Even or Odd?: The player, being asked the question "Even or odd?", chooses one of these choices. Then the asker chooses one of these. The player wins if the choices are the same.
Guess the Number: The challenger chooses a random number in a range. The player then tries to guess it, doing some tries and choosing a number in the range.
Bulls and Cows: a four digit number is chosen by the challenger where all digits differ. The player then tries to guess it, doing some tries and choosing a number in the range. Then bulls and cows are fed back, where a bull denotes a correct number in the correct place, and a cow denotes a correct number, yet wrong place.
Bache's Game: Given n items, and two players, they pick at most k items. Whoever picks the last item, loses. [Variation: Whoever picks the last item, wins.]