Discount Gambling

Does Card-Counting Work For Spanish21?

Posted in spanish21 by stephenhow on February 24, 2009

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.

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.

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One Response

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  1. ZenMaster_Flash said, on April 10, 2010 at 5:41 pm

    Counting DEUCES when you could just as easily count SIXES as low cards is self-defeating.

    The following metrics apply to the re-double 6 deck H17 game:

    The E.O.R. (of a 6 is much greater than that of a 2)
    In this H17 game the E.O.R. Difference is VERY significant:
    +0.29 (for a 2) vs. +040 (for a 6)
    Threes and Sixes are identical at +0.40
    Fives and Fours are 0.65 and +0.56
    Sevens weigh in at an irrelevant +0.04

    As far as the High Cards go:
    Aces = −0.73
    Faces = −0.44
    Nines = −0.17
    Eights = −0.21

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