I thought of this strategy to answer multiple choice questions that seems to beat the odds.
Assume that there are 4 choices.
- Pick one at random
- Eliminate one of the other 3 (assume that you can eliminate one of the options because you know it cannot be right)
- Switch to one of the other 2 options that remain.
So, it would now seem that the probability that you get the question correct is $3/4 * 1/2 =3/8$ which is higher than what would be expected if you eliminated the option and then picked at random ($1/3$).