Baccarat: Conditions for Positive Expectation on Side Wagers

In simulating different conditions of a Baccarat shoe, the following instances were observed:

  1. Wager refers to the wager type studied – Pairs, Wins on Natural 9s (WN9) and Wins on Natural 8s (WN8).
  2. Win % Probability indicates the percentage probability of that result occurring.
  3. Expectation, based on 11:1 for Pairs and 8:1 for Wins on Natural 8s and 9s, shows the expectation (player’s edge) of the respective wagers with the state of the shoe on the right.
  4. 1 – K indicates how many cards of that value have been dealt.
Wager Win % Probability Expectation 1 2 3 4 5 6 7 8 9 0 J Q K
Pairs 8.66% 3.9% 5 23 23 23 23 23 23 23 23 23 23 23 23
Pairs 25.02% 200.2% 5 5 30 30 30 30 30 30 30 30 30 30 30
WN9 14.27% 28.4% 25 25 25 25 25 25 25 25 5 5 5 5 5
WN8 13.21% 18.9% 25 25 25 25 25 25 25 5 25 5 5 5 5

While sufficient randomization would have occurred with the 26-card cut at the end of the shoe as well as with standard burn-card procedures; this table shows that while only under specific circumstances, it IS possible for the expectation of a side wager to turn against the House and towards the player.

These 4 examples are just some of many possible states.

In the first Pair example, we see a modest 3.9% expectation for the Player, meaning that the Player is expected to win 3.9 cents on the dollar. As a means of comparison, the 2nd Pair example shows an extreme expectation of 2.002 dollars for the player per dollar wagered.

Food for thought and perhaps further study.

Good luck.

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