I’ve heard all the stories about card-counting, and almost managed to watch the entire movie “21”, but I never really saw how card-counting could help against a 6-deck shoe. Well, since it was really easy to add to my Spanish21 program, I devised a simple hi/lo balanced count:
| Cards | Value |
|---|---|
| 2, 3, 4, 5 | +1 |
| J, Q, K, A | -1 |
Next, I wanted to see the correlation between the running count of the shoe, and the expectation value (EV) of the next hand out of the shoe. So I ran the simulator for a million shoes, and plotted the average hand net result vs. the running count:
Simulation of simple hi/lo count for Spanish21.
I was surprised to see the very linear correlation between the running count of the shoe, and the profitability of the next hand out of the shoe. Counting works. I never saw this data before (probably because few people want to see this type of thing), but it’s the clearest way for me to see the benefits of counting. And these results were obtained by playing the unmodified basic strategy for the game. Note that the player has almost a 2% edge when the count is +10. And the game is always profitable when the count is positive. (Oh, if we could only sit out while the deck is negative …) Obviously, results will improve by implementing more complicated counting systems (e.g., true counts, based on shoe depth, modifying basic strategy for the count, etc.). But, it’s nice to know that the most basic type of counting yields a positive edge for the game.
As another simple experiment, I added a simple modified betting strategy based on the count:
| Condition | Bet |
|---|---|
| count ≤ -5 | 0 (sit out) |
| -5 < count < 0 | 1x |
| 0 ≤ count < 10 | 2x |
| 10 ≤ count < 15 | 3x |
| count ≥ 15 | 4x |
where a bet of 1x indicates your standard bet, and 2x is twice your standard bet, etc. This simple betting strategy using the simple running hi/lo count, and the unmodified basic strategy made the game net profitable (+0.41% of the 1x bet), vs. the normal -0.45% loss rate.
