Jackpot probability

[ClickeyMouse]

Hello

Yesterday during the jackpot hunt, there was some talk and discussion about probability and statistics. It was late into the night, and there was a lot of misunderstandings so I promised to write an in-depth post about probability. 

I will use the example from Mega Joker jackpot, where I was told the probability of hitting the jackpot is 1/50.000

Let me start by saying: The probability of hitting the jackpot on the next spin, do not change no matter how many times you spin.

In this post I am talking about the probability hitting the jackpot after a certain amount of spins. A lot of people (wrongly) believe that the cumulative probability of hitting the jackpot is a linear function, where the probability goes up by 1/50.000 for each spin. If this was true you would have a 100% chance of hitting the jackpot in 50.000 spins, which you naturally do not, as the jackpot hasn't been hit in +200.000 spins. 

Instead the probability is calculated this way: 

We hit the jackpot: 1/50.000 = 0,002%

We do not hit the jackpot: 49.999/50.000 = 99,998% 

Number of spins: 50.000(example) 

Formula: (probability of not hitting the jackpot)^(number of spins)

99,998%^50.000= 36,79% risk of not hitting the jackpot in 50.000 spins

1-36,79% =63,21% chance of hitting the jackpot in 50.000 spins

This probability formula holds for all examples, so feel free to plug in your own numbers if you feel like knowing how unlucky you are.

Hope this helps

 

 

[ClickeyMouse]

Just a quick follow up. I have calculated various %s of hitting the jackpot and plotted them: 

As you can see, the first many spins it is more or less linear, but takes more and more spins to increase probability by 10%