The Ties That Bind

Claiming that most pattern based baccarat strategies are based on temporary (and thus inconsistent) biases and thus do not offer a true mathematical edge, Michael Brannan proposed a card counting method which supposedly indicates when conditions favor ties.

His reasoning is simple:  remove all of the odd valued cards from the shoe, and since the remaining even valued cards can only add up to even sums, the chances that ties occur drops from 1-in-10 to 1-in-5, effectively doubling the probability for ties to occur.  Since ties pay 8-to-1, betting ties when the odds become 1-in-5 seems like a sure way to consistently beat the casino!

His advanced tie count assigns positive counts to the odd valued cards and negative counts to the even valued cards, with the exception of 2 and 8, which are assigned positive counts.  If odd valued cards are coming out of the shoe more often than negative valued cards, the count becomes positive.  Once the tie count reaches a certain positive threshold, the strike count, the shoe is relatively rich in even valued cards, conditions favoring ties, according to Brannan.  So, after the strike count, start betting ties.  The more positive, the better for ties.  In fact, Brannan uses a negative betting progression (increasing his bet as he loses), since he believes the chances of getting a tie increases the more positive the count becomes.

However, my statistical and experimental evidence in Baccarat Simulations Series 8 on data from 100,000 baccarat shoes (ref. My Baccarat Shoe Factory) contradict Brannan’s claims.

1.  Frequency of Ties vs. MB Tie Count

First, I examined how frequently ties occur in relation to Brannan’s advanced tie count.  If Brannan was right, ties would occur significantly more frequently for positive counts than negative.  However, I found that they show a completely symmetric distribution about a count of zero.  That is, ties occur just as frequently for every negative count as it does its corresponding positive count, as seen in the following graph:

2.  Percentage of Ties per Hands vs. MB Tie Count:

Next, I recorded the tie count for every hand, which allowed me to calculate the percentage of hands that ties would occur for each of Brannan’s advanced tie count.  As the following graph shows, the percentage of ties per hand for each tie count is around 9.5%, practically identical to the theoretical tie percentage 9.5156%.  So, contrary to Brannan’s claims, a more positive tie count is not associated with a greater percentage of ties.  (The spike for the most positive bin is due to insufficient statistics at that extremely high count.)

3.  Both of the above statistical findings in and of themselves already doom Brannan’s method to fail.  For sake of completeness, I performed full baccarat simulations over the 100,000 shoes, betting for ties after strike counts of +30, +40, +50, and +60.  In every case, the player’s advantage was found to be practically the same as the theoretically expected -14.3596%.  That is, Brannan’s method does no better than simply always betting tie every decision.

If Brannan is actually winning with his method, he is probably doing so by inadvertently taking advantage of the same kind of temporary (and unreliable) biases which he identified as a weakness for pattern based methods.  If that is true, Brannan’s method would still be relatively inefficient, since I found that betting opportunities where the tie count exceeds +30 arise less than 3.5% of the time.  That is, on average for every 100 decisions, less than 4 offer betting opportunities where the tie count exceeds +30.

In the long run, such patience is not rewarded, and it makes no difference whether you use Brannan’s method or bet ties every decision.  The latter is a lot easier and faster, and just as ineffective.

Related topic: Frequency of Ties in 1M Baccarat Shoes.

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.