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Quick poker primer
• Basic (straight) version: 5 random cards in your hand
§ 2 of same rank: pair (e.g., 3C 3D 5D 6H 7S) § 3 of same rank: three of a kind ( 5C 5D 5H 6H 7S) § 4 of same rank: four of a kind ( 6C 6D 6H 6S 7S) § Two separate pairs: two pair ( 5C 5D 6D 6H 7S) § 3 of one rank, 2 of another: full house ( 5C 5D 6D 6H 6S ) § All cards in rank sequence: straight ( 5C 6D 7D 8H 9S ) § All cards of same suit: flush ( 5H 7H 8H 10H KH ) § All in seq. and same suit: straight flush ( 5D 6D 7D 8D 9D )
• Less probable hands beat more probable hands
• Some games have > 5 cards; you choose 5 cards
Goal for this lecture
- Plan: randomly deal out N hands (like maybe a million) and see how many are full houses, straights, etc. The ratio of the number of straights dealt to N is an estimate of the probability of being dealt a straight.
- This requires us to extend our Hand class so that it can recognize all eight poker hands. We’ll do this, develop testing code along the way, and then answer the question with this Monte Carlo experiment.
What are the probabilities of all the
various poker hands, with varying
numbers of cards in the hand?
multi-way comparisons x < y < z means x < y and y < z w == x == y == z means w == x and x == y and y == z One difference: middle operands are not evaluated twice. conversion to Boolean in conditionals 4.0 + 2 automatically converts 2 to float if x: … automatically converts x to bool. if n: means if n != 0: —for numeric types: zero is false, nonzero true if lst: means if len(list) != 0: —for sequence types: empty is false, nonempty true
Stage 2: start testing
• Form a plan for testing the whole class
• Start by setting up tests for the first methods
• Python features:
§ positional and keyword arguments
§ assert statement
• New patterns:
§ init with multiple disjoint ways to initialize
§ streamlining test cases with lists
Stage 3: complete implementation
• Counting suit and rank histograms is useful
• Also simplifies generalization to more cards
• Python features:
§ augmented assignment (+= and friends)
§ str vs. repr
• new patterns:
§ computing sums using a for loop
§ computing several sums in parallel
§ computing a maximum using a for loop
augmented assignment x += y is shorthand for x = x + y One difference: expression on the left is not evaluated twice. special methods str and repr We have seen the special method str that is called to generate a readable string representation of an object. There is also repr which does something similar. str is used by str() and print. Meant for the user to read. repr is used by repr(), the interactive prompt, and back- quotes (x). Should be unambigous, for the programmer. Ideally, repr() returns exactly what you would put in your program to create that value—recall how strings work.
Boolean to integer conversion Conversions involving bool go both ways. When you convert a bool to a numeric type, True is 1 and False is 0. Example: x += (y > 3) increments x by 1 if y is greater than 3.
Monte Carlo methods
• In CS, “Monte Carlo” is the idea
of a program that runs a random
experiment many times to
estimate some value.
• It can estimate many quantities
for which it is very hard or
impossible to derive formulas.
• A nice example of trading long
computation time for ease of
programming!
Casino de Monte Carlo in Monaco. Wikimedia commons / Wigulf "
