Penney's game

One suggested variation on Penney's Game uses a pack of ordinary playing cards.

The Humble-Nishiyama Randomness Game follows the same format using Red and Black cards, instead of Heads and Tails.

The cards are then turned over one at a time and placed in a line, until one of the chosen triples appears.

The winning player takes the upturned cards, having won that "trick".

As this card-based version is quite similar to multiple repetitions of the original coin game, the second player's advantage is greatly amplified.

The probabilities are slightly different because the odds for each flip of a coin are independent while the odds of drawing a red or black card each time is dependent on previous draws.

Note that HHT is a 2:1 favorite over HTH and HTT but the odds are different for BBR over BRB and BRR.

Below are approximate probabilities of the outcomes for each strategy based on computer simulations:[4] If the game is ended after the first trick, there is a negligible chance of a draw.

Recently Robert W. Vallin, and later Vallin and Aaron M. Montgomery, presented results with Penney's Game as it applies to (American) roulette with Players choosing Red/Black rather than Heads/Tails.