May I note that all this mathematically obvious "variance" is clearly putting everyone under stress and questioning about what to do or not?

This time he is waging the same amount of money (around 170B), so that there is not even the illusion of a "strategy"...

Really, I feel spiritually changed.

I wasn't meaning "looking" at a graph, but being actually on the "roller coaster" ;-)

Guys I think I never knew what "variance" really was before looking at the swings in my profit on just-dice in these days :-D

Yes, in this sense just-dice has collected many players into a single one which is now playing against an almost equivalent one. For sure this was not the intention of dooglus and attracted a lot of attention and perplexities that were not initially considered. What I mean is that possibly nakowa himself has a lot of money invested in the website (partly playing against himself, yeah) and in that case his bankroll may be, in total, even larger than the one of all the others players all together. Thus it would be a rational plan to bet a lot against a small player (even if he is in advantage with probabilities) and he would not be the victim of the gambler fallacy at all.

Please Rampion tell me your opinion on this hypothesis.

https://bitcointalk.org/index.php?topic=301412.0

I am getting more and more convinced that nakowa is one of the main investors of just-dice and he is just advertising the website

If we were in the world of mathematics I would have no doubt that keeping the max bet to 0.01% is the only choice. But in the real world people have, blame them, feelings. Now I run some simulations with a player who is playing at max bet, lets say that three over four of them are satisfactory, in those cases we are making money with no problems, but one over four is more or less like that (initial capital is one bitcoin):



Now think we find ourselves in the middle, the heavy gambler has taken half of our pot. I want to know how many people will believe in mathematics (waiting for the inevitable return to gaining) and how many people (normal people having emotions and knowing that the world is not mathematics) will think that actually the website is scam.

Our best customer has 1/4 probability (lets say, I would like to have a more precise computation) to make us think the website is scam. So mathematically, taking into account that humans are complex, that is actually not our best customer.

I think dooglus did an excellent choice and was brave enough to make it on time.

Now we are having this discussion but consider a parallel universe where this afternoon nakowa was max betting 300 euros and the bankroll was down to 20K. Then we would not see "paladins of the kelly criterion", "defender of the justice of the never changing website" or the people who "disagree on lowering the max bet". We would see a mob of angry people who would claim the website is scam, nakowa is dooglus and that the bitcoins were just stolen. Dooglus would be in quite much trouble NO MATTER HOW MUCH MATH HE COULD EXPLAIN.

No one could foresee the whale betting 13M and dooglus made the wise choice of lowering the variance, at least for the sake of proving that nakowa is not cheating us.

If I were him I would have 0.001% max bet, I felt we still risked a bit this afternoon :-)

Well I think it is partially true. People may well see that the current 1% is 30000 euros and can conceive that it does not exist a gambler ready to pay that amount of money for a single gamble. Did you really think that a whale existed? One playing 13M euros in just one day? I did not and I think many people did not as well and this kind of reasoning is sort of out of the math and is personal, of course they do not write it in the website.

In any case I never divested in any moment :-)

Even though I agree on many points you say, I believe Kelly criterion is too much an aggressive way to play against a massive gambler. Have you run some simulations? I did and the plots of the earnings are scary (some of them are nice too). Suppose that we keep playing with this maxbet and the bankroll still shrinks, then a lot of people will be very scared and will quit the website thinking it is scam or else, then what do we do, we play 100B bankroll? Then we really will wait a lot

dooglus is right, nakowa himself said he wants to play with low bets in order to show that it is not necessary to bet high to win. So even though it is a bit an "ad-hoc" move, it is agreed with the player.

If he was losing he would not have said on the chat, he boasts after getting the lucky strike... a real statistical proof would be to repeat the lucky strike ten or more times.

Secondly, he is reading the forum and he is worried that dooglus actually lowers the max bet, and if he is worried it means that it is not cheating at all, but he is just trying to play out the bankroll (which is easier with max bets).

Thirdly, I fear that dooglus is getting stressed about this issue, for many reasons (people are getting nervous and the situation is new). I hope no one here is really thinking that the whale has the "right martingale" or that they can "analyse the betting pattern". COME ON! What is happening is that the whale just wants to make dooglus nervous by exploiting the unpredictability of luck.

dooglus please do not get stressed, do not believe in martingales or as such and do not lose confidence in yourself. Until a STRONG AND CONVINCING statistical proof arrives, the whale is just a gambler with tons of bitcoins.

Yes, but if he bets lower amounts, like 20B, and he consistently wins in an unlikely fashion (for example he wagers 20000 and wins other 20000), then we could really think he compromised the server.

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

I think you never tried some simulations with a player who is always playing at 1% with 49.5% probability. You will see many cases even worse than this one.

I disagree with dooglus on this point. Now the investors are in the situation they cannot understand if nakowa is cheating or not, because with large bets what happened in these days is still somehow plausible. Indeed, if you run some simulations as elm did 242962.msg3222672#msg3222672date=1379981987 you can see that few times nakowa is winning. However if you run the same simulations with a much smaller max bet, like 0.01% or so, but the same amount of wagered money, you may check that the same behavior is ridiculously improbable. If he is cheating he would surely reveal the cheat on a lower max bet (less than 1 euro) and the website must surely be stopped.

Note that even if he is not cheating (which is what I think) the kelly criterion is known to be quite aggressive (in the world of poker online for example), and again if you run some max betting simulations you may see that some of them are quite scary from the point of view of an investor.

Of course I cannot make other important considerations on lowering the max bet, maybe we are to the point that investors could vote for it, for example.

waiting...