Quote from: Deprived on September 25, 2013, 04:05:18 AM

Quote from: Peter R on September 25, 2013, 03:15:18 AM

Quote from: infested999 on September 25, 2013, 03:04:28 AM

Quote from: Peter R on September 25, 2013, 03:00:41 AM

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That doesn't make any sense, why would he wait 2 rolls for everything?

It doesn't make sense to me either. I think I either made a mistake, or there are errors in the file I downloaded from dooglus.

If you look at Nakowa's actual bet data, he makes a bunch of small bets mixed in with his large bets. If you take his actual data, but just shift one colum so that he wages what he actually wagered 2 rolls earlier, then most the losses line up with the small bets and most of the profits line up with the large bets. This should be statistically impossible. So either I made a mistake, there is an error in the file, or the seed was known by Nakowa and he left a clue for us to find.

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.

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.