Effect of Card Value Removal on Expectancies in Baccarat

In this analysis, I remove specific card values from 100,000 8-deck shoes to examine how depletion of those values affects long term expectancies of Banker (B), Player (P), and Tie (T) decisions.

Theoretically expected values (theo) from combinatorial analysis are also provided for reference.

Card Values Removed	B	B (theo)	P	P (theo)	T	T (theo)
None	-1.06%	-1.06%	-1.24%	-1.24%	-14.27%	-14.36%
0	-1.10%	-1.12%	-1.17%	-1.15%	-7.41%	-7.26%
1	-0.90%	-0.90%	-1.39%	-1.39%	-13.64%	-13.74%
2	-0.81%	-0.86%	-1.50%	-1.44%	-14.78%	-14.93%
3	-0.87%	-0.92%	-1.42%	-1.38%	-13.69%	-13.68%
4	-0.69%	-0.74%	-1.61%	-1.56%	-14.69%	-14.73%
5	-1.21%	-1.25%	-1.08%	-1.04%	-14.80%	-14.84%
6	-1.49%	-1.52%	-0.80%	-0.77%	-16.85%	-16.91%
7	-1.37%	-1.40%	-0.93%	-0.89%	-16.43%	-16.34%
8	-1.19%	-1.22%	-1.09%	-1.06%	-9.66%	-9.65%
9	-1.13%	-1.15%	-1.16%	-1.13%	-11.32%	-11.16%
2,3,4	-0.59%	-0.66%	-1.68%	-1.62%	-4.67%	-4.69%
5,6,7	-2.33%	-2.29%	0.06%	0.02%	-16.98%	-17.10%
1,3,5,7,9	-1.18%	-1.23%	-0.89%	-0.84%	62.00%	62.02%
2,4,6,8	-1.13%	-1.09%	-1.16%	-1.19%	-13.48%	-13.49%

Raw numbers of decisions (dec) are tabulated in the following:

Card Values Removed	B dec	P dec	T dec	Total dec
None	3,825,581	3,722,432	794,652	8,342,665
0	2,620,574	2,553,099	593,278	5,766,951
1	3,545,391	3,438,000	741,236	7,724,627
2	3,559,713	3,444,036	732,578	7,736,327
3	3,556,104	3,445,937	742,754	7,744,795
4	3,568,981	3,443,868	734,356	7,747,205
5	3,531,818	3,448,277	729,838	7,709,933
6	3,504,327	3,443,208	707,212	7,654,747
7	3,507,869	3,437,051	710,880	7,655,800
8	3,438,852	3,356,533	758,259	7,553,644
9	3,458,697	3,371,117	746,525	7,576,339
2,3,4	2,999,256	2,888,362	697,483	6,585,101
5,6,7	2,832,496	2,836,373	576,061	6,244,930
1,3,5,7,9	2,077,319	2,032,555	902,148	5,012,022
2,4,6,8	2,568,053	2,503,063	539,373	5,610,489

Expressed in terms of percentage of totals, including ties (3 left columns) and excluding ties (2 right columns):

Card Values Removed	B	P	T		B	P
None	45.86%	44.62%	9.53%		50.68%	49.32%
0	45.44%	44.27%	10.29%		50.65%	49.35%
1	45.90%	44.51%	9.60%		50.77%	49.23%
2	46.01%	44.52%	9.47%		50.83%	49.17%
3	45.92%	44.49%	9.59%		50.79%	49.21%
4	46.07%	44.45%	9.48%		50.89%	49.11%
5	45.81%	44.73%	9.47%		50.60%	49.40%
6	45.78%	44.98%	9.24%		50.44%	49.56%
7	45.82%	44.89%	9.29%		50.51%	49.49%
8	45.53%	44.44%	10.04%		50.61%	49.39%
9	45.65%	44.50%	9.85%		50.64%	49.36%
2,3,4	45.55%	43.86%	10.59%		50.94%	49.06%
5,6,7	45.36%	45.42%	9.22%		49.97%	50.03%
1,3,5,7,9	41.45%	40.55%	18.00%		50.54%	49.46%
2,4,6,8	45.77%	44.61%	9.61%		50.64%	49.36%

Data Set: Virtuoid 100,000 shoes (ref. My Baccarat Shoe Factory).

Note that while depleting shoes of all odd valued cards appears to result in highly favorable player expectancies for betting ties (+62%!), translating this ideal condition into a profitable strategy using a particular counting method has been shown to be impossible in practice.  (Reference: Data: Simulation Series 8: MB Advanced Tie Count, and Discussion: The Ties That Bind.)

Disclaimer: The betting strategies and results presented are for educational and entertainment purposes only. Gambling involves substantial risks, and the odds are not in the player’s favor by design. The author does not state nor imply any system, method, or approach offers users any advantage, and he shall not be held liable under any circumstances for any losses whatsoever.