Satoshi Dice -- Statistical Analysis

[nibor]

Or someone is managing to roll back zero-conf losing transactions!

[1713566718]

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[1713566718]

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[dooglus]

This satoshidice guy is pretty unlucky.

Here's a graph of how the profit for the site has been at the end of each block since it started.  I don't know if it's bad luck, or if someone is cheating.



There was a reasonably big loss overnight.  Someone bet 5 BTC twice in the same transaction: 5 BTC on "under 1500" and another 5 BTC on "under 6000".  Both bets won.  This seems like a good way of partially evading the low maximum bet limits, since the same random number will be chosen for all bets in a single transaction.

[dooglus]

Here's the same thing but with dates instead of block numbers on the X axis:

[etotheipi]

My guess is that someone found a vulnerability and exploited it for 1000 blocks, and is waiting for the site to "refill" before doing it again.  The sequence of losses is just way too extreme over that 182k-184k region to be luck, unless it's based mostly on long-shot bets.  But from the previous postings, there haven't been a ton of long-shot bets..

Or the vulnerability was found and fixed.  I'm not really sure.  But as an attacker, it might be more beneficial to let the site recover and skim money instead.  So you get the benefits of running a gambling website without actually having to run one!

[DeepBit]

This satoshidice guy is pretty unlucky.

Depends on what his goal is.

[apetersson]

My guess is that someone found a vulnerability

how likely is it someone could brute-force the daily secret hashed and published in advance?

[dooglus]

My guess is that someone found a vulnerability

how likely is it someone could brute-force the daily secret hashed and published in advance?

Not very.  More likely is that they could double-spend their losing bets using pre-mined blocks, and only let their winning bets confirm.

If I control a lot of hashpower, I make sure that every block I mine contains a spend to myself.  Each time I find a block, I double-spend that transaction in the form of a "less than 512" bet at SatoshiDice.  I wait a few seconds to see if I win.  99% of the time I'll lose, but if I win, I throw away the block I mined and let my winning bet confirm, otherwise I submit it to the network as normal, causing the lost bet to never be confirmed.  By waiting to see if I win the bet, I risk my block being orphaned, but my expected win is enough to cover that risk so long I can bet high enough at SatoshiDice.

Is there any flaw in that system?  Have any steps been taken to stop it happening today?

[etotheipi]

My guess is that someone found a vulnerability

how likely is it someone could brute-force the daily secret hashed and published in advance?

In a perfect world, the methodology is secure, and this would be extremely difficult.   Even with millions of bets there should be no way to reverse-engineer the secret from the HMAC operation, especially knowing only the last two bytes.  (is the full output of HMAC(secret,TxID) shown?)

It's my understanding that there has not been a lot of confirmed double-spend [attempts].  I could be wrong though.

But the world isn't perfect.  The machine holding the secrets and doing the calculations must be connected to the internet.  Maybe someone found a way to get the server to leak information.  I'm sure interested peoples have isolated a "direct" connection to this node, and even if they don't "hack" it, may be able to get useful information out of communicating with it.

[dooglus]

Even with millions of bets there should be no way to reverse-engineer the secret from the HMAC operation, especially knowing only the last two bytes.  (is the full output of HMAC(secret,TxID) shown?)

sha256(secret) has been published for all the secrets that will be used in the next 10 years, and the full output of HMAC is shown.  See this 'recent bet':

Secret and Transaction Hash

Verify that the hmac sha512 with secret and transaction_id hash to the bet hash
hmac_sha512(hidden,69468dfc1a10bc9ae98d6913a715436eb1bd795bf023ea2aa0ff1d5f07f22b97) -> 1695547cca9f140b91a127664c43369d8ec9a70cc3c509d2c25f179a4d4c8dc3

[Stephen Gornick]

More likely is that they could double-spend their losing bets using pre-mined blocks, and only let their winning bets confirm.

How about the potential that there are multiple wagers with the same transaction hash?  That would appear in the results.

 - http://bitcointalk.org/index.php?topic=77870.msg883119#msg883119

[nibor]

Only defence to premined blocks seems to be to ensure payout is never more that 50BTC then there is no point withholding the blocks when you do win.

[dooglus]

How about the potential that there are multiple wagers with the same transaction hash?  That would appear in the results.

That's an interesting attack.  I'll check and see if there are any duplicate transaction IDs with SatoshiDice bets in them.

