HistoryBot

import random

class HistoryBot(object):
    def __init__(self, index):
        self.pastWins = []
    def select(self):
        if not self.pastWins:
            return 1
        return random.choice(self.pastWins)
    def update(self, choices):
        unique = [x for x in choices if choices.count(x) == 1]
        if unique:
            self.pastWins.append(min(unique))

Implementation of user2390246's comment:

What about this then? Start with 1. After the first round, keep track of the winning values and pick randomly from them with probability equal to the number of occurrences. E.g. if the winning values in the first three rounds are [2, 3, 2] then in round four, pick [2] with p = 2/3 and [3] with p = 1/3.