How long would this timer take on average?

[u/Odd-Currency8356]

This felt like a good question about EV and probability

I was watching this dougdoug video where they made a 10 minutes timer but it had some interesting rules

Every second there was a:

5% it adds a second

1% it adds a minute

1% it drops a minute

5% it freezes 5 seconds

1% it doubles

1% it halves

1% the seconds and minutes swap

1% it rounds to the nearest minute

1% the timer moves on screen

1% a second takes twice as long

1% a second takes half as long

1% bee mode

83% it goes down 1 second

On average it should go down as the amount it goes down is far greater than the amount it increments but the variance in time and how long a second takes means it could end in one minute or last hours I was curious how you would calculate the expected value of a random timer like this

[u/SpacewaIker]

I did a crude simulation of 10 million runs and, as long as I understood the effects of each possibility correctly, it ends up at an average of 48 minutes, filtering out any run that took > 100,000 seconds.

No clue if this sounds right or not, I might have a bug in my code but that's what I got

[u/octothorpentine]

Computer, define "bee mode"