I looked at just the bets during the period of heaviest losses for SatoshiDice, the 800 blocks 182800 through 183599, and found the following.  My theory of it being double-spent longshot bets is clearly wrong.  The vast majority of the losses were from "under 32000" bets - pretty much coin tosses.  "under 4000" had the highest RTP, but much smaller losses, due to smaller volume of bets:

  Address   Target   Should Win |  #Bets |    Win |   Lose |        In |       Out |    Profit |     RTP
-----------------------------------------------------------------------------------------------------------
 1dice1e6p        1      0.00002 |     51 |      0 |     37 |      0.20 |      0.00 |      0.20 |    0.0%
 1dice1Qf4        2      0.00003 |     32 |      0 |     29 |      0.27 |      0.00 |      0.27 |    0.0%
 1dice2pxm        4      0.00006 |     20 |      0 |     17 |      0.26 |      0.00 |      0.26 |    0.0%
 1dice2vQo        8      0.00012 |     47 |      0 |     44 |      0.96 |      0.00 |      0.96 |    0.0%
 1dice2WmR       16      0.00024 |     26 |      0 |     25 |      1.18 |      0.00 |      1.18 |    0.0%
 1dice2xkj       32      0.00049 |     20 |      0 |     20 |      1.48 |      0.00 |      1.48 |    0.1%
 1dice2zdo       64      0.00098 |     49 |      0 |     47 |     10.43 |      0.03 |     10.40 |    0.3%
 1dice37Ee      128      0.00195 |    506 |      0 |    502 |     42.46 |      0.11 |     42.35 |    0.3%
 1dice3jkp      256      0.00391 |    115 |      1 |    111 |     19.39 |     10.06 |      9.33 |   51.9%
 1dice4J1m      512      0.00781 |    107 |      0 |    106 |     34.24 |      0.14 |     34.09 |    0.4%
 1dice5wwE     1000      0.01526 |    222 |      2 |    215 |    120.98 |      1.27 |    119.71 |    1.1%
 1dice61SN     1500      0.02289 |     37 |      1 |     35 |     56.35 |      0.31 |     56.03 |    0.6%
 1dice6DPt     2000      0.03052 |     94 |      2 |     92 |     56.92 |      1.25 |     55.66 |    2.2%
 1dice6gJg     3000      0.04578 |    105 |      3 |    101 |     83.61 |      1.26 |     82.34 |    1.5%
 1dice6GV5     4000      0.06104 |    135 |     12 |    123 |     94.54 |    224.38 |   -129.84 |  237.3%
 1dice6wBx     6000      0.09155 |    232 |     20 |    211 |    851.87 |   1168.98 |   -317.11 |  137.2%
 1dice6YgE     8000      0.12207 |    384 |     37 |    340 |    186.28 |    112.71 |     73.57 |   60.5%
 1dice7EYz    12000      0.18311 |   4309 |    819 |   3488 |    626.54 |    861.54 |   -235.00 |  137.5%
 1dice7fUk    16000      0.24414 |   3124 |    793 |   2322 |    427.20 |    467.04 |    -39.83 |  109.3%
 1dice7W2A    24000      0.36621 |   1342 |    501 |    824 |   1483.96 |   1635.54 |   -151.58 |  110.2%
 1dice8EMZ    32000      0.48828 |  50458 |  24498 |  25726 |  24846.77 |  26874.90 |  -2028.12 |  108.2%
 1dice97EC    32768      0.50000 |   3569 |   1783 |   1754 |   2187.61 |   2476.62 |   -289.00 |  113.2%
 1dice9wcM    48000      0.73242 |   4849 |   3571 |   1251 |   4339.44 |   4312.58 |     26.86 |   99.4%
 1dice9wVt    64000      0.97656 |    283 |    263 |     10 |    294.68 |    269.88 |     24.79 |   91.6%
-----------------------------------------------------------------------------------------------------------

(I'm ignoring bets which weren't paid out within the 800 blocks in question, though they count in the 'bets' column, and am also ignoring fees paid)

[unk1911]

i have noticed something off regarding SatoshiDice.    on june 25th, it appears they made some modifications  to the system, and it appears that if i add up all of the bets that i have sent to the following address:
1dice7fUkz5h4z2wPc1wLMPWgB5mDwKDx

that the payout odds coming back, were on average  1:7.91  instead of the approximately 1:4 that is advertised on the front of the website. of course, the payout had stayed at 4x.   something seems to be broken and maybe they need to look into this.   of course i'm a little bit pissed off because i have already lost a lot of money before i realized this was going on.  i could sense that something was off but by the time i actually sat down and did the counting of # of wins vs # of losses i didn't realize that the odds were stacked up against me at approx 1:8...

