Statistics - probability question?

Question

I am playing an online game and I want a certain event to happen.

If I spend 1667 units I have a 20% chance of the desired event happening. (even if I spend more that 1667 the max probability stays capped at 20%).

If I spend 167 units I have a 2% chance of the desired event happening.

I can try as many times as I want, until I get the desired event.

What is the better course of action? spend a little and keep trying with the 2% chance, or go for multiple 20% chances. Should I be indiferent.

I understand expected value EV = 5 *.20 or 50 * .2, so technically I will need 50 tries to suceed if I spend the smaller amount of resources.

Answer 1

Smaller bet.

The chance is a little smaller.  

But you can stop when the event happened.

Or you may stop other event make you change your mind.

Besides, you got to play 10 times more than larger bet.

Sometimes, playing is more fun than get it to happen.

Answer 2

There are two reasons for preferring the larger bet:

lower cost, higher probability.

If you bet the the lower bet 10 times,

it costs you 1670 units.

And you have 0.817 chance of failure.

(.98 ^ 10), so 19.3 percent chance of success.

The higher bet costs you 1667 units (3 less than the other way)

and you have 20 percent chance of success.

5 tries of the larger or 50 tries of the smaller do not guarantee success.

5 tries of the larger have .8^5 chance of failing = 0.32768

or about 67.232 percent chance of succeeding.

50 tries of the smaller bet have .98^50 chance of failing =

0.364 or 63.6 percent chance of succeeding.

Again, the larger bet is better, plus you spend fewer units.

The choice is clear.

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