Blackjack Compromise Strategies

What if I play the strategy for the wrong rules?

Both Basic Strategy and card counting strategies include variations for the H17 (Hit on 17) and Double after Split (DAS) rules. Some books do not bother with these variations and provide compromise tables. So, if you have learned the tables for one set of rules and play a game with the other rules, what is your loss?

Let's start with Basic Strategy in a six-deck game. This chart contains two sets of bars. The set on the left is for the S17 rule. In Basic Strategy, your edge is negative, so all bars point downwards. The cyan bar on the left set of bars is the house edge assuming that the S17 rule exists and you are playing correctly. The dark blue bar is the edge with the same rule; but this time you are using the strategy for H17. The small difference is the cost of using the wrong strategy. The green bar is the edge in an H17 game playing correctly. The house edge is much worse with H17. The red bar is also an H17 game, but using the S17 tables. There is a bit of an additional loss for playing incorrectly. On the right side we see the same set of bars, except for the DAS rule instead of H17.

The first thing we see from this chart is that playing the right game is far more important than playing the right strategy. We also see that the red and green bars are very close on the left and the blue and cyan bars are very close on the right. This would indicate that if you wish to learn only one set of tables, you are better off using the S17 tables than the H17 tables and the non-DAS tables than the DAS tables. Of course if you run one set of rules 90% of the time, learn that set.

What about Card Counting?

Let's try the same experiment with Hi-Lo with the top 20 indexes. Here cyan is once again an S17 game. But here we display SCOREs for penetrations from 26 to 130 cards cut off. The thickness of the cyan area is the loss if we play using the H17 tables. The difference between the red and green lines is the loss playing an H17 game with S17 rules. There is barely any loss at all. What we see is a very small penalty for using incorrect tables. I did not include the DAS chart as it looks much the same.

Now a full set of indexes will make more of a difference. But few people use a full set with six decks. And single-deck would make more of a difference. But single-deck games with S17 or DAS are difficult to find.

Sim details

• Six decks, S17, DAS, LS 1 player, Hi-Lo, truncate, Sweet 16 & Fab 4 indexes, half-deck resolution, 26-130 cards penetration
• Six decks, H17, DAS, LS 1 player, Hi-Lo, truncate, Sweet 16 & Fab 4 indexes, half-deck resolution, 26-130 cards penetration
• Six decks, S17, LS 1 player, Hi-Lo, truncate, Sweet 16 & Fab 4 indexes, half-deck resolution, 26-130 cards penetration
• Six decks, H17, LS 1 player, Hi-Lo, truncate, Sweet 16 & Fab 4 indexes, half-deck resolution, 26-130 cards penetration
• Six decks, S17, DAS, LS 1 player, Basic Strategy, 4.5/6 penetration
• Six decks, H17, DAS, LS 1 player, Basic Strategy, 4.5/6 penetration
• Six decks, S17, LS 1 player, Basic Strategy, 4.5/6 penetration
• Six decks, H17, LS 1 player, Basic Strategy, 4.5/6 penetration
• Correct and incorrect strategies
• Optimal betting by full counts in Hi-Lo sims
• Ten billion rounds each