ABSTRACT

The card counting technique known as back-counting is treated analytically. The true count at which the back-counter should optimally enter the game is derived, based on maximizing his effective yield. That entry count is found to be in the range of +2 to +3 for a typical 6 deck game, depending on the back-counter’s risk profile. If he also adopts an “exit” strategy (abandoning play at a table whose true count has dropped below a lower threshold) and optimizes the entry and exit counts simultaneously, he can improve his performance slightly further; the optimal exit count is between -2 and -3. Since the risk of ruin is very low, he may in addition choose to bet more aggressively than he would if not back-counting; or, conversely, to “flat bet”. Criteria are examined for “departure” (abandoning the observation of a table whose true count has yet to reach the entry threshold).