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That last pic hahaha
Solo Bug Player - Vol. 1 Ch. 31
- Thread starter MangaDex
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Dex-chan lover
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@lionfromnorth 0.1% per person means you'd need 1k people for 100%.
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Fed-Kun's army
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Guys stop shaming other people for wanting to be stepped on
We all have our own weird fetishes
We all have our own weird fetishes
@lionfromnorth
@ShionSinX
Sorry for being a nerd, but just summing the 0.1% probability of each person gives you the wrong answer. To calculate the probability that invincibility is activated, you'd have to calculate the probability that it is activated for at least one person. Assuming that the events are independent, the probability of it not being activated for anyone would be (999/1000)^4, and therefore the probability of it being activated for at least one person is 1 - (999/1000)^4 = 0.003994..., which is not 0.4%, but extremely close. The reason for the sum being so close is that the linear approximation of the function f(x) = 1 - (1 - x)^4 at x = 0 is g(x) = 4x, and so for small values of x we have near equality of f and g.
For a party of 100 people, the probability is 1 - (999/1000)^100 = 0.0952... ~ 9.52%, so less than 10% chance of invincibility being activated.
For a party of 1000 people, the probability is 1 - (999/1000)^1000 = 0.6323... ~ 63.23%, a little less than 2/3.
For a party of 10000 people, the probability is 1 - (999/1000)^10000 = 0.9999... ~ 99.99%.
But wait, one of you might say, isn't it the case that the linear approximation of h(x) = 1 - (1 - x)^1000 at x = 0 is equal to y(x) = 1000x? Why don't we have near equality here? That's because the linear constant is much larger in the second case, and therefore the linear approximation "goes bad" much faster than in the first case.
TL;DR: Summing gives wrong probability, actual probability is given by P(x; n) = 1 - (1 - x)^n, where x is probability of invincibility being activated per person and n is number of people in the party.
@ShionSinX
Sorry for being a nerd, but just summing the 0.1% probability of each person gives you the wrong answer. To calculate the probability that invincibility is activated, you'd have to calculate the probability that it is activated for at least one person. Assuming that the events are independent, the probability of it not being activated for anyone would be (999/1000)^4, and therefore the probability of it being activated for at least one person is 1 - (999/1000)^4 = 0.003994..., which is not 0.4%, but extremely close. The reason for the sum being so close is that the linear approximation of the function f(x) = 1 - (1 - x)^4 at x = 0 is g(x) = 4x, and so for small values of x we have near equality of f and g.
For a party of 100 people, the probability is 1 - (999/1000)^100 = 0.0952... ~ 9.52%, so less than 10% chance of invincibility being activated.
For a party of 1000 people, the probability is 1 - (999/1000)^1000 = 0.6323... ~ 63.23%, a little less than 2/3.
For a party of 10000 people, the probability is 1 - (999/1000)^10000 = 0.9999... ~ 99.99%.
But wait, one of you might say, isn't it the case that the linear approximation of h(x) = 1 - (1 - x)^1000 at x = 0 is equal to y(x) = 1000x? Why don't we have near equality here? That's because the linear constant is much larger in the second case, and therefore the linear approximation "goes bad" much faster than in the first case.
TL;DR: Summing gives wrong probability, actual probability is given by P(x; n) = 1 - (1 - x)^n, where x is probability of invincibility being activated per person and n is number of people in the party.
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@anon4172:
They wouldn't be, we're talking about a games code. The condition check would most likely just be;
Random_Value(0.0-100.0) < Player_Count * Spawn_Chance
(If a random floating point value (in the range of 0 to 100) is less than the player count multiplied by spawn chance)
Randomness in games are designed to so the player thinks they're fair, which often means avoiding real probabilities. For example displaying the chance as 50% on the UI to player, while actual internal chance is like 65%. Or increasing chance each time it fails to avoid player frustration (eg for item drops).
They wouldn't be, we're talking about a games code. The condition check would most likely just be;
Random_Value(0.0-100.0) < Player_Count * Spawn_Chance
(If a random floating point value (in the range of 0 to 100) is less than the player count multiplied by spawn chance)
Randomness in games are designed to so the player thinks they're fair, which often means avoiding real probabilities. For example displaying the chance as 50% on the UI to player, while actual internal chance is like 65%. Or increasing chance each time it fails to avoid player frustration (eg for item drops).
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@anon4172
Your math is good, assuming the game was designed that way.
But from what we’ve seen, I wager that it’s still possible that it was programmed with an additive probability.
Especially since
0.0001n
is a lot shorter to compute than
1-0.0001^n
The first would have to add the n number of players, then multiply by 0.0001.
This takes n+1 operations to calculate, before applying the probability.
The second would need to add the same number of times, then need to multiply 0.0001 by itself n-1 times, then apply the subtraction, taking 2n operations to complete before applying the probability.
There are ways to make it more efficient using memory and storage, but the first way is kinda just easier and shorter and less of a hassle to deal with.
And remember, the premise of this world is that it’s a buggy game. So you can’t really expect fair/balanced encounters.
Your math is good, assuming the game was designed that way.
But from what we’ve seen, I wager that it’s still possible that it was programmed with an additive probability.
Especially since
0.0001n
is a lot shorter to compute than
1-0.0001^n
The first would have to add the n number of players, then multiply by 0.0001.
This takes n+1 operations to calculate, before applying the probability.
The second would need to add the same number of times, then need to multiply 0.0001 by itself n-1 times, then apply the subtraction, taking 2n operations to complete before applying the probability.
There are ways to make it more efficient using memory and storage, but the first way is kinda just easier and shorter and less of a hassle to deal with.
And remember, the premise of this world is that it’s a buggy game. So you can’t really expect fair/balanced encounters.
@ShionSinX No, he didn't say it was additive, you're assuming that it's additive with a single data point, someone else might assume he is approximating 0.399% to 0.4%.
@StrangeStripes I don't think that's an issue, if the game can faithfully simulate bodies and consciousness, I don't see why it couldn't simulate real world probability.
@StrangeStripes I don't think that's an issue, if the game can faithfully simulate bodies and consciousness, I don't see why it couldn't simulate real world probability.
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@zekkendo Yeah, the situation is probably too ambiguous to tell, if the game is faithfully simulating his brain, then it would probably have to do things much more difficult than just exponentiation hundreds of trillions of times per second, calculating probabilities would be a drop in the ocean. But maybe it's not simulated, maybe it's a magical game, but then it might also be able to calculate anything regardless of computational expense. Or maybe the magic only affects the MC and the rest of the game is programmed traditionally. You're probably not supposed to think about it lol
