SCOREs with Different Card Counting Strategies

How much do strategies matter?

There exist numerous Blackjack card counting strategies. And each strategy can be varied by number of indexes and side counts. And each of these is affected by bet spreads and rules. No attempt will be made here to compare the millions of combinations. (See card-counting.com for comparisons.) However I will present a couple of charts to provide an indication of the degree of differences.

Here we will compare a level I, level II and level III strategy. The level of a Blackjack card counting strategy is defined by the magnitude of the tag values. For example, Hi-Lo, a level I strategy, counts cards as -1, 0 or +1. Zen counts cards as -2,-1, 0 +1 or +2 and is therefore a level II strategy.

The green area is the gain at different penetrations for Hi-Lo using the top 20 indexes with a bet spread of 1-16 and common Las Vegas Strip rules. The red area indicates the increase in gain switching to the 1980 version of Zen, a level II strategy, and the blue area shows the increase by switching to Halves, a level III strategy. As we can see, the increase in complexity does result in some gain — but it is not large. The gains would be somewhat larger with more indexes as the higher level counts allow more accurate indexes. There may also be some negative offset of moving to a more complex strategy because of an increase in error rates.

What about single-deck?

The story with single-deck is a bit different. Here Hi-Opt I and Hi-Opt II are compared. These are level I and II strategies tuned for single-deck. Full indexes are used as indexes are more important in single-deck as we have seen previously. The difference here is more impressive.

See Card Counting Strategies for a list of strategies.

Sim details

• Six decks, S17, DAS, LS, 4 players, Hi-Lo, truncate, Sweet 16 & Fab 4 indexes, half-deck resolution, penetrations from 26-130 cards cutoff by the card
• Six decks, S17, DAS, LS, 4 players, Zen 1980, truncate, Sweet 16 & Fab 4 indexes, half-deck resolution, penetrations from 26-130 cards cutoff by the card
• Six decks, S17, DAS, LS, 4 players, Wong Halves, truncate, Sweet 16 & Fab 4 indexes, half-deck resolution, penetrations from 26-130 cards cutoff by the card
• Single-deck, H17, 3 players, Hi-Opt I, truncate, max indexes, quarter-deck resolution, penetrations from 13-26 cards cutoff by the card
• Single-deck, H17, 3 players, Hi-Opt II, truncate, max indexes, quarter-deck resolution, penetrations from 13-26 cards cutoff by the card
• Two billion rounds each, all sims use optimal betting, full Kelly