Topic: Just-Dice.com : Invest in 1% House Edge Dice Game - page 145. (Read 435458 times)

Hmm, going crazy here:

In[1285]:=

profits =
  Table[betAmount[[j]]* RotateRight[winOrLose, 0][[j]], {j, 1,
    Length[betAmount]}];

Select[profits, (# >= 5 10^8) &] // Length
Select[profits, (# <= -5 10^8) &] // Length
Select[profits, (# < 5 10^8 && # > 0) &] // Length
Select[profits, (# >= -5 10^8 && # <= 0) &] // Length

Out[1286]= 7185
Out[1287]= 7209
Out[1288]= 13893
Out[1289]= 14688

So, he won 7185 and lost 7209 of his 5 BTC and greater bets.

In[1290]:=

profits =
  Table[betAmount[[j]]* RotateRight[winOrLose, 2][[j]], {j, 1,
    Length[betAmount]}];

Select[profits, (# >= 5 10^8) &] // Length
Select[profits, (# <= -5 10^8) &] // Length
Select[profits, (# < 5 10^8 && # > 0) &] // Length
Select[profits, (# >= -5 10^8 && # <= 0) &] // Length

Out[1291]= 10347
Out[1292]= 4047
Out[1293]= 10731
Out[1294]= 17653

Now, after shifting by 2, it says he would have won 10347 and only lost 4047 of his 5 BTC and greater bets. 

What am I missing?  Excel is telling me the same thing.  Maybe there is a problem with the file...

Cheers,
Peter

Thanks.  Yeah, I am probably missing something--I have certainly made mistakes in the past. Thing is, I was convinced my Mathematica code must of had a mistake so I imported the huge file into Excel and got the same result.  I couldn't find the problem after searching for a long time, so I thought I'd throw it out for discussion. 

But have you actually looked at the data from dooglus's nakowa2.txt file?  There are always sequences of small bets mixed with his large bets.  It seems like shifting 2 makes a lot more of the wins hit the big bets, while shifting by one makes a lot more of the wins hit the small bets.  It's weird.  I am going crazy trying to see how I could be messing up something that should be simple....

I can very confidently say that both 3 and 4 are wrong.  Somewhere you messed up.  Note how 3 and 4 are VERY similar sizes but opposite sign?  Note also that he was nealy always betting high.  So most of the time shifting a win would stay a win.  The only way you'd get that result for real was if he exactly alternated big/small bets and the RNG generated in high/low alternating sequence as well.  And if he did that, shifting 2 would be roughly same results as he actually got.

Your program is broken.

Well shifting it is fundamentally flawed for a (pretty obvious) reason.

Consider any significantly winning session of play which contains a mix of very high bets and very small bets.  The result of the session are determined ONLY by the high bets - what happens on the very small bets is irrelevant.  If you changed all the small bets to wins OR to losses the overall result would still be a significant win.

So we already know that a much higher percentage than average of the higher bets won - but if the results were genuinely random we know nothing at all about the results of the small bets as they're irrelevant to how we picked the sample.

If you take this session which has a much higher than average set of winning roll on BIG bets and an indeterminate set of tolls on SMALL bets and shift the results then, on average, the final result will be significantly lower.  Because some of the lucky big bets will now be moved to small bets - and replace by rolls with an indeterminate lucky factor.

In short, not only is there no reason why shifting SHOULD produce the same results, there's actually a good reason why it should NOT : that being how the sample for analysis was picked.  This is Bayes Theorem at its most basic.

It does, however, follow on from this that there IS an analysis which could be done to find a smoking gun.  The means by which the sample was picked (i.e. why his rolls are being looked at all) DOES define what we should expect to see in big bets (more wins than expected) but says nothing about the very small ones.  i.e. the small bets can be considered to be a genuinely independent sample not influenced by selection criteria.

IF he knows the seed OR has some means of otherwise predicting series then we'd expect to see a LOWER than usual win-rate on the small bets.  Whilst if everything is genuinely random then the results of the small bets would be unrelated to him winning overall on the big ones.

IF a smoking gun exists then where you'd see it is in far more losses than expected on small rolls - where if there was no unfair advantage there'd be no reason for it to correlate with the opposite results in the big bets.  We already know that his overall results on big bets are very significantly above average.  By looking at the small bets seperately (we CAN legitimately treat it as a seperate data set) we can see if the results there are similarly significantly BELOW average.  Such an analysis should be done by simply measuring his luck - not by factoring in varying bet size (as if a few small bets are much larger than the rest that would lead to no significant result).

