# -*- coding: utf-8 -*-
"""
使用済みの手札や、自分が持っているので
他が出さないことがわかっている札の情報を無視した計算
(相手の出す札の分布が自分の出す札以外の均一な分布と仮定する)
確率論的に導出したのを全探索で一応確認する
"""

TEST = []
def prob_win(my, N=52):
    """
    全N枚中、下からmy番目(0-origin)のカードを出した際の
    自分が中央値になる確率
    """
    c = my * (N - my - 1) * 2
    p = float(c) / (N - 1) / (N - 2)
    return p

def prob_gt(my, other, N=52):
    """
    自分以外の特定の1人がotherより大きな点で勝つ確率
    """
    if my < other:
        c = (N - other - 1) * (N - other - 2) / 2
    elif my > other:
        c = (N - my - 1) * (N - my - 2) / 2
        d = (my - other - 1)
        c += ((my - 1) * 2 - (d - 1)) * d / 2
    else:
        c = (N - my - 1) * (N - my - 2) / 2
        

    if TEST: return c, (N - 1) * (N - 2)
    return float(c) / (N - 1) / (N - 2)

def _prob_gt(my, other, N=52):
    c0 = c = 0
    for i in range(N):
        if i == my: continue
        for j in range(N):
            if i == j: continue
            if j == my: continue
            c0 += 1
            if my < i < j and other < i:
                c += 1
            if j < i < my and other < i:
                c += 1
    return c, c0

def _prob_lt(my, other, N=52):
    c0 = c = 0
    for i in range(N):
        if i == my: continue
        for j in range(N):
            if i == j: continue
            if j == my: continue
            c0 += 1
            if my < i < j and other > i:
                c += 1
            if j < i < my and other > i:
                c += 1
    return c, c0

def prob_lt(my, other, N=52):
    """
    自分以外の特定の1人がotherより小さな点で勝つ確率
    """
    if my > other:
        c = other * (other - 1) / 2
    elif my < other:
        c = my * (my - 1) / 2
        d = (other - my - 1)
        c += ((N - other) * 2 + (d - 1)) * d / 2
    else:
        c = my * (my - 1) / 2
        
    if TEST: return c, (N - 1) * (N - 2)
    return float(c) / (N - 1) / (N - 2)


def _test():
    global TEST
    TEST = True
    assert prob_lt(3, 5, 10) == _prob_lt(3, 5, 10)
    assert prob_lt(3, 6, 10) == _prob_lt(3, 6, 10)
    assert prob_lt(6, 6, 10) == _prob_lt(6, 6, 10)
    assert prob_gt(3, 5, 10) == _prob_gt(3, 5, 10)
    assert prob_gt(3, 6, 10) == _prob_gt(3, 6, 10)
    assert prob_gt(6, 6, 10) == _prob_gt(6, 6, 10)

    
if __name__ == "__main__":
    _test()