Baccarat Simulations Series 1 Discussion: Single Side, Rp, Opp, RO

I provided the numerical and graphical results of my first series of baccarat simulations in the previous post, Baccarat Simulations Series 1 Results.  I generated a wealth of statistics but posted only the most important.

In this first series, I was just warming up, testing the program and putting it through its paces.  Five elementary methods were examined:  1) Single side betting of Player, 2) Single side betting of Banker, 3) Always bet Repeat of the last decision, 4) Always bet Opposite of the last decision, and 5) Always bet Repeat, except bet Opposite after two chops (toy strategy illustrated in Check, Please!).  For each method, I tested 3 money management procedures and 2 betting methods, flat betting and U1D2M2 (ref. Money Matters).  In addition to P/B, I also based upon R/A another set of simulations with all of the above variations.  R/A are derivatives of P/B.

The single most important statistic is the Player’s Advantage (P.A.), which is the net units won after commissions divided by the total units bet, expressed as a percentage.  The more positive the P.A., the better.  P.A.= +100% means a perfect game where all bets were won and no commissions were paid (all Player bets).  A negative P.A. indicates a net loss.  P.A.= -100% means all bets were lost.  P.A.=0% is break-even.

Single-side, flat betting of Player and Banker yielded P.A.s close to what are theoretically expected.  For Player, P.A. = -1.36%, where the theoretical expectancy is -1.24%.  For Banker, P.A. = -1.18%, where the theoretical expectancy is -1.06%.  The closeness in values provides further confirmation that the program is working properly and the statistics are accurate (ref. Check, Please!).  (Update:  Thanks to Rick for pointing out here that if ties are not considered, the theoretical expectancy for P is -1.36% and for B is -1.17%, and since indeed I did not include tie data in the data set for these simulations, my experimental values are completely consistent with what are theoretically expected.)

For the Player-Banker simulations, the different money management routines did not significantly change the P.A., in some cases marginally better, while in others, slightly worse.  While the graphs show that money management significantly reduced the absolute amount lost and the rate of loss, the essentially identical P.A.s indicate money management would simply delay the inevitable.  Likewise, whether flat betting or using U1D2M2, the P.A.s remained fairly constant.  Again, the graphs show that the total amount lost using U1D2M2 exceeded that of flat betting, simply because the bet sizes were greater, but the P.A. remained basically the same.

Money management did significantly increase the percentage of shoes won, but because this resulted in no increase in advantage overall, the total score of the extra winning shoes with money management balanced out the total score of the fewer winning shoes without money management.

Of course, money management’s most noticeable effect is in significantly lessening the worst score.  Again, because this resulted in no increase in advantage overall, money management’s effect of reducing the worst score was balanced out by increasing the number of shoes with relatively small losses.

When using R and A as the basis, the results do not significantly change, and yield similar P.A.s for all cases.

So far, the results suggest that betting Repeat, Opposite, or both in a simple combination such as in the Repeat-Opposite toy model yield long term expectancies not significantly better than single side betting Player or Banker.   Moreover, for methods with overall negative expectancies, money management does not appear to significantly help improve performance, but merely delays the inevitable.  Over the long term, whether using flat betting or U1D2M2 does not make a significant difference in the P.A. for these simple methods.  Using U1D2M2 simply loses more in a shorter period of time.  The overall results do not significantly change whether using P/B or R/A as the basis for determining bets.

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 players 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.