Chances of reaching a certain amount of presses

[deedeedont]

Every time you press the button, the chance of failure goes up by one, so for any independent button press, the chances of winning can be calculated using the function: (100 - n)/100 (where n is the press you are on. However the chances of reaching a certain score on a run is not independent, so in order to find that we can use a more advanced function called a product. The function looks like this now: https://imgur.com/NKal4ZK (x is the score reached) here is a graph of that function for those interested: https://imgur.com/x7FaK6Y . using this function we can find

The chances of reaching 51 (the highest score as of 6/4/2023) are 0.000000075 (7.5 * 10^-8) in one or 1 in over 13 million (roughly the odds of giving birth to identical quadruplets

The chances of reaching 99 (the highest theoretical score in the game) are 0.00000000000000000000000000000000000000000093 (9.3 * 10^-43) in one or one in 1 tredecillion. (there are 100 tredecillion grams of matter in the milky way galaxy)

Thank you for reading!

link to desmos graph: https://www.desmos.com/calculator/9t3sv2jndk

[Blisterexe]

theres a guy with a score of 100 -_-

[Elendow]

Originally posted by Blisterexe:

theres a guy with a score of 100 -_-

A cheater, I've removed their score already :)

[Bami]

There was someone with 53 :') they gone now tho

[1404Daniel]

Originally posted by Elendow:

Originally posted by Blisterexe:

theres a guy with a score of 100 -_-

A cheater, I've removed their score already :)

how do you tell when they are cheating?

[Elendow]

Originally posted by nOOdles:

Originally posted by Elendow:

A cheater, I've removed their score already :)

how do you tell when they are cheating?

I just can, I don't want to share too much, cheaters can use this info to cheat even more.

[1404Daniel]

Originally posted by Elendow:

Originally posted by nOOdles:

how do you tell when they are cheating?

I just can, I don't want to share too much, cheaters can use this info to cheat even more.

cool np. Just don't want to be banned wrongly somehow

[GCP42]

This game is a fun exercise for calculating probabilities!

I would argue with the original poster that the chance to reach X is rather (100-n)/100 for n in the range of 0 to X-1, not for n in the range of 0 to X. Here’s why:

The chance to reach 1 is the chance of not dying at 0, which is 100%.
The chance to reach 2 is the chance of not dying at 0 and 1, which is 100% * 99% = 99%.
The chance to reach 3 is the chance of not dying at 0, 1, and 2, which is 100% * 99% * 98% = 97.02%.

And so on and so forth…

The chance to reach X is calculated as the chance of not dying at 0 to X-1, which is 100% * 99% * ... * (100-x+1)%.

By following this calculation, the chance to reach 51 (the current record) is about twice as high as the original estimate, approximately 1 in 6.5 million.

This refers to the number of GAMES you have to play.

Another interesting question is the number of clicks you need to make. Out of those 6,517,802 games, 651,780 will end after click on "1" (2 clicks), 129,052 after click on "2" (3 clicks), and so on. Going all the way, you'll need about 86 million clicks to reach the record. At a rate of 3 clicks per second, it would take about 5 years of constant gaming. Considering there are 3 of those records, it adds up to about 15 years! (Obviously, one person does not have to play all that time, but it serves as an estimate of the collective playtime of all players playing the game.)

P.S. I just saw that the record is now 56. If it is legitimate, that translates into a 1 in 280 million chance and approximately 220 years' worth of clicking.

P.P.S. Feel free to poke holes in my calculations, there is no guarantee I didn't miss +1/-1 somewhere...

[GCP42]

These are the numbers you'd likely to reach, if you were to start playing at:

Beginning of the XX century (123 years ago): 55
When Giza pyramids were built (4500 years ago): 59
When dinosaurs died (65 million years ago): 69
The Big Bang (13 billion years ago): 73

[Pakopa]

I think the 1% chance should stack multiplicatively as that would remove the hard cap at 101 presses. Maybe for the sequel...

[Vosisdos12]

Originally posted by GCP42:

This game is a fun exercise for calculating probabilities!

I would argue with the original poster that the chance to reach X is rather (100-n)/100 for n in the range of 0 to X-1, not for n in the range of 0 to X. Here’s why:

The chance to reach 1 is the chance of not dying at 0, which is 100%.
The chance to reach 2 is the chance of not dying at 0 and 1, which is 100% * 99% = 99%.
The chance to reach 3 is the chance of not dying at 0, 1, and 2, which is 100% * 99% * 98% = 97.02%.

And so on and so forth…

The chance to reach X is calculated as the chance of not dying at 0 to X-1, which is 100% * 99% * ... * (100-x+1)%.

By following this calculation, the chance to reach 51 (the current record) is about twice as high as the original estimate, approximately 1 in 6.5 million.

This refers to the number of GAMES you have to play.

Another interesting question is the number of clicks you need to make. Out of those 6,517,802 games, 651,780 will end after click on "1" (2 clicks), 129,052 after click on "2" (3 clicks), and so on. Going all the way, you'll need about 86 million clicks to reach the record. At a rate of 3 clicks per second, it would take about 5 years of constant gaming. Considering there are 3 of those records, it adds up to about 15 years! (Obviously, one person does not have to play all that time, but it serves as an estimate of the collective playtime of all players playing the game.)

P.S. I just saw that the record is now 56. If it is legitimate, that translates into a 1 in 280 million chance and approximately 220 years' worth of clicking.

P.P.S. Feel free to poke holes in my calculations, there is no guarantee I didn't miss +1/-1 somewhere...

I did the same math as you but came up with a 1 in 325million chance to reach 50. im no expert but 6.5 seems wrong. also 6.5 is less than the 13 the OP sai.

[LynX]

Originally posted by nOOdles:

Originally posted by Elendow:

A cheater, I've removed their score already :)

how do you tell when they are cheating?

Every button press might have a seed value which the dev can just easily reproduce and check if the run was legit or not, many online gambling sites use the same system.
If you want to cheat properly then you might have to mess around with the game files and find a seed that can get you a high score

[Andoryu]

Originally posted by Elendow:

Originally posted by Blisterexe:

theres a guy with a score of 100 -_-

A cheater, I've removed their score already :)

well theres another one now, why even bother you get nothing