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Uniform Basic Strategy: does it work?
This article was originally published in the Blackjack Insider, a Blackjack e-mail newsletter edited and published by Henry Tamburin, author of "Blackjack: Take the Money and Run". The article was written by Dan Pronovost, President of DeepNet Technologies.
You have been practicing your blackjack strategy, feel ready and primed to play, hit the casino and… the game you mastered isn’t there! You memorized the tables for eight deck, double after splits (DAS), and dealer hits soft 17 (H17). The multi-deck games at this casino use continuous shuffling machines, which you refuse to play… but wait! They have a good double game: noDAS, S17.
You don’t know the right strategy tables for this game, but you really want to play. Is it still a winning game if you simply play the eight deck rules you memorized? What is the cost in expectation compared to playing the ideal tables and strategy?
This article explores this question with detailed analysis to determine statistically the cost of using uniform basic strategy. We usedBlackjack Audit, an advanced blackjack simulator from DeepNet Technologies, to perform all the statistical calculations in this article.
Basic Strategy Variations
Basic strategy defines the best possible plays to make with every hand combination (player hand versus dealer hand), such that the casino’s edge is minimized. But the science of blackjack is not quite this simple: the best basic strategy tables depend on the particular rules of the game you are playing. The primary rules that can affect strategy include: number of decks, DAS/noDAS, and H17/S17. A quick scan of the appendices of most blackjack books and Internet sites will reveal many tables with subtle variations for each permutation of these rules.
These differences can drive a player crazy as they hit different casinos. Attempting to memorize all the tables will typically result in play errors in all of the games. This is further complicated by the fact that advanced card counters using play indices to vary their actions will find that index values change significantly as well with rule changes.
Uniform Basic Strategy
One solution is to choose a fixed set of basic strategy plays to use for all games of blackjack. In theory, you are picking a set of plays that has the best overall performance for a broad range of blackjack rules. The question then, is what cost in performance does this have on your game?
The popular Knock-Out blackjack system(1) prescribes to this theory and includes a generalized basic strategy table to be used with all games.
The chart below shows the results ofBlackjack Audit simulations using different basic strategy tables with different rules. Since this is a basic strategy comparison, we used flat bets and no play indices. 75% shoe penetration was assumed for all multi-deck simulation runs, re-splitting of aces was allowed, and surrender was not permitted. The expectation is the percentage of each bet you should expect to win or lose, on average, given a specific set of casino rules and play method. It is calculated by dividing the total profit or loss for the simulation run, by the total sum of all wagers, expressed as a percentage.
Table 1: Expectations for different strategies in multi-deck blackjack, basic strategy only
Each row corresponds to one set of casino rules, while the columns represent the expectations for different basic strategy tables (i.e. ‘D8,DAS’ means eight deck, double after splits allowed). The ‘Maximum difference’ column is the difference between the best and worst expectations for that row. The last row shows the average disadvantage for that column’s strategy across all games (average of the difference of the column values to the best expectation from their corresponding row).
Notice that this data does not use different strategy tables based on whether the dealer hits soft seventeen (H17/S17). Although there are some relevant differences in single deck with H17/S17, we don’t recommend any play changes in multi-deck games due to the increased risk for very marginal gain (2). You can view the exact strategy tables we used in these simulations at our web site: http://www.deepnettech.com/article1.html. Also, each simulation was run with 250 million hands of blackjack, yielding an accuracy in these expectations of at least 2 decimal places.
The Knock-out table differs from the eight deck tables only in the handling of splits, and is exactly the same table as "D8, noDAS". There are seven pair hands where hitting is recommended over splitting compared to the "D8: DAS" table: 22/2, 22/3, 33/2, 33/3, 44/5, 44/6, and 66/2. These are the only changes.
The bold table entries are expectations that are at least 5% better than the least value in the row. In terms of actual expectation, the maximum difference in any row is 0.029%, which is a 7.8% improvement (2 deck, DAS, H17).
These marginal differences show that there is no compelling reason to memorize different strategy tables for different multi-deck games. You’re going to sacrifice at most .03% in actual expectation, representing an average difference of less than 5% from the ideal strategy.
The last row of Table 1 shows that choosing the ‘D8, DAS’ or ‘D2, noDAS’ basic strategy table will yield good overall results in all games. Since the two deck table introduces additional double plays that increase losses for marginal gain, we recommend the ‘D8, DAS’ table as the one strategy to use in all multi-deck games.
Single-Deck Basic Strategy Analysis
The analysis of single deck blackjack is a bit more complicated since perfect basic strategy is affected by H17/S17. The options are: single deck, flat bets, no play indices, 50% shoe penetration, re-splitting of aces allowed, no surrender.
Table 2: Expectations for different strategies in single-deck blackjack, basic strategy only
In the multi-deck games, the maximum difference between the best strategy and worst strategy was 0.029. In single deck, the largest gain in expectation is 0.07 in the ‘DAS,/S17’ game. Although the differences are only slightly larger, the affect is more significant given the casino’s marginal edge. In the DAS/S17 game, playing the correct strategy actually yields a slight positive expectation compared to Knock-Out (D8,noDAS).
The last row of Table 2 shows that choosing the ‘DAS/H17’ basic strategy table will yield good overall results in all single deck games. If you want to play only one basic strategy for all games regardless of the number of decks, use the same ‘D8,DAS’ we recommended for multi-deck. It outperformed the Knock-Out (D8,noDAS) by nearly a factor of two.
For a basic strategy player, there is almost no benefit in memorizing additional tables for different casino rules. Although playing the perfect strategy clearly yields the best expectation in every case, the difference is marginal at best. You can safely use whatever multi-deck table you want, but the eight deck/DAS strategy matrix delivers good performance in all games.
As you play fewer decks (or single deck), players should recognize that the negative affect on expectation increases when playing with less than ideal basic strategy, but only marginally. For single deck play, the ‘DAS/H17’ table performs well in all games.
Some readers may note that comparing expectations is not the ideal metric for this analysis; the best comparison is to measure average hourly return rates. For all games, the average total wagers per hand ranged from $5.57 to $5.70 using our flat $5 bets. We can compute the maximum loss per hour in dollars as follows:
(maximum disadvantage) x (maximum average bet/hand) x 100 hands/hr
Hence, using the worst possible strategy matrix in the worst game situation cannot make us lose more than an additional 40 cents per hour, using flat $5 bets and assuming 100 hands per hour.
Next up: generalized strategy and card counting
All of the results so far are for basic strategy play only. Are these results equally true if you are using a card counting system to vary your bets and/or plays? We’ll provide detailed analysis on this topic in the next issue of "Blackjack Insider". Stay tuned!
1) "Knock-Out Blackjack", Olaf Vancura & Ken Fuchs, Huntington Press, Las Vegas, Nevada. 1998.
2) The three play differences that are sometimes recommended for H17 (versus S17) in eight deck are: ace-8/6: double, 11/ace: double, and ace-7/2: double. The marginal increase in expectation (.005%) is not worth the additional financial risk introduced by these marginal doubles. The gain is warranted for the first two double plays in single and double blackjack (and is used in our recommended tables), while the third is not helpful at all in single or double deck blackjack.
Multi-Deck Basic Strategy Tables
These are the exact basic strategy tables used in the simulations shown in our article "Uniform Basic Strategy: Does it Work?", as published in issue #30 of the Blackjack Insider by Henry Tamburin.
Single Deck Basic Strategy Tables
These are the exact basic strategy tables used in the simulations shown in our article "Uniform Basic Strategy: Does it Work?", as published in issue #30 of the Blackjack Advisor by Henry Tamburin.