Not really a brain teaser per se, as I don't know the answer, but I'm playing a game and I can't quite figure out the math needed to determine if my outcome is 'good' or not.
So in short:
I'm playing a game, and I gain tokens (for the sake of the conversation). I use those tokens to buy bonuses at random.
Some bonuses are good, some suck. I get them at fairly predictable percentages.
I can calculate the chances of any particular configuration of bonuses given repeats and the fact that order doesn't matter.
But I don't really know how to combine that with the fact that some bonuses are good and some aren't to determine if I should 'accept' the bonus, or 'try again'.
Real world example:
There are 7 bonuses.
Bonus | % Chance to Get | Benefit |
A | 20% | 300 |
B | 20% | 80 |
C | 20% | 400 |
D | 20% | 40 |
E | 6% | 20 |
F | 6% | 800 |
G | 6% | 300 |
H | 2% | 0 |
So I know that for any combination of A though H, it has an XXXX chance of happening. And I can then multiply it by the 'benefit' of that configuration to get a sense of the weighted value of that configuration. But I don't know how to compare that against the likely outcomes I should be able to expect given the conditions.
Any help? / Anything I can clarify that didn't make sense?