>>> So let's say you live in this country. You get a knock on your door one day and find out you've been summoned to be a part of the current iteration. What is your chance of survival, 35/36 (~97%) or ~10%?
Depends.
1) if by chance of survival you meant "survival from the current iteration" then the chance is always 1/36. (no matter how many people participate)
2) if by chance of survival you meant "survival from the current and next iterations" then the fact "you are shot" can be decomposed in the following disjoint events: - either you are shot in the current iteration (probability P1 = 1/36) - or, assuming that you escaped for the first iteration (probability 1-1/36 = 35/36), you are shot in the next iteration (probability 1/36). This event has probability P2 = (1-1/36) * 1/36 - or, assuming that you escaped for the second iteration (probability (1-1/36)), you are shot in the third iteration (probability 1/36). Without this assumption, the probability is (1-1/36)^2 * 1/36... - In general, assuming that you are being shot after N iterations, you escaped previous (N-1) iterations, therefore the probability is (1-1/36)^(N-1) * 1/36
Since these events are mutually disjoint, the total probability of being shot in any of these events would be: P = P1 + P2 +... + P_n where N is large enough such that there are not enough people for the next iteration.
which makes sense, since the negation of this event is "you escaped after N iterations) which has the probbility (1-1/36)^N.
>>> Does this chance of survival change when you're actually standing before the tyrant and he's about to roll the dice? If so, why?
No. In the interval of time after being chosen, and before rolling the dice, there are no temporal events that would increase/decrease your probability of survival.
Anyway, it is curious that no gamma-ray bursts occured in our galaxy (yet). It is supposed that such an even would generate enough gamma rays to wipe out the ozone layer, and cause life extinction on earth.
Slashdot Mirror
For those interested, here is a true picture of the Google Container in action.
It's the small rectangular box at the bottom of this picture
>>> So let's say you live in this country. You get a knock on your door one day and find out you've been summoned to be a part of the current iteration. What is your chance of survival, 35/36 (~97%) or ~10%?
...
... + P_n where N is large enough such that there are not enough people for the next iteration.
...
... + Pn = 1/36 * (1 + (1-1/36) + (1-1/36)^2 + ... + (1-1/36)^(N-1)) = 1/36 * (1 - (1-1/36)^N)/(1 - (1-1/36)) = 1 - (1-1/36)^N
Depends.
1) if by chance of survival you meant "survival from the current iteration" then the chance is always 1/36. (no matter how many people participate)
2) if by chance of survival you meant "survival from the current and next iterations" then the fact "you are shot" can be decomposed in the following disjoint events:
- either you are shot in the current iteration (probability P1 = 1/36)
- or, assuming that you escaped for the first iteration (probability 1-1/36 = 35/36), you are shot in the next iteration (probability 1/36). This event has probability P2 = (1-1/36) * 1/36
- or, assuming that you escaped for the second iteration (probability (1-1/36)), you are shot in the third iteration (probability 1/36). Without this assumption, the probability is (1-1/36)^2 * 1/36
- In general, assuming that you are being shot after N iterations, you escaped previous (N-1) iterations, therefore the probability is (1-1/36)^(N-1) * 1/36
Since these events are mutually disjoint, the total probability of being shot in any of these events would be:
P = P1 + P2 +
But we have:
P1 = 1/36
P2 = (1-1/36) * 1/36
P3 = (1-1/36)^2 * 1/36
P_N = (1-1/36)^(N-1) * 1/36
So, P1 + P2 +
which makes sense, since the negation of this event is "you escaped after N iterations) which has the probbility (1-1/36)^N.
>>> Does this chance of survival change when you're actually standing before the tyrant and he's about to roll the dice? If so, why?
No. In the interval of time after being chosen, and before rolling the dice, there are no temporal events that would increase/decrease your probability of survival.
It's actually about colliding neutron stars...
:-)
Anyway, it is curious that no gamma-ray bursts occured in our galaxy (yet). It is supposed that such an even would generate enough gamma rays to wipe out the ozone layer, and cause life extinction on earth.
Wait... why dinosaurs dissapeared again?