Perchance...

This is going to be a pretty long and intricate read, just so you know.

Part I. Chris Moore is a pretty smart fellow, he's on my radar because he's been doing a lot of work independently tracking and auditing the revenue, expenditure and profit of SatoshiDice (S.DICE). Something like this :

There's a lot of work traversing the blockchain involved into extracting the base data for making a graph like that, and indeed the independent audit of S.DICE is very valuable.ⁱ

The other day, while going through the forum digest my minions prepare for my periodic consumption, I found the following funny bit :

gambling question - changing house edge by altering bet size?

I've always thought that it's not possible to change the expected return of a game with fixed odds by altering your bet size. I've seen this stated all over the place.

For the last hour or two I've been playing roulette at luckybitcoincasino, and seem to have found a way of reducing my expected return.

I was betting the 3-36 line over and over, starting with 100 chips. I was betting 2 chips each spin, but whenever I fell below 70 chips I was reducing my bet to 1 chip per spin, and increasing it back to 2 chips per spin when I got back to 70 chips.

I counted my wins and losses. Each time my number of wins was exactly equal to half my number of losses, I noticed my balance was a little lower than the previous time it happened.

I would expect that since a win pays out twice as much as a loss loses, having N wins and 2N wins should mean I was breaking even, but that wasn't the case.

I tried to understand why, and came up with this thought experiment:

Suppose you're tossing a fair coin, and getting fair odds, but decide to play 2 chips per flip when you have 1000 or more chips, and 1 chip per toss when you have less than 1000 chips.

Your expected return is 0; you'll neither win nor lose in the long run, since you're getting fair odds. We can suppose the house is willing to give you unlimited credit, so going bust isn't a concern.

If I have 1000 chips and lose, I now only have 998 chips and will start playing for 1 chip each flip.

I'm not going to get back to 1000 chips until my following sequence of plays has 2 more wins than losses (N losses, and N+2 wins, say), at which point I'm going to start playing for 2 chips per flip again.

Each time I lose at 1000 chips, it takes a total of N+1 losses (including the loss of 2 coins) and N+2 wins to break even.

Since in the long run I can expect my number of losses to be equal to my number of wins, doesn't that imply I can expect to not break even, long term, since each time I cross the 1000 threshold I need 1 extra unmatched win to make up my loss?

So what's wrong with the above argument? It looks to me like I've found a strategy that reduces my expected return, making it negative in a zero-expectation coin toss game. I must be missing something. Mustn't I?

The guy is pretty smart, educated, knows about statistics and has obviously spent a lot of time and has a lot of practice working this side of the math cube, and yet... and yet he's managed to scare himself, in the immortal words of that cute little chickenhawk.

This isn't to impeach him in any way, once the error was stated he immediately understood the problem and all was well. This however is to show a little anecdotal proof of a universally true and universally ignored fact : that everyone is perfectly capable of knotting their own fingers while trying to be dextrous with an Essence.ⁱⁱ

Part II. As I was saying, I was playing Dragon's Tale, which is pretty much entirely based on chance. I wasn't doing too bad at it, either. (There's a YOLA ⁱⁱⁱ shot on the left).

I've been pretty much whaling through the whole game, making level 6 (of something like 10 maximum at the moment I think ?) in about a day. I have 37 or so records, which puts me squarely in the first position on that leaderboard, the next contender has half or something like that. My secret ? Bruteforce and martingale everything. Right on. There's a quest to fish for 20 BTC ? Find a lake which allows 100 MilliBTC bets and click 200 times. Need to win five BTC collecting coconuts ? Find the 1 BTC tree and do it till it drops. Etc.

This strategy served me pretty well all through, I did two of the three tasks for level 7 and then... well... then there was farming. The problem with farming was that it was asking me to make 100 BTC, and I balked - not in small part because some test runs I did with 1 BTC a pop seeds returned in the 50% range, which was a little more than I was willing to throw away. Fact of the matter is, farming has huge variance built in.

So I slowed down, talked a little to my mentor who provided me with the lore & wisdom as collected by the players up to that point^iv and eventually decided to do a lot of 1 MilliBTC runs to get the hang of this. Here's me tending my crops :

And here's some of the pages I've filled with accounting of my various attempts :

I went through one thousand little seeds (total value, 1 BTC) trying out extensively all sorts of theories. Some people think the ground matters, some disagree. Some people think the ground only matters inasmuch as you shouldn't plant consecutively in the same spot, most agree (my mentor disagrees). The game has some in built "Framing information" which includes a 15 minute time counter referred to as a "season". Most people agree this matters somehow : plants grow better in some seasons than in others, plants grow better at beginning of season etc.

