First decision: Do you go on and try for $64,000 given that you have already won $32,000 and if you answer incorrectly you still get to keep the $32,000? The answer is obviously "yes," and a no-brainer. But, let's evaluate the no-brainer. Assume you have a 50-50 chance of getting the question correct.

Expectation value of the decision to try for the $64,000:

Expectation Value = -(.5)(0) + (.5)($64,000 - $32,000) = $16,000

The first term is a 50% chance of missing the question and is multiplied by the amount you lose as a result of missing the question. You lose nothing, so the loss is zero. The first term is zero.

The second term represents the effect of answering correctly. We stand to win an extra $32,000 ($64,000 total winnings minus what we have already is our net gain possible in making the decision to try for the question) And, we have assumed that we have a 50% chance of winning which contributes the 0.5 factor to the second term.

Hence, the "average" we would expect to win is half of the $32,000 or $16,000. Not trying for the question would be like walking away from $16,000 on average.

Notice also that if by missing the question, we actually lost the $32,000, the zero would be replaced by $32,000. The first term is negative and the net expectation value would be zero saying the decisions to go on and try for $64,000 and the decision to stay with the $32,000 would be equivalently desirable from a mathematics standpoint.

Second Decision: We have won $64,000 and contemplate trying for $125,000. Again, we assume we have a 50-50 chance of answering the question correctly. (Suppose we have no clue about what the answer is, but we have our 50-50 lifeline left)

Expectation value of the decision to try for the $125,000:

Expectation Value = -(.5)($64,000 - $32,000) +
                                 (.5)($125,000 - $64,000) = $14,500.

The first term says that we have a 50% chance of answering incorrectly and we lose $32,000 of the $64,000 we have already won. The rules of the game never let us lose the $32,000. So our net loss is $32,000 if we lose.

The second term represents the 50% assumed chance that we will answer correctly and win an additional $61,000 in addition to the $64,000 we already have, bringing our total winnings to $125,000.

Notice that the expectation value of "Going for the $125,000" is nearly as large as the expectation value of making the "no-brainer." Yet, many people will walk away from this $14,500. They value the $32,000 they already have more than they value the additional $61,000 they stand to win by going on. They are Bernoullied.