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.