None of this turned out to be in fact measurable. Sure, you get patterns, of course you get patterns. But if you have any idea of statistics then you already know that merely seeing a pattern means nothing at all.

So I shrugged, filled up on 100 mBTC seeds and just planted them one after another in the same one spot until I was done, in complete disregard of anything. Net result ? 95 BTC spent, 102 BTC harvested (that's a 107% return on a game that's supposed to pay 95% on average and people were saying I should count myself lucky if I even get 70%), a few fireworks and a draining of the pool from 8.96 to 8.1 something^v.

Variance.

Part III. Now let's wrap all of this up.

People have the innate ability to imagine patterns and to then recognise patterns they've imagined. This is quite biological, has a lot to do with how we (and all other species) evolved (specifically, it is better to try and find food someplace where there isn't any food than to not try and find food someplace where there's some) and it won't be going away. Against it any stack of read books, any ledger of hours of practice and any tools to sharpen the mind labour in vain (as illustrated by Part I above).

When confronted with a stressful environment (because the perspective of loss is actually a lot more discouraging than the perspective of gain - yet another little tidbit that ties into evolution) which is governed entirely by chance humans will try to afford themselves the completely imaginary solace of "knowledge", which somehow controls the uncontrollable.

Since there's no practical way to be right - chance is chance after all - the only alternative is to... not... play. And so, complex schemes of how to play "correctly" evolve, which all have one fundamental thing in common : you're supposed to not play. If followed they will never be proven wrong in practice for the very simple reason that that's exactly the one and only thing they do : they make it impossible to play, and thus to lose, and thus to prove them wrong. And so therefore... they must be right.

All this ties in nicely with the discussion around Climax, and it explains quite elegantly both why people want shackles for themselves and why kids can't get along with adults in any time and in any place.

The alternative, obviously, is accepting death. For most living things that's a bridge too far.

1. Which, as an aside, takes us to something that will probably become the most important question of the XXIst century, once Bitcoin replaces fiat currencies and wreaks all the havoc on the rest of modern culture & civilisation that it is going to unavoidably wreak - all that good stuff I've been hinting at such as the end of compulsory taxation (not as a practice, but outright as a possibility) and the irretrievable dissolution of the welfare state.

   Specifically : things such as the revenue, expenditure and income of private enterprises can be independently audited, by the very nature and structure of Bitcoin. This auditing provides a significant and valuable service to the community in general, and to the enterprise itself (provided that it's honest) : it builds and verifies its credibility.

   The key however is that said auditing has to be independent - if it's done by the enterprise itself it's quite worthless, no longer actual auditing but something closer to shilling (note that we're discussing things in principle here, it doesn't matter if it actually is shilling or not, in practice).

   So here's the problem : on one hand the auditor does something useful for the enterprise. On the other hand, the enterprise can not pay for this value it receives, because in doing so it would ruin the very value in question. What to do now ?

   Obviously the two simple answers, ie, "pay anyway and rely on boyscout's honor as a guarantee that no smelly stuff will ever happen" and "don't pay and rely on the auditor's own goodwill to expend his time and effort doing something to your benefit" are both practically dysfunctional. Sure, they may work in some cases (the latter is working in the case of SatoshiDICE for instance) but that doesn't make them actual solutions to the problem.

   Traditionally this was resolved by having everyone in a field licensed, which practically means, guy with big stick comes about, forces everyone to pay X fee, that fee is used to pay independent auditors. Not only does this not work in practice as we all know, but even theoretically regarding it, it's nonsense - all it does is add an extra layer to the cake, it's a way to fight fire by putting another log in between the fire and the log the fire is currently burning through. Add to this the plain impossibility of forcing anyone to do anything with his Bitcoins and that's pretty much the end of the story - it won't happen.

   What will the solution be ? I have absolutely no idea, but I'm pretty convinced it's going to be one of the top problems we're going to be trying to solve, as a civilisation. [↩]

2. Chance being, of course, the most essential of all ousia. [↩]
3. A YOLA photo is that obnoxious sort of photography consisting of some random douche of either gender with some famous landmark in the background. You know, like this. [↩]
4. Guy's game name is Umuri, and he's quite knowledgeable btw. [↩]
5. The way skill games work in Dragon's Tale is that the system will adjust payouts so as to match the historical results with expected results. So if the game expects to pay on average 95% and I turn 100 seeds into 105 seeds it will reduce the repurchase value of a seed by 5%. [↩]