Topic: Satoshi Dice -- Statistical Analysis - page 76. (Read 192896 times)

Despite increasing the maximum bets far in excess of safe levels, SatoshiDice appears to be prospering:

Maybe.  Lotteries usually have really bad house edges (around 50% or so), whereas SatoshiDice only currently takes 1.9%.  So you're less likely to be unlucky at SatoshiDice, mathematically speaking.  But when the flying spaghetti monster is out to get you, mathematical odds don't matter.

I don't have very good luck with lotteries. Does the same carry over into bitcoin? :-P

It's 0 through 65535 inclusive.

So when you play "lessthan 48000" you should win 73.2% of the time, and when you play "lessthan 64000" you should win 97.6% of the time.

I played lessthan 48000 3 times yesterday and only won once (luckily biggest of the 3 bets was the one that won).  But the games are proveably fair - you can get the secret number they used to pick your magic number and validate that they did the maths correctly.

One guy was saying he lost over 60 "lessthan 8000" games in a row the other day, so long losing streaks are definitely possible, just very unlikely.

Tried it a few times last night. Even picked the higher numbers. Lost every time.

What is the pick range of the magic number?

I fixed a bug in the analysis script that was misclassifying some small "lessthan 64000" and "lessthan 48000" wins as refunds.

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.