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

Roulette excel isn't the same as mechanical wheels

I've spent  a lot of time so far giving you the tools on how to calculate probabilities and check if staking plans work in excel.

The game of roulette isn't played in Excel, it's played on a mechanical wheel (unless you are playing online in a non-live roulette game and then you may as well be playing in Excel).

So what's my point:

If your number based system (martingale, reverse martingale etc)  doesn't hold up in Excel, it won't hold up in the real world either.

Ahhhhh, but you said in the real world, it's mechanical wheels, so there are wheel biases, dealer signatures etc, so maybe my system does hold up in the real world and not in Excel?

sure maybe, but that's blind luck.   does every dealer have the signature, every wheel have the same bias?  if that's what you think then you're crazy.

If you want to look at real world advantage play then we'll get to that but if your number based system doesn't hold up in excel it won't hold up with mechanical wheels.   if you want something to hold up with mechanical wheels then you need a different strategy.   and we'll get to that.

hope this helps

Martingale stake formula

I've spent a few posts now showing why employing Martingale against fair odds (or in the case of red or black in roulette less than fair odds), that you're always gonna lose.  If you want to read a bit more about it read my post on martingale in roulette begin very bad.

If you've forgotten what martingale is, it basically means everytime you lose, double up your previous bet

Calculating your martingale stake

In one of my earlier posts, i showed you this table, where for a losing streak, how much you'll have to bet to recover

I thought it might be useful to provide a formula that calculate the stake required to cover your losses during a martingale

And that is S = I * (2^(n+1))

I = Initial Stake
n = length of streak
S = Stake Required

Which means Initial Stake * (2 to the Power of the current length of the streak)

So in the scenario where our initial stake is £10 and we've lost 10 times and we need to make our eleventh bet.  Our new stake would be:

£10 * (2 to the power of 10) = £10 * 1024 = £10,240

Obviously you'd be better throwing your money down the toilet but there ya go.  But if you want to calculate it, that's how you do it.

And if you wanna do it in Excel

To do this in Excel with a table like the following

In the cell B4 (stake column row 4) just enter

=POWER(2,A3-1)*$B$3

Obviously you can also calculate it in excel, you can just double up the previous stake.  but the point is to show you how to do when you just know the initial stake and the bet number.

Please don't do martingale with roulette kids, not worth it.

High-Odd-Black vs High-Odd-Red in Roulette

So I read this interesting article at

http://www.roulette30.com/2013/08/an-observation-on-even-chances.html

Which basically says you have a higher probability of losing if you bet High-Odd-Black than you do if you bet High-Odd-Red.

So the idea is that if I place a bet on High Numbers, Odd Numbers and Red Colors then there is only 5 numbers that can make me lose:

2, 4, 8, 6 and 10

But if I bet on High, Odd and Black then there is theoretically only 4 numbers that can make me lose

12, 14, 16 and 18

And then the article did some math wizardry showed that with each bet being evens then the "probability" of losing all your bets would be 1/8 (1/2 * 1/2 * 1/2).   BTW, the article ignores zeroes.  So i will too.

However, he points out if we were to bet on High-Odd-Black the probability of losing all your bets is
4/36 (ignoring zeroes) which simplifies to 1/9  but..... if we bet on High-Odd-Red the probability of losing all your bets is... 5/36 or 1/7.2

So should I bet on High-Odd-Black instead of High-Odd-Red?

Errrr, no......   Because you don't win bets on how many unique numbers lose.   These are not combinator bets.    If I was offered odds of 1/8 for all my bets to lose then sure this is a winning strategy and I'd say take the house to the cleaners.   As 1/9 will yield profit on 1/8 you'd have your own edge.

That's not the bet.   The bet is 3 separate bets whose results are paid out in isolation   This is not a trixie bet, this is 3 individual bets.   And sometimes you will win more than once for a certain number.   What we really should be looking is how many times can I win across these bets.

Well, here we go....

High-Odd-Black

Oh, look, we have 54 possible wins.    Shall we see how that breaks down

• 14 numbers offer as a single win (only one bet wins (High, Odd or Black)
• 14 numbers offer as a win on two bets (High and Odd, High and Black or Odd and Black)
• 4 numbers off a win on all threes bets (High, Odd and Black)

High-Odd-Red

And we still have 54 possible wins.  And shall we see how that breaks down also

• 13 numbers offer as a single win (only one bet wins (High, Odd or Red)
• 13 numbers offer as a win on two bets (High and Odd, High and Black or Odd and Red)
• 5 numbers off a win on all threes bets (High, Odd and Red)

What does this mean?

Don't get me wrong, it's an interesting observation but it's not gonna help you win more.   the odds of winning with High-Odd-Black are still the same as High-Odd-Red (But i applaud the observation skills)

It just means, that if we bet High-Odd-Black then sure we have a greater coverage of winning numbers than High-Odd-Red but we'll win less.

It all evens out.   We're betting individual bets.  And as shown they have a different distribution.   But at the end of the day.   There are only 54 possible winning bets.....  regardless of which way you bet

And just in-case you wanna check out the math.  here is a spreadsheet with my breakdown.

https://www.dropbox.com/s/fwcgk8eb0171lus/Kavouras%20HighOddBlack.xlsx?dl=0

Hope this helps

Hot numbers in roulette

I'm not gonna name the site but I was looking at yet another person peddling their roulette strategy based on tracking numbers (no genuine advantage play).

Basically, you stick in the last 6 numbers and voila, it will tell you where to bet.   If the wheel spins 3, 4, 5, 14, 15 and 17.   You should probably bet on 19-36, cause those numbers are due....

Just for fun, let's see how that looks in the Excel Simulator

The Random Numbers

This is what my Excel Random Number generator produced (feel free to replicate this experiment yourself)

3, 14, 9, 9, 3, 21, 35, 3, 29, 0, 19, 36, 4, 9, 5

The distribution

Oh look the number 3 came up 3 times (surely that's a hot number)????  BTW, that was sarcasm.   We know enough about random numbers now to know that that can easily happen.  However this could be an interesting blog post in the future.   Hot numbers.

What might be more interesting is the ranges, which is what they were betting on in this system.

Their system was either avoid betting on 1 to 12 because it's hot.  but it might have been bet on 1 to 12 because it's hot.

There is no hot....  It's just some random numbers.   nothing is due or not due....

The kicker

And here was the kicker.  Don't worry, if you lose, just martingale and it'll recover your losses.

And we know how that ends...

Anyways, you know my thought on this sort of thing already.  I could type up their system into Excel and formally disprove it.   But you can always do that yourself if you want.

We know enough about random numbers, streaky numbers and martingale to know this is a silly strategy.

For more info on Martingale, read my martingale post (and feel free to download the excel tool)

For more info on streaks, read my post on streaky coin tosses

For generating roulette numbers in excel, read my post (or look at the martingale one)