Topic: Satoshi Dice -- Statistical Analysis - page 29. (Read 192914 times)

The graphs only show confirmed payouts, so the big lessthan 1 bet isn't included yet, but it does show up as a pending liability, and in the bottom line:

If they were sane, they wouldn't keep that much online, I'd imagine for all payments greater then $foo there's probably some oversight. But yes, there's no reason it shouldn't have been sent by now.

Same question

Address : http://blockchain.info/address/1GH1PJjbL5KXLzAAjnYEcJrqCwJVJ9r8zs

why can't i find the actual winnings payment TX?

Damn, now that is a nice win !!! almost $ 140.000 

http://www.satoshidice.com/full.php?tx=d602ad09f967f11d50fcb2f98df8d001a812ce4965d6e69340f8961aeb32f27c

 

Some of the recent big bets:

The recent activity seems to be someone betting 5 BTC on lessthan 256 over and over, and winning once:

http://www.satoshidice.com/lookup.php?tx=dc0c383dabfaeec4

Simulation results:



This histogram is the result of running a thousand repetitions of 1127422 trials and record the longest number of losses in a row. From the simulated results, we can say that the probability of less than 16 in a row and more than 31 in a row is less than one in a thousand. So I'd say 65 in a row is significantly improbable.

Since I'm home now I've looked for the paper I thought I had but can't find it. The histogram looks familiar though and I think it might be an extreme value distribution, but I'm not sure. I'll keep looking.


If you want to try the simulation for yourself, especially if you have a faster computer than my macbook air and want to try more than a thousand repetitions, here's the R script I wrote:

It's 32000/65536.

The 'lucky number' is a 16 bit number (0 through 65535).  You win 'lessthan N' when this lucky number is less than N...

No, "Mr. ooc" is my grandfather. "ooc" is fine.

Good point - you do have an aim here.

Even if you think you don't:

The only way you can show if anything unusual is going on is by a theoretical comparison. Otherwise you have no idea how unlikely what you are observing actually is. That's ok if you have lots of data points - you can always say "from this sample we expect blah blah to happen blah times". But if you have one data point then you can't generalise

I'll have a go at the theoretical result when I get home. In the meantime I can rustle up a quick simulation and get confidence intervals from that. Can you post the probability of winning the less than "lessthan 32000" for me? Can't get on to SatoshiDice at work.

What do you think about the 65 losses in a row on "lessthan 32000"?  Is that statistically significant?  It seems to me very unlikely to have happened in just 1,127,422 bets.  I would think we can expect around 10 losses in a row in 1000 bets, and maybe 20 in a row in a million bets.  But 65 losses in a row?

See https://bitcointalksearch.org/topic/m.1632802 for the stats.

Mr. ooc, or just ooc?

Anyway, immediate history is interesting. I do not think I am trying to prove that SatoshiDice is fair or not; it seems to me that it is indeed fair considering the secrets, the hashes, the lucky numbers, etc. They can't cheat you, but it is possible for players to cheat them.

I don't really know why I am investigating this or analyzing the numbers, I just find it interesting. I mean, we have 3.7 million bets already. I am also playing the game (or rather, I'm gambling my 0.01 coins.) so the results interest me in what is possible, especially since this is practically a game of chance that is provably fair (after the secrets are revealed.)

Please don't call me that. "Mr. organofcorti" is my father. Just "ooc" will be fine.


No, it's not a guess. That's why it's called "Theory". Are you really so certain that SatoshiDice are not playing fair that you want to find the slightest variation from the expected values?


There is no "formula for consecutive losses". There is one for expected consecutive losses in n trials, in the same way that there is an expected number of shares that can solve a block.


You're not understanding how to analyse this.It is a little complicated, and you have a bit of a learning curve ahead, but you're still confusing the expected or average number of consecutive wins/losses in n trials with a probabilistic confidence interval. The reason some results are closer to the expected value than other has to do with how likely a particular run of losses is.  For this we use probability rather than statistics.

For example, if there are twice as many losses in a run than expected, we can calculate the probability of that occurring, assuming that SatoshiDice is playing fair.

If you're trying to prove  SatoshiDice is not playing fair, then you use statistics, providing a null and an alternative hypothesis and proving your point with a certain level of confidence (usually p < 0.05).

The problem with trying to find these confidence intervals using real life data is that you will need hundreds of repeats of the data to find out if it agrees with theory.

So you pick a game, decide on the number of trials you want to investigate (say 100) and consecutively split the data into runs of 100 trials. Find the largest number of consecutive losses in each run, and take the average. Only then can you compare the theoretical expected value with the actual average value.

If you want to find the probability of a particular number of runs occurring, using the same data you recorded as above, divide the longest runs into percentile groups. Say you record 10000 runs of 100 trials of a coin flip, and 0.001% of the runs there are more than say 20 consecutive losses. You can say for the sample group that the probability of more 20 losses is 0.001%, and that 99.999% of the time the number of consecutive losses in 100 trials will be smaller than this.

If you compare the quantile groups you calculated to theoretical quantiles, or the probabilities to theoretical probabilities, you can again calculate the probability of the dataset belonging to the same probability distribution as the theoretical probability distribution.

Edit: By all means carry on with your investigations. I find this sort of thing very interesting too, and it might provide a great opportunity for you to learn more about statistics and probability. Personally, I find it hard to learn things unless I need to solve a problem in which I'm interested. Perhaps the same will be true for you.

Hi Mr. organofcorti,

The theoretical part can be computed with formulas, but that's just a guess. Here, we have the actual historical data of what actually happened. The odds of winning are very close to the actual win:loss. The formula for consecutive losses isn't as close to actual losses especially with that weird 65 losses in a row.

Correct me if I'm mistaken, but statistics is based on actuarial data. Theoretical possibilities or probabilities are just that, it's possible or it's probably, but not necessarily what already happened. It can still happen.

In any case, both the formula and the historical data are interesting. Why do some match and why do others not seem to match... or will these numbers change a few years from now, or will it be more of the same ... or it doesn't matter since the house always wins.

You're really wanting a theoretical analysis than a statistical one. I think you're looking for probabilities of various runs in various games.

When you look at maxima there will be a lot of variance, so it's meaningless to point at one result and say "This the maximum you can expect". Instead, it would be better to point at a result and say "There's a 5% probability a run will last long then n losses in a row". I'll post how to do that when I get home.