I have no idea what the outcome of that would be.

I feel that I shouldn't have posted that graph!  (But I am still hoping someone will check it!)

1.  The sum of the profit column in dooglus's nakowa2.txt file is 17,264 BTC (after removing the small amount of bets not with 49.5% odds) .

2.  The total amount wagered according to the file was 985,847 BTC over 42,648 bets (several were small bets).

I agree that the probability of this is not *that* unlikely and can be explained by big balls and good luck.

3. Now, if all you do is calculate what he WOULD have won had the dice result been shifted by 2, then I calculate +420,784 BTC! 

4. If you shift it by 1, I calculate -427,822 BTC! 

If what I said in point 3 and 4 are correct, then you wouldn't find this fishy?  Almost like he was purposely leaving a trial?

Out of curiosity, what would be the probability of winning 420,784 BTC given Nakowa's bet sequence and assuming even a 1,000,000 BTC bankroll?  More or less likely than brute forcing a private key?

Excellent point.  It would be interesting to see the distribution of bet outcomes across different shift values to see if it is warrants looking into, or if this is simply the result of cherry-picking.

Correct or not, I appreciate the effort put into this analysis.

[/quote]

......................... but those are all perceptions, and reality (the facts) is telling us there's something wrong here. Not even the PnL of this 'whale' but the fact that there's this gaping security hole/conflict of interest. A good con(fidence) man gains your (take a guess) CONFIDENCE!

[/quote]

this was really a good one thanks for that

On the first paragraph you clearly made an error somewhere - as he's not up by anything like half the amount wagered.  Or even 5%.

On the second paragraph you seem to be arguing with yourself here.  You agree that him winning 4400 before losing 10k was actually a (small) favourite - but then seem surprised that if you shift the rolls you end up with a different result.  When if you shift the rolls you then need to shorten or extend the series until +4400 or -10000.  At a glance I suspect something's more basically wrong - as your results graph seems way too close to hugging the expectation line anyway.

You still haven't explained why you chose to shift by 2 rather than by 1 or by 3.

Do you mean to change the player's server seed while they are playing?  That breaks provably fairness, since you can't know for sure exactly when we saw the new block, we can pretend not to see it for a while, and then see it at the time most advantageous for us (ie. when it changes a big bet from a win to a loss).

Or do you mean use the blockchain to add entropy to the random number pool?  The random seeds are generated using openssl's cryptgraphically strong random number generator, which in turn is seeded from the operating system's entropy pool, which collects entropy from all over.

You may have found Nakowa's strategy.  If he is looking 2 rolls back to determine his current bet, then shifting the data by 2 rolls might result in something like this.

Any decisions made yet ? Nak might try to clean up investors before the changes.

Thanks for responding.  I think this type of discourse is very helpful to forum members trying to learn about probability.  

First, I want to say again that I think either that file is wrong, or I made a mistake somewhere.  I hope someone has another look.  

But perhaps you would reconsider the validity of my analysis should the file (and my number crunching) turn out to be correct.  I am not talking about randomizing Nakowa's rolls until the winning rolls hit the large bets.  I am simple shifting his wagers so that they correspond with the result of the roll two previous.  If you generate 40,000 fair dice rolls, and use this to drive Nakowa's bet sequence, you never get anywhere near earning a profit of 1/2 the amount wagered no matter how many simulations you do.  Shift this data all you like, but you'll never make it fit. If the file is correct and I didn't make a mistake, then this is a smoking gun.  

Think of it like this:

I open up two boxes full of 100, 100-sided dices.  Box #1 shows half "99"s and half "1"s while Box #2 shows a mix of numbers 4, 10, 95, 34, 5, 66....32, 47.  I then ask you "what box did I shake?"  Both "microstates" are equally likely, but there are a bunch of macrostates that look like Box #2 and very few that look like Box #1.  Obviously I shook Box #2 and carefully arranged Box #1.  There is no way you'll get all 50 of the 100 sided dices saying "99" and 50 saying "1" no matter how many times *you* shake the box.  This is the same problem.  

But again, maybe I made a mistake or there is a mistake in that file. But if not, there is no way that result could be random.

