Blackjack Calculation using Composition-Dependent Strategy
iGaming Pal calculation for Classic Blackjack from Microgaming
At the begging of each game (after placing bets) the player gets 2 cards and the dealer gets 1 from a 52-
card deck. So the number of all possible cases is 66300*. But we don't have to calculate each of the
66300* situations - for example card suit has no impact at all in blackjack. We therefore reduce 66300*
cases to a smaller number of logical cases. Each logical case has its own Weight (repeating frequency).
Example: If the dealer has 8 and the player has two 5, then the frequency is 24.
After determining all starting cases we calculate the probability for each case and for every action (hit,
stand, double and split). Hit-action: For every possible card to hit, we recursively repeat the probability
calculation.
In the end, we get for our 8/5;5 example the following numbers:
Blackjack
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Comparing Composition-Dependent Strategy with Basic Strategy
This two blackjack strategies are different, so our strategy cannot be directly compared with Basic
Strategy. Example: (Players Hand / Dealer's card = Decision)
Basic strategy : 12 / 3 = Hit
Our strategy : 10, 2 / 3 = Hit
Our strategy : 9, 3 / 3 = Hit
Our strategy : 8, 4 / 3 = Stand
Our strategy : 7, 5 / 3 = Stand
But if we calculate the average probability/decision/action for all 2-card cases with sum 12 (hard-hand),
then we get also Hit as the best play. So we compared all average 2-card cases with the Basic strategy
table and get exactly the same results.
Our 2-card Basic Strategy approximation is here
The values in the first row are dealer's winning chances expressed in percentages (%). The values in the
second row are chances for push (push means no one wins), The player's winning chances are given in
the third row. The sum of these 3 values per decision/action is always 100.00%
The final game winning chance is shown in row 4= row3-row1 and for double and split row4= (row3-
row1)*2. In our example Double Down is the best strategy.
In the end - The house edge is the sum of the best final game winning chances divided by the sum of all
bets (from all starting cases). As a result we get the house edge of 0.0809573009677919%.
Explanation for the Final Game Winning Chance
(4th. row values from our example above):
If you play a lot and 8/5,5 comes many, many times and your bet is always 1$ - then the numbers above
(for double) say:
On an average of 100 (8/5,5) games you will lose in approximately 38 games 2$ per game. In
approximately 7 games you will get your money back; and you will win 2$ per game in approximately 54
or 55 games.
On an average of 100 (8/5,5) games your win will be close to this calculated value: 38.3396*(-2$) +
7.1766*0$ + 54.4838*2$ = 32.2885$
* Number of all starting cases is 66300 = 52C2 * 50, C is for combination.
* Final Game Winning Chance = EV = Expected Value
Statistical Simulation
The most reliable and ultimate proof of a concept is always the statistical simulation; so we have
simulated millions of games. In game-simulation the dealer and the player get random cards, the
software calculates the best play and we record if the player wins or loses. As the number of the
simulated games grows, the similarity of simulated house edge and the calculated house edge must
grow too if our calculation is correct. So after 46.080.000 game simulations with 1$ bet per game we get
the sum of all bets of 49,911,988.00$ (by double and split the bet doubles) and the loss of 39,227.50$.
This means the simulated house edge is 0,078593%. This number is close enough to the calculated
house edge of 0.080957% to show, that our calculation and our blackjack strategy are reliable and
correct.
Composition-Dependent Strategy
As the name says, this blackjack strategy shows the best play based on every composition of the
player's cards. The composition-dependent strategy is based upon the exact cards dealt to the player
rather than just the total of the player's hand. Analyzing every possible game situation, this blackjack
strategy gives players the biggest possible win chance. In other words, the smallest possible house
edge. The fewer the decks the more advantageous the composition-dependent strategy is - if compared
to the basic strategy. By using the composition-dependent strategy when playing certain single-deck
blackjack games, the player can cut in half the house edge (comparing to the basic strategy).
Usability of the Composition-Dependent Strategy
There are three ways to use any blackjack strategy: To memorize all strategy cases, to use a strategy
table or to use a software. Despite the superiority of the composition-dependent strategy it is very difficult
to memorize thousands of game play decisions/cases. On the other hand, the basic strategy has less
then 300 cases. It is possible to use the composition-dependent strategy with strategy tables, but it is
exhausting and slow. The best way is, to use a software that calculates the best play for every game
situation. Try our free Blackjack software using Composition-Dependent Strategy here.
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