Which gives you better odds on Trivia Crack: Bombing or Double Chance? There is something puzzling me about this "Trivia Crack" bonuses.
In the game, you have to answer a question by choosing one of the four selections. Only one of them is correct. And you have two bonus features which can be used anytime:
1) Double Chance: You will have the right to make two selections, instead of one. (Costs 3 credits) 2) Bombing: The computer will remove two wrong answers. (Costs 6 credits)
The question is: Assuming you are making completely random choices, which option gives you better odds, and how to prove it mathematically?
I mean, i know the trick:
At first you think by Bombing you get %75 chance, because you have will be able to remove 3 selections. But with Double Chance you have the odds of %50, since you will be able to remove only two selections.
But that's not the case. Because by bombing you can't hit a "correct" answer, but only remove two "wrong" choices, which means you will be left with 2 choices, which makes your chance %50. "Just like the Double Chance"... Or is it?
I know the Monthy Hall routine, but don't know how to implement it to this issue. I know AI knows the correct answer and it effects the calculation, but does it affect the mathematical odds too? Or the advantage appears if the selection process is not random, since the player is a human and already have an idea about the question?
 A: This has nothing to do with Monty Hall since the wrong answers are revealed before the user picks an answer, not after.
Bombing means you're trying to pick $1$ correct answer out of $2$ options: assuming completely random selection, the probability of a correct answer is $\frac12$.
With double choice, you're essentially choosing a set of two answers out of four. The probability that the right answer is in your set is $\frac12$.
If that doesn't convince you since you're worried about order, think of it this way: The probability of getting it right the first time is $\frac14$. The probability of getting it wrong the first time and right the second time is $\frac34 \frac13$, or $\frac14$. Therefore the probability you get it at all is $\frac14+\frac14$, or $\frac12$.
So they're both the same: both powerups give you a 50-50 shot of getting the right answer.
A: The probability analysis is correct, but often you have at least some insight into the available answers. Therefore, Bombing is often better than Double Chance because having only two choices to choose from allows you to focus better on the available possibilities and better hone in on the right answer.  
But Double Chance is clearly better than Bombing if know that two of the original four answers are wrong. Using Bombing in such a scenario may leave you with the two answers that you think might be correct, which does not help you. 
