Topic: Satoshi Dice -- Statistical Analysis - page 14. (Read 192896 times)

It's going to be a bad month for dividends

Or you can look at it this way:

50% of the country has at least 1 girl - contributing P/2 to the girl population
25% of the country has a 2nd girl - contributing P/4 to the girl population
12.5% of the country has a 3rd girl - contributing P/8 to the girl population
...

so the total number of girls is P(1/2+1/4+1/8+ ...) = P.

Anyway, what do you want first, the good news or the bad news? 


The whale seems to be back...  and he seems to be winning...

Put another way, even if a player makes N bets or until the player is ruined, probability really doesn't care that the next bet comes from someone else when someone leaves early.

Schools need to teach more probability and formal logic.
This is a great analogy. Let's see if a written approach can help:

Separating the trial-end condition from the trials themselves, we know that on average, the distribution should be equal. However, if it's not inherently obvious that the trial-end condition doesn't affect the probability, consider this:

Half of the pairs will have a boy on the first try.
The other half will have a girl on the first try.

Now, set aside the first try and the male births. Start over, ignoring the first birth, with all of the couples who had girls.
Half of them will have a boy on this try.
The other half will have a girl on this try.

Wash, rinse, repeat.

50% of the country has one male child.
25% of the country has one male and one female child.
12.5% ... 2 females, one male
6.25% ... 3 females, one male
3.125% ... 4 females, one male
etc etc

If there were 100 couples, it should be obvious from the definition that there would be 100 boys, since each couple has a boy. But how many girls would there be? On average, 100.

Mathematically:
The population of females is the sum of the sequence (n-1)/(2^n) from n=1 to infinity
The population of males is the sum of the sequence (1)/(2^n) from n=1 to infinity
I can go into more detail, but both of these sequences converge, and both of them are equal to 1. (Thus each parent will have, on average, 2 children.)

What most likely throws people off is the different "speeds" at which these functions change. Plug them into Wolfram Alpha and compare the graphs.

Exactly the same still. Probability is a continuum regardless of how you go about it.

Same as in the neighboring country, I would guess? (Many boys just after a war, many girls just before one).

Relevant analogy :

If there is a country where every husband and wife decides to have children until they have a boy, what is the distribution of boys vs. girls in the country?

The other difference is that the "ahead" is a state that may never happen for some players, if they lose their first few bets and never recover those losses.  On the other hand, given the 1.9% house edge, the "behind" state will happen for all players if they just keep playing long enough.  In fact so will the "lost it all" state if they play enough times.


For the purposes of analysis, imagine there's an endless line of players who take on SatoshiDice one at a time, like in a kung-fu movie.  Each one starts with 100 BTC and plays until he has lost it all, then quits forever.

We can say that after the Nth player has finished playing, the house profits will be 100*N BTC.

And we can also say that on average each player bets a total of 100 / (1.9/100) = 5263.16 BTC.

I think I've satisfied myself (though probably nobody else) that people's tendencies to quit only when they've lost their bankroll doesn't affect the house's percentage profits, and that the current better-than-expected profits are merely the result of some good house luck earlier this year.  Even if that whale was always intending to keep playing until he lost it all, that process could have taken him 10 times longer than it did.  The house profits would be the same as they are now, but they would then be less than expected instead of being more than expected as they currently are.

Me too.


Since this is all a bit fuzzy and I haven't the foggiest idea how to even approach analysing it, I'm probably wrong, but here goes:

The difference is that  "quitting while we're ahead" means the first time you're ahead, which will probably happen early on with only a small amount bet gained.

"Quitting while you're behind" in this case means you've lost all you can afford to lose, which won't necessarily be a small amount.

This isn't about dilution.  There are 100 million shares, of which 13 million are currently available.  When this went up from 10 million to 13 million there was no dilution.  Each share still gets one 100 millionth of the monthly profits as a dividend.


I don't know, and it hurts my head to think about.

Everything I know about probability tells me that there's no way of changing the expected profit by changing your betting strategy.  "Quitting while you're behind" is a betting strategy, and so shouldn't affect the house edge.

If it did then we could beat the house by all "quitting while we're ahead", right?

As far as the bottom line is concerned, there's no difference between one big player and another.  It doesn't matter if each individual player stops when they are down a lot; it's just a stream of bets, each of which is paid out 1.9% less than the 'fair' amount.  That has to lead to a 1.9% profit overall I think in the long run.

Could it be that actual profit is considerably higher than expected profit because gamblers on average stop more when they have been exceptionally unlucky? (Whereas the house always continues to play also when exceptionally unlucky)

That looks like a whale! Thanks for reporting

He's the only one that can promise it as he is the only one speaking for the majority shareholder, who is the only one with the power to print more shares.

Shareholder dilution is the best way to take away value from shareholders. Similar to printing money.

The majority shareholders promising to not print more shares is a critical element whether to invest in that company/shares or not. 

Erik recently said he will never release more tranches of shares. Not sure how or why he can promise that, but he did.

I guess we can expect the next shares dumping by "unknown" investor... soon.
Do not worry, it will be dressed up as big favor to all the current share holders and shills will cal it "lowering the average cost of investment" or similar bs.

Could it be our old friend back again?

http://www.satoshidice.com/lookup.php?tx=1BDDDQ8VhXPF11m2rDoVJXj1BgWPazEttz

Edit: notice the similarity between the balance of that address over time and the recent satoshidice profits (upside down):

Here's today's.  What a difference a day makes!

I should switch the table around so that it's in the same order as on the homepage.


It's actually a 1 in 65536 chance of winning.  The fact that 'only' 48000 times more bets have lost than have won is why that particular bet is currently losing money for the house.  The house edge is about the same on that bet as for all the others, but that's the bet that's hardest to win, and so it has the highest variance.

You only have to play once to get a chance of winning.  Every play has the same chance of winning.

I generated the report yesterday, but got distracted before posting it (it's been a while since I received any donations to keep me focussed ).  Here it is:

Thanks, I wasn't reading the table properly, I thought it was the order on the homepage, where the highest chance win / small return addresses were on top.

Now it makes much more sense.

1:47,000 to win on 1dice1e6p, yeah I can see that not being a effective strategy to win... You would have to play 100 times a day for over a year to get a chance at winning with a minimum spend of 470 Bitcoins...