Topic: Satoshi Dice -- Statistical Analysis - page 76. (Read 192918 times)

I've spent all day re-downloading the blockchain after a hard drive failure corrupted my copy.  Here's an update to the SatoshiDice stats.  Looks like the site is up over 1000 BTC since the last time I posted.

Well, unlike games of chance where you need to trust a machine or a human, SatoshiDICE's results are verifiable, thanks to cryptography, once the secret is released (the next day).

This can be verified without needing any software installed.  Here's how:

So for your wagers from Jul 10, 2012 (UTC), get the secret from:
 - http://satoshidice.com/secretlist.php

That has been released, and it is:
  ctygmtZjw7xTnLou7u9cWVYiOd79xAMJK5aJJBBD3w2Su8vGMHPDwP1f4O1eBPek

Then create the SHA-256 hash of that secret with:
 - http://md5online.eu/3,sha-256

Which yields:
 - d75e37bc91915af566276e34624e7477c2a6771fb7898bc4dd1b30ccc0022cfe

Then verify that the resulting hash from that jives with the has from hash.keys for Jul 10, 2012:
 - https://s3-eu-west-1.amazonaws.com/satoshidice/hash.keys

So next you grab the transaction ID for your transaction (from the Transactions tab of Bitcoin.org client).

Then plunk those values in ... for Text to convert, paste the Transaction ID, and for Shared Secret Key use the secret for the day that you verified above.

 - http://www.online-convert.com/result/3a4827ec61a06ed23ce463afd509c4ce

After you click Calculate hash, you'll get a hex string in the results.  The first four alphanumeric characters is the hex representation of your lucky number (from 0000 through ffff hex, or in decimal, 0 through 65,535 decimal).  You can convert those values to decimal here:

 - http://www.binaryhexconverter.com/hex-to-decimal-converter

So if you had bet the "less than 8,000" wager and your lucky number was 8,000 or higher, ... that specific wager didn't win.

As long as the hashes to the secrets are known in advance (and they are, that hash.keys was published in April, a copy of which has been archived here) you can always verify if you should have gotten a winning payout or not:
 - https://raw.github.com/sgornick/satoshidice/master/hash.keys

Here's an example of a recent 1 BTC bet winning at "lessthan 8000".

The 1 BTC bet was paid out 7.90977999 BTC, which would have been 7.91027999 before the 0.0005 BTC transaction fee was removed.

This one is a losing 1 BTC bet.  The player was returned 0.0045 BTC (0.005 BTC including the fee), or 0.5%.  So the expected return from a 1 BTC bet is:

7.91027999 * 8000/65536 + 0.005 * (65536-8000)/65536

which is very close to 0.97 BTC.

So the house edge is 3.0% if you include the amount which is returned when you lose!

I was thinking the house edge wasn't including the returned amount, because the site used to say something like "house edge 1%" and "when you lose we return half the house edge to you".  But that's changed now.

The house edge is determined by the payout when you win.  The chance of winning is always the same - it picks a number between 0 and 65535 and you win if the number is less than 8000.  Your calculation is off a little because 1 - 8000/65536 isn't 7/8, it's a little more than that.

I make it a one-in-17399 chance of losing all 75 bets, so still really unlucky.  But then again 1-in-17k shots do happen.  About once every 17k bets.  And there have been over 600k bets.

 >>> 1 / ((1 - 8000/65536.0) ** 75)
  17398.822919111808

Here's the same for losing a 50/50 (less than 32768) bet 3 times in a row to sanity-check the calculation:

 >>> 1 / ((1 - 32768/65536.0) ** 3)
  8.0

and as you would expect, that's a 1-in-8 chance.

What's puzzling me is the payout for the SatoshiDice bets.  A 0% house edge would pay out 65536/8000 = 8.192x.  And so a 3% house edge should pay out 3% less than that, or 7.94624x.  So why does the SD website say it pays out 7.910x?  7.910 * 8000/65536 is 0.965576171875, ie. a house edge of 3.44%.

Not that it makes any difference to you, since you only get the payout if you win a bet...

so today i was completely wiped out by the dice. i was playing the "1/8 bet" address:
lessthan 8000   1dice6YgEVBf88erBFra9BHf6ZMoyvG88    12.2070%   7.910x   3.000%   97.000%   0.0010   25.0000

after 75 consecutive losses i was wiped out, because i was placing relatively large bets. i have decided not to play this game any more. 
i must be very  unlucky or because if i'm not mistaken, the probability of getting 75 consecutive losses on a 12.20% dice  are  1/(7/8)^75 .   so basically this occurs once in every 22,356 turns, assuming a house edge of 0%.  if the house has an edge of 3%, the occurrence is slightly more frequent 1/(0.87875^75) =   once every 16,221 turns... still, i must be one unlucky bastard...

Pretty incredible to see over a million dollars wagered already.

Note that the profit is almost up to what would be expected if the house had a 1% house edge all along:

I'm sure someone could give some figures on how often these results could be expected by chance.

Though since today seems to be the day for silly theories.

It was pointed out on IRC that you could do somewhat tidy laundering this way.


Identity X with dirty coins gambles until they lose Y coins.

Then using identity Y, they make more bets, and someone with knowledge of the MAC secret filters their candidate transactions  to help them win until they've won Y/2 (or whatever).

This would be pretty hard to distinguish, except for the weird effect would have on the odds, especially if they weren't careful about the distribution they drew the winning bets from... and it would be impossible to connect the parties beyond they were both participants at some point in the game.

It would also explain rapid, almost certainly bot-based, playing of a negative ev game, reasons for capping the total (make the distribution of bets more regular).  Plus elvis came down from a UFO and told me it was true.

How is it even possible that such a large population of independant events (those bets up to 4 and those above 4) can differ so heavily from the mean (0 level)? Shouldn`t they even themselves out?

Since I wrote that, the effect has stopped.  Now the big bets are more profitable than the small bets.

I don't think so.  The dice don't care whether your bet of 5 BTC is part of a martingale chain or not.  Each bet has the same (slightly negative) expectation no matter what your previous and next bets are.

Is this just a natural consequence of martingale type betting strategies? Players start with small bets, go on a losing run, doubling up each time, so there are string of profitable small bets for SatoshiDice and then player finally gets a winning (larger) bet, so those larger bets are less profitable from SatoshiDice's point of view.

Also, have you talked to zipconf? I dunno how exactly their service works - is it transaction or address based? - but it'd make for an interesting, high-visibility, high-risk test case. IE: maybe they'd give you a discount on the fees.

Question is are you being actively scammed?
What have you learnt about zero-confirmation transactions and how safe they are?

We know there are theories as to how you could be scammed etc.. but would be interesting if they are actually occurring in the wild, and if there are any changes the bitcoin that could fix it or at least make it harder.

Having to wait 1-6 confirmations is one of bitcoins few weaknesses, so knowing if zero confirmation transactions were reasonably safe in the real world would be "news".

Yeah, I wish the big bets had been paying out better for SatoshiDice, but we've been unlucky thus far. We lowered the max bet down to 5btc for a while to help curb the losses, and now have raised it back to 25btc.

As of today, SatoshiDice is back in the black after a fairly gruesome couple weeks. Needless to say, it is stressful running this site but hopefully the players are having fun!

It makes sense after you've seen people argue that their 'losses' and betcaps are "proof" that a favored gambling strategy is a "sure win".

Same reason casinos promote grand stories of card counting blackjack sharks bilking casinos and pretend to be concerned about card counters,  while simultaneously employing multi deck continuous shuffling machines that moot card counting.