogether.