Calculating the true probability of Satoshi Mines (25 squares, 3 bombs)

In my last post, i explained how to play a bitcoin game called satoshi mines

In this post, i'm gonna explain how you can calculate the probabilities of the game.   I'll start with 25 square, 3 bomb grid.

If you need a refresher on calculating probabilities, i'll do one here but you can always refer to this post.

If you want to play the game, you can play satoshi mines here

Calculating the probability

It's pretty simple,.   There are 25 squares, 3 of which have bombs.   

First guess

That means the probability of me NOT HITTING a square on my first guess is....

22/25 or 88.50% (or decimal odds of (1.136)

Yes there are 22 squares out of 25 squares that are empty.   So I have an 88.5% (22/25) chance of not hitting a bomb in my first attempt.

If I had an original stake of 100 bits, i'd need to win over 13.6 bits for me to be able to beat the game,  as you could see from my previous post.   The actual payout is 13 bits.  So the house has an edge of about 0.5% (which is actually pretty low for a game)

Second guess

So it's a little harder for me now.  Now there are 21 squares (i clicked a square remember) that are empty and 3 squares which have bombs.  So I a smaller chance of hitting an empty square.  So the probability of me not hitting a square in my second attempt is.....

21/24 or 87.5% (or decimal odds of 1.143 roughly)

So now that I am staking 113 bits (initial stake of 100 plus my 13 bits from last win), i really need to win around 16 bits for this to be fair to bring my cumulative wins to 129 bits.   Well you've probably figured that isn't gonna happen.   The win is 15 bits bringing my stake / win unto 128 bits

So how is cumulative probability calculated.

Basically for each guess, it is

probability of current guess * probability of previous guesses

so for 2 guesses, it'd be

(22/25) * (21/24)

for 3 guesses, it's be

(22/25) * (21/24) * (20/23)

etc etc

Anyways, hopefully now when you're playing Satoshi mines, you'll be able to calculate the true probability.   i've put a handy chart below for you to see the true probabilities of the 

25 square 3 bombs game true probabilities 

In the next posts, i'll look at the probabilities of the various combinations   And look at giving you, your best strategy.

In true bitcoin tradition, if you found this article useful and want to donate me some spare bitcoins my wallet address is:  17QCjNaaXUWyG5WWaV3KVDQG7HdVkSDLs1

Hope this helps