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After splitting, you double down on your first hand and stand on your second. The dealer goes bust, giving you a rare 3x win.
My second program plays a large number of hands using basic strategy and collects statistics about the outcome. Here is the main program:.
The matlabpool command starts up many workers copies of MATLAB on the cores or processors available in a multicore machine or a cluster.
These workers are also known as labs. The random number generators on each lab are initialized to produce statistically independent streams drawn from a single overall global stream.
The main program on the master MATLAB creates an array B , and then the parfor loop runs a separate instance of the sequential simulator, blackjacksim , on each lab.
The results are communicated to the master and stored in the columns of B. The master can then use B to produce the plot shown in Figure 3.
With "only" 25, hands for each player, the simulation is still too short to show the long-term trend. The computation time is about 11 seconds on my dual-core laptop.
If I do not turn on the MATLAB pool, the computation uses only one core and takes almost 20 seconds. Figure 3. Four players in a parallel simulation.
Green wins, red nearly breaks even, cyan muddles through, and blue should have quit while he was ahead. This run can also produce the histograms shown in Figure 4.
The cumulative return from the four players is the dot product of the two vectors annotating the horizontal axis. The average return and a measure of its variation are shown in the title of the figure.
We see that in runs of this length, the randomness of the shuffle still dominates. It would require longer runs with millions of hands to be sure that the expected return is slightly negative.
Figure 4. Histograms for each player. Blackjack can be a surrogate for more sophisticated financial instruments. The second shows the performance of our blackjack simulation playing hands a day for each of the days the stock market was open that year.
More important than these final results is the fact that both instruments show large fluctuations about their mean behavior.
Over the short term, stock market daily behavior and card shuffling luck are more influential than any long-term trend. Figure 5. Short-term random fluctuations dominate any long-term trend.
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