Debate Over the Equivalence of Speed and Luck

[modern tiger]

So, there's a game with a feature called Gamepass that speeds up the item rolling process by 3x times. (In this game, rolling for items is free, testing your luck, for example you have a 1 in 1000 chance of obtaining a specific item it's based on RNG.) However, someone says that rolling 3x faster is equivalent to having 3x the luck
i would like to know if it's true or not based on math with explanation etc..

[rotund bone]

so we’re considering two things here

the probability of getting an item on a roll and the rolls per second

do you have 3 times the luck? no

i flip a coin twice

i get heads once i get tails once

i flip a coin 50 times

law of probability says that on average, i will get heads around half that time

so does your luck change? no

but

for example

every time i flip a coin i get one dollar

i can only flip a coin once a second

so every minute i would average around 30 dollars due to law of probability

if i could flip a coin 3 times a second

then i would flip it 180 times within a minute

so by law of probability i would get around 90 dollars

it increases the amount you earn overall , but it doesn’t increase the ratio of successful attempts to unsuccessful attempts

does that answer your question well?

[modern tiger]

i came up with this (sorry for late reponse) "it doesnt change your chance per roll but with 3x more rolls you are going to get things (on average) 3x faster, and the same logic would apply with 3x luck"
The person still says that 3x faster is 3x luck but i don't think it is

[rotund bone]

no thats factually incorrect

again flipping a coin faster doesnt change your probability of landing on heads

if the only thing that was changed was the speed of rolls that has no affect on the probability

[modern tiger]

came up with "it doesnt change the probability but it'll make you land on heads faster on average because you are doing more attempts"

"its more likely for someone to land on heads in 3 flips than 1 flip
same logic applies with the items; Speed roll = get things 3x faster (on average)
which would result in the same thing as a 3x luck gamepass even though they alter the gameplay differently"

"the speed roll doesnt change the probability of getting an item but you will on average get things 3x faster
luck changes the probability of getting an item and you will on average get things 3x faster"

[floral bronze]

If you are talking about a specific game, normally the statistics on which a certain probability depends are not linear. You should check if luck works like that.

As I see it, the obtaining rates in both cases are the same, but since they are different cases, it depends on other factors if one is more suitable than the other.

[modern tiger]

Basically with the gamepass you roll items 3x faster than usual and without u roll slowly and hes saying that since u have that gamepass u get things 3x faster its the same as 3x luck gamepass

[modern tiger]

so 3x speed and 3x luck are not the same right?

[floral bronze]

If both are linear, they are the same.

[rotund bone]

if the luck stays the same and only the speed increases

the speed has no effect on the probability

[floral bronze]

Both are equivalent, not the same

Something like:
total = time (speed)*(probability)
total = time (roll /time)*(probability)

total = (roll )*(probability)
So
(3*roll )*(probability)
=(roll )*(3*probability)

[modern tiger]

yea thats the thing

[modern tiger]

Player A (with Quick Roll Gamepass):

Total Attempts: 3000
Probability of Success per Attempt: Unchanged (1/1000, for example)
Expected Number of Successful Attempts: 3000 * (1/1000) = 3

Player B (with Increased Luck):

Total Attempts: 1000
Probability of Success per Attempt: Tripled (3/1000, assuming 3x luck)
Expected Number of Successful Attempts: 1000 * (3/1000) = 3

so they're the same but through different mechanism?