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@ -90,50 +90,133 @@ def find_hands(table):
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"straight flush": find_straight_flush(table),
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}
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def find_hand_averages(result):
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output = {}
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for hand in result:
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output[hand] = 0
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for hand_type in result[hand]:
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output[hand] += result[hand][hand_type] / len(result[hand])
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return output
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def sanity_check(table, result):
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for hand_type in result["one pair"]:
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if result["one pair"][hand_type] and not result["high card"][hand_type]:
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print(f"Invalid result at one pair of {hand_type} but not high card")
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print(table)
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print(result)
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for hand_type in result["two pair"]:
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[rank1, rank2] = hand_type.split("+")
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if result["two pair"][hand_type] and not (result["one pair"][rank1] and result["one pair"][rank2]):
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print(f"Invalid result at two pair of {hand_type} but not respective one pairs")
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print(table)
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print(result)
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for hand_type in result["three of a kind"]:
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if result["three of a kind"][hand_type] and not result["one pair"][hand_type]:
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print(f"Invalid result at three of a kind of {hand_type} but not one pair")
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print(table)
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print(result)
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for hand_type in result["straight"]:
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i = LOOPED_RANKS.index(hand_type)
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if result["straight"][hand_type] and not (result["high card"][LOOPED_RANKS[i-4]] and
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result["high card"][LOOPED_RANKS[i-3]] and
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result["high card"][LOOPED_RANKS[i-2]] and
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result["high card"][LOOPED_RANKS[i-1]] and
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result["high card"][LOOPED_RANKS[i]]):
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print(f"Invalid result at straight of {hand_type} but not high cards")
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print(table)
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print(result)
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for hand_type in result["full house"]:
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[rank1, rank2] = hand_type.split(" over ")
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if result["full house"][hand_type] and not (result["three of a kind"][rank1] and result["one pair"][rank2]):
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print(f"Invalid result at full house of {hand_type} but not respective three of a kind and one pair")
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print(table)
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print(result)
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for hand_type in result["four of a kind"]:
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if result["four of a kind"][hand_type] and not result["three of a kind"][hand_type]:
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print(f"Invalid result at four of a kind of {hand_type} but not three of a kind")
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print(table)
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print(result)
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for hand_type in result["straight flush"]:
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if result["straight flush"][hand_type] and not result["straight"][hand_type]:
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print(f"Invalid result at straight flush of {hand_type} but not straight")
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print(table)
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print(result)
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# def find_hand_averages(result):
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# output = {}
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# for hand in result:
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# output[hand] = 0
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# for hand_type in result[hand]:
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# output[hand] += result[hand][hand_type]
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# output[hand] /= len(result[hand])
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# return output
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def find_probabilities(size):
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results = [find_hands(sample(DECK, size)) for _ in range(SAMPLE_SIZE)]
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output = {}
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results = []
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for _ in range(SAMPLE_SIZE):
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table = sample(DECK, size)
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result = find_hands(table)
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sanity_check(table, result)
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results += [result]
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# The idea was to find the probability of each hand this way:
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# for each hand
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# for each hand_type of this hand
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# find the probability of this hand_type with occurrences / SAMPLE_SIZE
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# find the probability of the hand by averaging the probability of each hand_type, that is
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# sum everything and divide by the number of types (= len(results[0][hand]))
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# We don't use this approach becuase finding the intermediate probabilities for each hand_type introduces
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# division, which comes with rounding errors.
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# To avoid this we postpone division as much as possible, working with integers as much as possible
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probabilities = {}
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for hand in results[0]:
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output[hand] = {}
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occurrences = 0
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for hand_type in results[0][hand]:
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output[hand][hand_type] = 0
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occurrences_per_type = 0
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for i in range(SAMPLE_SIZE):
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if results[i][hand][hand_type]:
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output[hand][hand_type] += 1/SAMPLE_SIZE
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return find_hand_averages(output)
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occurrences_per_type += 1
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# probability_per_type should be occurrences_per_type / len(results[0][hand]) but
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# it's better to postpone divisions as much as possible to prevent rounding errors
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occurrences += occurrences_per_type
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probabilities[hand] = occurrences / (SAMPLE_SIZE * len(results[0][hand]))
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return probabilities
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# output = {}
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# for hand in results[0]:
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# output[hand] = {}
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# for hand_type in results[0][hand]:
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# output[hand][hand_type] = 0
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# for i in range(SAMPLE_SIZE):
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# if results[i][hand][hand_type]:
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# output[hand][hand_type] += 1
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# output[hand][hand_type] /= SAMPLE_SIZE
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# return find_hand_averages(output)
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groups = tuple(range(5, 52, 5))
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global_results = {
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"high card": (),
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"flush": (),
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"one pair": (),
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"straight": (),
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"two pair": (),
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"three of a kind": (),
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"straight": (),
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"flush": (),
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"full house": (),
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"four of a kind": (),
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"straight flush": (),
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"four of a kind": (),
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}
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for size in groups:
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print("=========================")
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print("cards on table:", str(size).rjust(8))
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print("-------------------------")
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results = find_probabilities(size)
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for hand in global_results:
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global_results[hand] += (results[hand],)
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results = sorted(results.items(), key=lambda hand: -hand[1])
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print("===========================")
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print(" cards on table:", str(size).rjust(9))
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print("---------------------------")
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for (hand, p) in results:
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str_p = f"{p:.2%}"
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print(" " + hand.ljust(15) + str_p.rjust(8))
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print("=========================")
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str_p = f"{p:.4%}"
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# str_p = f"{p}"
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print(" " + hand.ljust(15) + str_p.rjust(10))
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print("===========================")
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print("")
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print("")
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@ -157,5 +240,3 @@ ax.legend(loc='upper left', ncols=3)
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ax.set_ylim(0, 1.05)
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plt.show()
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