The 'Best' Winning StrategyNo matter what sequence Player A chooses, Player B can make a selection with a higher probability of winning.
For the greatest chance at winning, Player B takes the middle coin of Player A's prediction, flips it over and places it at the front of Player A's sequence. The first three coins of this new sequence are taken as Player B's choice. See diagram [left]. |
Think About it.In terms of the example selections above, consider the sequence on the right.
If HHH appears at the beginning of the sequence, this has a 1/8 chance of occurring. However, if HHH appears later in the sequence, it must be proceeded by a T. Therefore, the probability of THH succeeding over HHH becomes 7/8. |
What are the Chances?
In order to work out the probabilities of Player B succeeding over Player A with specific sequences, there is quite a bit of complicated mathematics involved. Options include, but are not limited to, the use of infinite sums of geometric series as well as Conway's algorithm (a method using binary that is explained here).
In terms of the 'best' winning strategy, the table below represents the probabilities as well as the odds of Player B winning each round:
In terms of the 'best' winning strategy, the table below represents the probabilities as well as the odds of Player B winning each round: