Poker ICM计算器在Python中不正确

Question

您好，我正在尝试建立一个扑克ICM计算器，以确定每个玩家的期望值基于堆栈大小和支出结构。当我在桌上插入3个播放器时，它是有效的，但只要我尝试4，它就会吐出不正确的值，我正在努力找出原因。下面是我的代码：

# starting vars
players_remaining = [ "p1", "p2", "p3" ]
players_remaining_stacks = [ 4500, 2700, 1800 ] 

# first place pays $84, second $36
payouts = [ 84, 36, 0 ]

# calculate total chips among all players
total_chips = 0
for stack in players_remaining_stacks:
    total_chips += stack

# STEP 1:    
# create a list of all possible finish positions, each possibility has
# the remaining players finishing in a different order
possible_finish_positions = list(itertools.permutations(players_remaining, len(players_remaining)))

# STEP 2: 
# Build matching list of possible_finish_probabilities
# to match possible_finish_positions, probability for each
# position in each scenario
possible_finish_probabilities = []

# loop through every permutation
for finish_positions in possible_finish_positions:

    # % chance of each player finishing where they finish in this permutation
    # this will get tacked onto possible_finish_probabilities when finished
    perm_probabilities = []

    # total amount of chips we've deducted for this permutation
    perm_chips_deducted = 0

    # loop through each finish position
    for x in range(len(finish_positions)):

        player_name = finish_positions[x]
        index = players_remaining.index(player_name)
        player_stack = players_remaining_stacks[index]

        # the odds of this player finishing in this position is
        # their chips divided by remaining chips
        probability = player_stack / ( total_chips - perm_chips_deducted )

        # add to the probabilities for this permutation
        perm_probabilities.append(probability)

        # deduct this player's chips from remaining chips
        perm_chips_deducted += player_stack

    possible_finish_probabilities.append(perm_probabilities)

# now we have two matching lists, 
# possible_finish_positions and a matching possible_finish_probabilities

# STEP 3:
# we can now create the probabilities of finishing in each position for
# each player by looping through all of the scenarios for each player
finish_probabilities = []

# loop through each player
for player_name in players_remaining:

    # initialize probability as 0 for this player
    # finishing in each position
    this_p_probabilities = []
    for x in range(len(players_remaining)):
        this_p_probabilities.append(0)

    # loop through scenarios
    for x in range(len(possible_finish_positions)):

        # this permutation is one possible scenario
        permutation = possible_finish_positions[x]

        # determine where the player finishes in this scenario
        position = permutation.index(player_name)

        # initialize the probability as the probability
        # for the player who finished first in this scenario
        probability = possible_finish_probabilities[x][0]

        # now if this player is not the player who finished first,
        # need to adjust the probability by mutliplying it by
        # the probability for every player in the scenario ahead of this
        # player
        if position != 0:

            print("position not 0, adjusting")

            # loop through everyone in front of this player
            # in the scenario
            for y in range(0, position):

                # adjust the probability
                probability *= possible_finish_probabilities[x][y + 1]

        # if player is 1st in this scenario, their probability
        # is set to this probability of finishing first.
        # otherwise we add it to any other probabilities of the
        # player finishing in this position
        if position == 0:
            this_p_probabilities[position] = probability
        else:
            this_p_probabilities[position] += probability

    # finished probability for this player
    finish_probabilities.append( this_p_probabilities )


print("finish_probabilities=")
for x in range(len(finish_probabilities)):
    print(str(finish_probabilities[x]))


# now I can calculate the EV of each player
# multiply the probability of each position times the 
# payout for that position
player_EVs = []
for x in range(len(finish_probabilities)):

    # get the probability of player finishing
    # in each position
    probabilities = finish_probabilities[x]
    EV = 0

    # multiply probability of each position by the payout
    # for that position
    for y in range(len(probabilities)):
        EV += probabilities[y] * payouts[y]

    # store
    player_EVs.append( EV )

print("player_EVs")
print(str(player_EVs))

让我抓狂的是，这段代码根据https://www.icmpoker.com/icmcalculator/#RXui的ICM计算器为这3个玩家生成了正确的ICMEV值。但是，如果我将顶部的3个变量更改为：

players_remaining = [ "p1", "p2", "p3", "p4" ]
players_remaining_stacks = [ 4500, 2700, 1800, 1000 ] 
payouts = [ 84, 36, 0, 0 ]

这将第四个玩家添加到场景中，而这里的EV值是很远的。特别是，当我在代码末尾输出finish_probabilities时，每个球员的概率看起来都是正确的，因为他们先完成的概率是正确的，但是其他3个都是关闭的，每个球员每个位置的概率加起来都大于1。

我已经逐行梳理了这段代码，就我所知，它正在做我认为它应该做的事情。我不明白为什么它对3个玩家是正确的，但是当我添加第四个玩家时，它不起作用。任何帮助都将不胜感激。

Answer 1

感谢所有看过这篇文章的人。我相信我发现了这个问题，我会把这篇文章张贴出来，因为我没有看到任何其他的Poker ICM问题。

问题是，在某些情况下，我会重复计算概率。例如，有4个玩家，有24个玩家可以完成的顺序排列，其中2个示例是

p1, p2, p3, p4
p1, p2, p4, p3

关于p2获得第二名的情况，我将这两种情况的概率(以及p2获得第二名的任何其他排列)加在一起，以确定p2获得第二名的总概率。然而，这实际上是p1第一次完成，p2第二次完成两次，所以在计算p2的第二名的概率时，计算中应该只包括其中的一项。

我插入了代码，以确保在计算p2的排名第二的概率时(或者在场景中在他们之前的玩家与其他场景相同的任何其他玩家)，只包括这些“相同”场景中的1个。

代码现在对任何玩家都有效。谢谢