Probability of a desired experiment within X zaps
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I... got bored and did some maths c: As we know, we can choose to pay 400k sp and 15 wizard tokens for a guaranteed experiment zap. This is a calculation of the probability of receiving the desired experiment within a certain number of zaps.
maths
There are currently 43 experiments. Choosing to pay the 400k sp will give you a 1/43 chance of successfully getting the experiment you want, every time you zap.
The probability of getting the desired experiment on exactly the first zap is 1/43.
The probability of getting the desired experiment on exactly the second zap is: chance of failure * chance of success, aka 42/43 * 1/43.
This pattern continues to X number of zaps. To calculate the probability of getting the desired experiment on exactly X number of zaps, you would need to calculate: (42/43)^(X - 1) * 1/43 This can also be written as: (42^(X-1))/(43^X) It doesn't really look that pretty, I know!
But this only calculates the probability of getting the desired experiment on EXACTLY X number of zaps. To calculate the probability of getting the desired experiment WITHIN X number of zaps, you need to sum the probabilities for every number of zaps from 1 to X.
Thankfully, I've already calculated some of these for you below: Within 10 zaps (4mil sp and 150 wiz tokens), there is just over a 1/5 chance of getting your desired experiment (0.209670217244706) Within 20 zaps (8mil sp and 300 wiz tokens), there is over a 1/3 chance of getting your desired experiment (0.37537883448997) Within 30 zaps (12mil sp and 450 wiz tokens), there is just over a 1/2 chance of getting your desired experiment (0.506343289958099) Within 50 zaps (20mil sp and 750 wiz tokens), there is under a 7/10 chance of getting your desired experiment (0.691651570411781) Within 100 zaps (40mil sp and 1500 wiz tokens), there is just over a 9/10 chance of getting your desired experiment (0.904921245970479)
Anyway, this has been my TED talk ugh I hope the maths is correct
Thank you! Today is my zap n° 30 and I still can't get a Experiment 870 ): I'll keep trying I guess... Good luck !!