[dooglus]

i have noticed something off regarding SatoshiDice.    on june 25th, it appears they made some modifications  to the system, and it appears that if i add up all of the bets that i have sent to the following address:
1dice7fUkz5h4z2wPc1wLMPWgB5mDwKDx

that the payout odds coming back, were on average  1:7.91  instead of the approximately 1:4 that is advertised on the front of the website.

How many bets have you made to that address since June 25th, and how many won?

SatoshiDice is provably honest - they use a publicly known mathematical function to decide whether you won or not, using secret numbers decided before the game started.  A hash of the secret numbers was also published before the game started, so they can't change it.

Looking at the blockchain since June 25th (I started counting at block 186101), I can see that they have processed 3808 bets to that address. 1 was refunded for being over the max bet, 3 haven't yet been paid out either way, and of the remaining 3804, 885 won.  That's 23.26% of them that won (1:4.298).  We would expect 24.41% to win in the long run (1:4.096), so that's pretty close.  It's certainly nowhere near the 1:7.91 that you saw.

[dooglus]

Here are updated stats, along with a graph showing profit over time, along with expected profits given 1.0% and 1.5% house edges.

Results: 2012-Jun-29 12:47pm

   Address   Target   Should Win |    #Bets |       Win        |  Lose  | Refunds |    BTC In    |   BTC Out    |    Profit    |   RTP% 
-----------------------------------------------------------------------------------------------------------------------------------------
 1dice1e6p        1      0.00002 |     5968 |      0 (0.00000) |   5716 |     251 |        20.07 |         0.01 |        20.05 |   0.096
 1dice1Qf4        2      0.00003 |      865 |      0 (0.00000) |    798 |      67 |         7.06 |         0.00 |         7.06 |   0.025
 1dice2pxm        4      0.00006 |     1372 |      0 (0.00000) |   1342 |      30 |        11.93 |         0.00 |        11.92 |   0.047
 1dice2vQo        8      0.00012 |     1087 |      0 (0.00000) |   1051 |      36 |        14.93 |         0.00 |        14.93 |   0.032
 1dice2WmR       16      0.00024 |     1335 |      0 (0.00000) |   1308 |      27 |        20.23 |         0.01 |        20.21 |   0.075
 1dice2xkj       32      0.00049 |     3067 |      1 (0.00033) |   3055 |      11 |        88.65 |       100.38 |       -11.72 | 113.224
 1dice2zdo       64      0.00098 |     4425 |      5 (0.00113) |   4403 |      17 |       175.83 |       110.74 |        65.08 |  62.983
 1dice37Ee      128      0.00195 |     5739 |     12 (0.00210) |   5702 |      25 |      1087.25 |      1141.67 |       -54.42 | 105.006
 1dice3jkp      256      0.00391 |     4352 |     19 (0.00438) |   4321 |      12 |       458.06 |       256.56 |       201.50 |  56.010
 1dice4J1m      512      0.00781 |     5285 |     32 (0.00606) |   5248 |       5 |       701.77 |       330.41 |       371.35 |  47.083
 1dice5wwE     1000      0.01526 |     6367 |     87 (0.01367) |   6277 |       2 |      1257.79 |       655.93 |       601.85 |  52.150
 1dice61SN     1500      0.02289 |     5019 |    107 (0.02134) |   4907 |       5 |      1380.24 |      2091.00 |      -710.75 | 151.495
 1dice6DPt     2000      0.03052 |     5498 |    171 (0.03112) |   5324 |       3 |      1595.74 |      1459.85 |       135.88 |  91.484
 1dice6gJg     3000      0.04578 |     5394 |    272 (0.05048) |   5116 |       6 |      3476.60 |      4491.24 |     -1014.64 | 129.185
 1dice6GV5     4000      0.06104 |     5378 |    333 (0.06195) |   5042 |       3 |      1578.36 |      1378.16 |       200.19 |  87.316
 1dice6wBx     6000      0.09155 |     9136 |    856 (0.09373) |   8277 |       3 |      5842.87 |      6421.04 |      -578.17 | 109.895
 1dice6YgE     8000      0.12207 |     9609 |   1166 (0.12134) |   8443 |       0 |      2813.96 |      2430.33 |       383.62 |  86.367
 1dice7EYz    12000      0.18311 |    14200 |   2709 (0.19088) |  11483 |       5 |      5857.29 |      6191.28 |      -333.98 | 105.702
 1dice7fUk    16000      0.24414 |    35530 |   8609 (0.24235) |  26914 |       5 |      8893.77 |      8541.12 |       352.65 |  96.035
 1dice7W2A    24000      0.36621 |    23601 |   8726 (0.37022) |  14844 |      30 |     10701.69 |     10988.45 |      -286.76 | 102.680
 1dice8EMZ    32000      0.48828 |   266842 | 129874 (0.48693) | 136844 |     117 |     80094.30 |     81849.88 |     -1755.57 | 102.192
 1dice97EC    32768      0.50000 |   105161 |  52539 (0.49990) |  52561 |      60 |     35780.42 |     35176.72 |       603.69 |  98.313
 1dice9wcM    48000      0.73242 |    65717 |  48254 (0.73463) |  17431 |      31 |     37953.57 |     36577.94 |      1375.63 |  96.375
 1dice9wVt    64000      0.97656 |     5687 |   4598 (0.97457) |    120 |     968 |      4901.49 |      4709.70 |       191.79 |  96.087
-----------------------------------------------------------------------------------------------------------------------------------------
                                 |   596634 |
-----------------------------------------------------------------------------------------------------------------------------------------

