I’m working on simulating different Black Jack strategies

I’ll be simulating Vegas style Black Jack in which the players are only concerned with betting against what cards the dealer has. In this game there are no doubles, the house pays out 4:1 for Blackjack and the dealer uses 6 decks. You can review the rules for Vegas Style Black Jack here.

In the following simulation I’ll be evaluating how well the strategy of hitting until you reach 17 works. This is the strategy that the dealer is forced to abide by. The following charts show a Monte Carlo Simulation of 1,000 players, playing 1,000 rounds, all starting with $10,000 in cash and betting $100 each round.

Here are the summary statistics:

count   1000.000000
mean   22307.600000
std     4052.654222
min     7100.000000
25%    19600.000000
50%    22350.000000
75%    25100.000000
max    35800.000000
Percent of players who made money: 99.7 %
Percent of players who lost money: 0.2 %
Percent of players who went broke: 0.0 %

So this shows that following the dealer’s strategy is actually a fairly effective strategy. In the future, I’ll be working on simulating different Black Jack strategies; with my ultimate plan being to create an evolutionary algorithm, where say many of each of the different strategies is represented in a 1,000 round generation and where all of the players who made money survive to the next round and reproduce. However, when they reproduce they’ll have a chance for mutation that can affect variables such as when you stop hitting, and how much you bet each round. I believe that over many many generations of this evolutionary algorithm/simulation I’ll be able to create a very good Vegas Black Jack strategy.

Here I’ve visualized a smaller simulation of 10 players playing 500 rounds. The first series of visualizations shows the outputs of the players using the dealers strategy to great success while the second series shows the players using what is known as Basic Strategy which is supposedly the mathematically principled way of playing any given Blackjack hand. With this later strategy, almost all of my players went broke. This indicates to me that my algorithm needs significant work.

This shows the progression of how each player performed during their 500 matches using the basic strategy. You can mouse over one of the lines to see exactly how much money each player had at each round interval. You can also zoom in and out of the plot by drag and scrolling.

Here is the plots for the simulation that utilizes basic strategy. Almost all of these players went broke so I saw no need to visualize a bubble chart of the outcome.

This shows the progression of how each player performed during their 500 matches using the basic strategy. You can mouse over one of the lines to see exactly how much money each player had at each round interval. You can also zoom in and out of the plot by drag and scrolling.