Lastly, if you look at my earlier posts in this thread from this time yesterday, you will see that I was recommending people analyze the probability of Nakowa winning a session assuming he bets until he hits his target, or he busts through his large bankroll.  I even made plots showing that Nakawa as "cake" was actually more likely to reach 4400 BTC before he bust his (assumed) 10,000 BTC bankroll.  So we agree on this point.  

Exactly, max bet is the key of the story.

Don't know. Every site has 1% or lower house edge

I was also thinking another, rational, explanation for this heavy gambler. Suppose he invested two third of the money (now it would be 20K) of the current bankroll (30K) and decides to advertise the website (like putting on reddit "he is the whale of just-dice"). If he wages totally  50K he has an expected loss of 167B, but then in a couple of days the website may as well gets 50K in other wages (thanks to the "advertisement of the whale") and then he would earn 333B. The fact he keeps playing could be explained by a lower adversarial variance he has since he would be both an investor and a player.

Also in this case lowering the max-bet would make this strategy difficult

You need to be very careful with analysis like this.

What's special about shifting the bets 2 places rather than 1 or 3?  Did you just try different shifts until you found one with results matching your theory?

If you try different shifts then a few things are true:

1.  You'll find one that matches your theory.
2.  As his actual results aren't a favourite to happen from the number of rolls he made (they're only a favourite from the strategy - not one sample of its execution) then most shifts won't match actual results anyway and will tend to be be much nearer expectation.

The thing here is that nearly ALL analysis being done is fundamentally flawed - and relies on the actual bets he made/rolls he did rather than the strategy being followed.  Nearly everyone is looking at the probability for entirely the wrong things.

Let me give an example to explain HOW all the rerunning same bets multiple times, calculating probabilities etc is horribly flawed. For this example I'll assume no house edge - I'm just showing how the calculations are fundamentally of the wrong thing, not what actual numbers are.

Consider someone who makes a small series of bets every day.  And every day they win exactly 1 BTC.  What they're doing is a simple martingale - starting with 1 BTC bet at 50/50, then 2 if they lose, then 4 if they lose etc.

Now here's how someone using the sort of math used when looking at the bets here would work it out:

The likelihood of them winning on one day is exactly 50% - as the last bet is 1 BTC larger than the sum of all previous bets so whether they win or not is decided entirely by that bet.  The odds of them winning 10 days in a row (from a fixed starting date) are thus 1 in 1024 - so there's only a 0.1% chance of it happening.

Someone running an analysis where they ran exactly the same bets a load of times would come up with a very similar result.

Yet those results are entirely incorrect - and the odds of it happening aren't 0.1%, 1% or even 10% : it's actually very heavily odds-on that it will happen.  Where the math and the modelling both fail is that they fail to account for the strategy of the player - that they'll stop when (and only when) they have a winning roll or exhaust their bank-roll/hit the max-bet limit.

You can do perfectly valid math, analysis or modelling - but when you don't base it on what actually happened (which includes modelling/accounting for decisions made by the player) then the results have little relevance.

That doesn't so much apply to the quoted post here as to much of the other analysis of the topic.  I already highlighted the main problem with this particular theory - that it seems to have started with a general theory then presented only one of many possible result sets which, of course, happens to be the one that matches their theory.

Where my point DOES tie in very much with the quoted post is this:

Consider the guy rolling martingales above - where he quits every day winning 1 BTC.  Now imagine if you moved his bets around by 1 day = each day doing the previous day's bets.  What would you see?  Would he still win every day?  Or would the results look more 'normal'?  Yet he isn't cheating, doesn't know the seeds etc.  If you take a specific set of RESULTS which differ greatly from the norm then OF COURSE if you shuffle them around the results will tend to look much more average.  And if you try various shuffles and pick the one that looks most like the expected average then OF COURSE it will be near the expected average.

Graph showing total wagered as well.  I hope I made a mistake or that the nakowa2.txt file has errors.

I think someone else needs to check the nakowa2.txt file before we take this further.  If that graph I posted is correct, the odds would be astronomically small (as in it couldn't have happened in a fair game).   

Nothing impossible, but how improbable is it? 5%, 1%, 0.001%? There is a certain point of improbabiltiy that the chance of a server seed compromise would be more than dumb luck but we need to see the stats to prove it.