Cumulative Wagers:             208853.68253522 BTC
Cumulative Rewards:            209038.94171709 BTC
Cumulative Fees Paid:             300.23065000 BTC
Cumulative Unreturned:              3.31029257 BTC
----
SD Profit on Completed Bets :      -488.80012444 BTC
----
Since Satoshi Dice started, there have been:
Blockchain Tx:  1692649  :  SatoshiDice Tx: 1113632  (65.8%)
Blockchain MB:  718.9  :  SatoshiDice Tx: 453.4  (63.1%)

[byronbb]

Reminds me of my poker playing days where you can only ever lose. But I was never good enough to run this badly:

[dooglus]

Here's an interesting graph:



It splits the profit/loss into that caused by bets under 4 BTC and that caused by bets of 4 BTC or more.

There's a marked difference.  Small bets are very profitable.  Big bets are very expensive.

If it weren't for the big bets, SatoshiDice would be almost 4000 BTC up by now, but instead they're 500 BTC down.

Everything was looking fine until the first week of June.  Since then there's been a big difference between the profitability of "big" and "small" bets.

Edit: fixed the graph.  the >= and < labels were the wrong way around

[ZiggiStar]

Here's an interesting graph:



It splits the profit/loss into that caused by bets under 4 BTC and that caused by bets of 4 BTC or more.

There's a marked difference.  Small bets are very profitable.  Big bets are very expensive.

If it weren't for the big bets, SatoshiDice would be almost 4000 BTC up by now, but instead they're 500 BTC down.

Everything was looking fine until the first week of June.  Since then there's been a big difference between the profitability of "big" and "small" bets.

Edit: fixed the graph.  the >= and < labels were the wrong way around

You mean Satoshi lose more money with big bets ? is the graph now right ?

He lose alote of money with big bets ans makes money with small bets ?
is this right so ?

[dooglus]

You mean Satoshi lose more money with big bets ? is the graph now right ?

He lose alote of money with big bets ans makes money with small bets ?
is this right so ?

Yes, that's what I mean.  The graph is right, but a little out of date.  Here's an up-to-date one;

Results: 2012-Jul-01 02:44pm (up to block 187092)

