What's the edge in Satoshi Mines 25 Squares 3 Bombs

In my last post, i showed you how to calculate the true odds for the bitcoin game satoshi mines

If you want to know how the game works, see this post.  Or if you want to play the game go here

In that post, i showed you the true odds of the game (25 squares and 3 bombs) and in my previous post, i showed you the payout odds (for 25 squares and 3 bombs)

I thought it might be worth comparing them....   The table below shows true odds vs actual odds (for 25 squares 3 bombs)

I think the interesting thing here, is the cumulative edge isn't a constant.   They offer a very low edge for your first bet and then the edge gets progressively worse until your 8th guess when the edge starts reducing.   I don't have their payouts beyond guess 16.   I might create a robot to get those numbers at some point.   Let's look at the edge changes as a graph.

So what does this tell me.......

It says to me you really shouldn't play beyond your first guess... for 25 squares 3 bombs
As the cumulative edge (unto guess 17 doesn't get better than that first edge on that first guess..

You'd be better to cash out your money, and then just play another round.   You'll have lower odds sure (as you'll always been playing with 22/25 probability) but you'll be playing with a lower edge, so you'll lose money over the long run.

It also tells me there maybe more value in the other variants of the game and we'll explore that in another post.

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

In the next article we'll look at some of the grids and options you have

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

How does Satoshi Mines work?

So I've spent some of time over the last few days looking at some of the bitcoin gambling sites.   Wow there is a lot to talk about in this subject.   Anyways I found myself playing a fun little game called Satoshi Mines, it's kinda like Minesweeper.

It's Bitcoin only so if you want to gamble, you will need a bitcoin wallet (a subject for another day) or    you can play in a practise mode.   I was playing in practise mode and recommend you do the same because I'll prove in my next post, that you can't really win.

How does the game work?

You start with a square (default is 25 squares) with a hidden number of bombs (default is 3).  You can change the number of bombs if you want (and i recommend you do).   Here is a screenshot.

You bet an initial stake (let's say 100 bits) and everytime you click on a square and miss a bomb, you win some bits.   You can either cash out your bits or risk those bits you just won against the chance of wining some more bits.  Obviously if you hit a bomb, you lose all the bits won (and your original stake).

What's the payouts?

I played the game for a little bit and captured the following payouts for a 25 square game with 3 bombs

As you can see the more squares you uncover as empty, your cumulative odds get better and you can win a good multiplier of your original stake.  As you can see above, the best I did was to manage 16 squares where i could win 23 times my stakes (if I won and cashed out).

So in the above example.

• My initial stake was 100 bits
• If i hit a mine, i lose all 100 bits.
• If I've guessed 10 times (i.e. picked 10 squares that don't have bombs in them), i'll have 466 bits (366 bits won plus my original 100 bits)
• If i want to guess another square (11th guess), i'll either win another 111 bits, making a total of 577 bits or i'll lose everything including my initial 100 bits stake.   Or I can cash out and take my 466 bits as winnings.

Okay, looks fun, can I win?   In the short term, sure.  In the long term, no.  Why?   Probability!   And that's what i'll explain in my next post

However the game does have some pretty low house edges (as i'll explain in my next post)

Warning:  This is a not a casino, not licensed and you're playing with Bitcoins.  I really do recommend you only play in practise mode.

Hope this helps