It is interesting to note that the probability of a tie is more or less near 12-14% and that, as we expected, it is equal to 0 when the hand is equal to 16 (since the dealer must draw on 16 and therefore a tie is not possible). For some reason which I ignore, R did not print in plain the probabilities of winning for the dealer, however you can easily get them from the table above or by calculating for each row 1 – Prob of Win – Prob of a tie, since the three events should (must) sum up to one. Why not run the simulation for each hand from 16 to 21 and then plot the results? Warning: your computer may yell at you after this demanding step!Īs we could expect, as the player’s hand gets higher, the probabilities of winning increases. In this case the odds seem to be a lot worse than before, by just subtracting 1 point to the player’s hand we raised the probability of win for the dealer from 28% to 43.4%. Let’s now simulate 2000*100 games with a hand equal to 18 and 3 decks and then average the probabilities: A tie is likely to occur 13% of the times. Let’s have a look at the results that we have got:īy simply standing with a hand equal to 19, you can expect to win 59% of the times, and loose 28%. Since the code looks pretty hairy, many explanations are provided.Ī small but important note: if you want to run the simulation, since it is a bit demanding computationally speaking, in order not to crash RStudio you may want to run a line a time and not the entire code all at once, or just maybe use only some functions, just be careful because since we run the simulation a big number of times and the functions are not the fastest to be run, your computer might complain a little. In the first one I looked for the probabilities for each possible event (that’s to say: “player wins”, “tie”, “dealer wins”). The code looks like messy, I know, If I had to do it now, I guess I would do many things differently, however, the results looks fine, and the code runs fine as well, therefore it is not entirely to be thrown away I believe. I have just decided to call it plain vanilla since neither double down or split pairs are allowed.

Here is a simulation I run with R in the same period I created the poker one.

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