   Address   Target   Should Win |    #Bets |       Win        |  Lose  | Refunds |    BTC In    |   BTC Out    |    Profit    |   RTP 
-----------------------------------------------------------------------------------------------------------------------------------------
 1dice1e6p        1      0.00002 |     6201 |      0 (0.00000) |   5943 |     256 |        21.36 |         0.01 |        21.34 |   0.090
 1dice1Qf4        2      0.00003 |      882 |      0 (0.00000) |    814 |      67 |         7.12 |         0.00 |         7.12 |   0.025
 1dice2pxm        4      0.00006 |     1382 |      0 (0.00000) |   1351 |      30 |        11.99 |         0.00 |        11.99 |   0.047
 1dice2vQo        8      0.00012 |     1092 |      0 (0.00000) |   1055 |      36 |        15.05 |         0.00 |        15.05 |   0.031
 1dice2WmR       16      0.00024 |     1349 |      0 (0.00000) |   1321 |      27 |        20.65 |         0.01 |        20.64 |   0.075
 1dice2xkj       32      0.00049 |     3075 |      1 (0.00033) |   3062 |      11 |        89.10 |       100.38 |       -11.27 | 112.650
 1dice2zdo       64      0.00098 |     4438 |      5 (0.00113) |   4415 |      17 |       175.99 |       110.74 |        65.24 |  62.927
 1dice37Ee      128      0.00195 |     5843 |     12 (0.00206) |   5803 |      26 |      1176.62 |      1142.07 |        34.54 |  97.064
 1dice3jkp      256      0.00391 |     4369 |     20 (0.00459) |   4335 |      12 |       458.47 |       330.67 |       127.80 |  72.125
 1dice4J1m      512      0.00781 |     5402 |     32 (0.00593) |   5364 |       5 |       723.43 |       330.50 |       392.93 |  45.685
 1dice5wwE     1000      0.01526 |     6570 |     92 (0.01402) |   6472 |       2 |      1306.15 |       695.34 |       610.80 |  53.236
 1dice61SN     1500      0.02289 |     5088 |    108 (0.02125) |   4974 |       6 |      1598.74 |      2134.22 |      -535.47 | 133.494
 1dice6DPt     2000      0.03052 |     5583 |    173 (0.03103) |   5403 |       3 |      1750.55 |      1619.07 |       131.48 |  92.489
 1dice6gJg     3000      0.04578 |     5445 |    275 (0.05057) |   5163 |       6 |      3608.20 |      4704.79 |     -1096.58 | 130.392
 1dice6GV5     4000      0.06104 |     5515 |    340 (0.06171) |   5170 |       3 |      1602.86 |      1402.21 |       200.65 |  87.481
 1dice6wBx     6000      0.09155 |     9358 |    879 (0.09400) |   8472 |       4 |      5961.81 |      6560.49 |      -598.68 | 110.042
 1dice6YgE     8000      0.12207 |    10325 |   1259 (0.12204) |   9057 |       0 |      2891.30 |      2498.25 |       393.04 |  86.406
 1dice7EYz    12000      0.18311 |    14500 |   2768 (0.19109) |  11717 |       5 |      5905.06 |      6230.00 |      -324.94 | 105.503
 1dice7fUk    16000      0.24414 |    35833 |   8688 (0.24253) |  27134 |       6 |      8967.36 |      8620.49 |       346.86 |  96.132
 1dice7W2A    24000      0.36621 |    23916 |   8841 (0.37015) |  15044 |      30 |     10783.37 |     11044.96 |      -261.59 | 102.426
 1dice8EMZ    32000      0.48828 |   270535 | 131680 (0.48700) | 138711 |     120 |     80495.15 |     82188.83 |     -1693.67 | 102.104
 1dice97EC    32768      0.50000 |   105990 |  52945 (0.49986) |  52975 |      61 |     36154.48 |     35516.80 |       637.68 |  98.236
 1dice9wcM    48000      0.73242 |    66124 |  48556 (0.73470) |  17534 |      31 |     38033.84 |     36657.31 |      1376.52 |  96.381
 1dice9wVt    64000      0.97656 |     5692 |   4598 (0.97457) |    120 |     973 |      4901.49 |      4709.70 |       191.79 |  96.087
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                                 |   604507 |
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Cumulative Wagers:             210867.93922406 BTC
Cumulative Rewards:            210773.98925246 BTC
Cumulative Fees Paid:             304.16610000 BTC
Cumulative Unreturned:             30.63706275 BTC
----
SD Profit on Completed Bets :      -240.85319115 BTC
----
Since Satoshi Dice started, there have been:
Blockchain Tx:  1737546  :  SatoshiDice Tx: 1128216  (64.9%)
Blockchain MB:  736.9  :  SatoshiDice Tx: 459.5  (62.4%)

[bitclown]

If it weren't for the big bets, SatoshiDice would be almost 4000 BTC up by now, but instead they're 500 BTC down.

Sounds like SatoshiDice is lazy and use big amounts for their statistics-skewing transactions masqueraded as real bets.</AlexJones>