Hand_results = pd.DataFrame(columns=column_names) Return tuple(() for _ in range(amount))įlush_cutoff = 150 # Increase this number to run the simulation over more hands.Ĭolumn_names = #%% What is the likelyhood of getting flush? Monte Carlo derivation Say, for example, you don't have a firm understanding of the combination or permutation math we went through above - which produced the exact answer to the question 'What are the odds of getting a flush?' We can run many simulations of this card game to figure out what that probability would be to a high degree of certainty. They can be quite elementary.Įven so, simulations are kind of magical because you can use them to brute force a solution out of a complex system even when a mathematical model of that system is hard to come by.

'Monte Carlo' is just an overly fancy and arbitrary name for 'simulation'. mostly because their name sounds so exotic. Side note: When I began learning about Monte Carlos I thought they were a sort of 'magical', mysteriously complex thing. In practice this is called a Monte Carlo simulation. To estimate the probability of getting a flush programmatically, you have to run that experiment many thousands of times over. What are the odds of getting a flush? A Monte Carlo solution So in the long run, one out of every 509 hands is a flush. Mathematically, that looks like:$$rac $$

then divide all that by the number of possible ways to draw any 5 cards.

then subtract by the number of Straight and Royal Flushes,.

Determine the number of ways to draw any 5 cards of the same suit,.

The likelihood of drawing a standard flush is calculated in three steps: What are the odds of getting a flush? The Mathematical solution Together, these hands are 3 out of the 5 most powerful hands in Poker.

Royal Flush - hold 5 cards of the same suit ordered in a series ending with an Ace.

Straight Flush - hold 5 cards of the same suit ordered in a series.

(The standard) Flush: hold 5 cards of the same suit not in a series.

You have a flush in poker when holding 5 cards of the same suit.

Calculating probability for poker hands