No, not really, and apparently I'm misremembering anyway.

I was told "The expected value for 28 or more losses is 410,427,273" without explanation.  I've asked for the reasoning.

I get confused between the expected number of rolls for something to happen and having a 50% chance of that thing happening.  It feels as if the (alleged) fact that you expect to have to roll 514 million times on average to get a 28 losing streak means that since we have less than that number of bets then we have a less than 50% chance of having seen a 28 losing streak.

But I don't think that feeling is true.

Consider rolling a 6 sided die until you roll a six.  The expected number of rolls to get a six is 6.

But if you only roll 4 times, you have about a 51% of seeing a six, even though you've rolled less than the expected number.

Does that answer your question?  Basically my intuition around this is off (and yet I bet 50 BTC on it)...

It seems kind of obvious that in a 0% edge game whoever has the biggest bankroll has the smaller chance of going bust...  Not to say that everything is intuitive with probability stuff, but in this case I think it makes sense.


Pretty sure they're assuming the max bet is a constant.  Casinos generally don't reduce the max bet as players win...

When the bankroll is crowd-sourced and changes dramatically over time like it does at JD it makes sense to set the maximums dynamically so they change with the bankroll.  That has a side-effect of vastly reducing the risk of ruin.

You have to deposit to JD before you can play.  All bets are off-blockchain.  You play with your balance, and withdraw when you're done.  In a sense you don't play with Bitcoins, you play with JD-IOUs.  When you're done, you click 'withdraw' and hope that we send you real Bitcoins in exchange for your IOUs, in much the same way you hope the casino is going to give you dollars for the clay chips you won.  They might not, but they always have so far.


As far as the house is concerned, isn't everyone the same player?  All the site sees is an endless stream of bets which either win or lose.  In a sense that's indistinguishable from a single player with an unlimited bankroll.  If we can handle an endless stream of finite bankrolls, can't we also handle a single player with infinite funds?

For a week or so before JD launched, we ran the site in "testnet" mode.  People could deposit testnet coins and play with them.  I also made up "fractional reserve" testnet coins out of thin air and gave them away generously.  The site was full of whales with huge bankrolls.  They didn't manage to get anywhere close to bankrupting the site.  Not that that proves anything.  Nakowa came closer with a few real coins than the testers did with their millions of fake testnet coins.


This is a chart showing the actual and (offset) expected profit since nakowa finished his insane run.  Notice how close the two lines run to each other:



There's an offset of some 36k BTC which nakowa "should" have lost but didn't.  We don't expect to ever make that back again.  The expectation is that we stay 36k below 1%, but that it becomes less and less significant over time.

By my estimation in about 100 years if we keep the same volume as this year and have average luck, the site profit will be around 0.99%.  

Edit: and what you should reply is: look at how the black line goes up twice as steeply as the green line since the start of March.  that shows the site has been keeping 2% of turnover when it should only keep 1%.  That's because players play until they bust.  I don't have an answer for that, except that the site has been consistently almost twice as lucky as expected since March.  Weird.

I'm not sure Ivey admits to using edge sorting.  The story I heard suggests that the dealer was colluding with him, placing the high cards upside down in the deck for him.  That would probably be considered closer to "cheating" than "advantage play" wouldn't it?

Poker is the most obvious +EV game in land casinos.  You're playing against other customers with the casino taking a rake, so as long as you're a good enough players that you can beat your peers and beat the rake, you make a profit.

Blackjack is another obvious example if you can find a game where you can count cards.  I used to count cards at Bitcoin casino strikesapphire.com until they changed the penetration and banned me.  Made a few hundred dollars, withdrew into five dollar Bitcoins and hedl.

And a third example is sign-up bonuses.  If a casino offers you 2x your deposit as a sign-up bonus, it's often +EV if you play the right games.  They often make you play through the bonus 20 times or something, in the hope that that's enough to make you lose it, but unless the edge is 5%, your expectation is positive even after playing through it 20 times.  You need to do the math carefully, but it's possible to find +EV promotions.

Some places offer "no zero" roulette, where all bets pay out their actual fair odds.  You get 36x for a single number for example.  That's a zero house edge.  I've seen it suggested that it's +EV for the house because people play until they bust, but I don't believe it.  I think it's offered as a loss-leader to get new customers, and then withdrawn in the hope that they'll play "proper" 2.7% edge roulette.

The problem with this is that while most of your players will play until they lose, one of them will never go below zero.  He will win enough that he'll never run out of funds, and the positive edge you've given him will allow him to use basic bankroll management techniques to safely keep playing for bigger and bigger stakes until he breaks you.

This guy was playing on Just-Dice today, betting at 90% chance to win (generally a pretty bad idea) and winning.  Notice his profit at no point went negative.



Now imagine he was playing with a significant positive expectation...


I don't know the term.  What's pre-funding?  And what figure?

This itself is a fallacy.  It doesn't matter why people play, or what they're thinking.  In a game with a 2% edge the house will average 2% profit on turnover in the long run(*).  Even if every player played until they bust, that doesn't change anything.  Some would get to play though their deposit more than 50 times over before busting, and some less.  On average they'd play through 50 times and so lose 2% of their total wagered amount.


Because that makes no sense at all.  In a game of no skill, psychology plays no part.  Actual returns approach expected returns over the long run.  Offer a +EV no-skill game and quickly go bust.

(*) I know, Just-Dice has a 1% edge but only 0.33% profit.  That's because "the long run" is longer than you think.

I would prefer that everybody understand the risks before they play.  If someone knows the risks, knows that there's a small edge in the house's favour and still decides to play, that's fine with me.  If they think they've somehow found a "system", and then are surprised when they lose, that's not so fine.

I've never tried to convince anyone that gambling is a good idea, and always try to explain the odds to anyone who is interested.

If the whole community one day decides that gambling is stupid and stops playing, that would be a good result for me.  Some of the people bankrolling the site may disagree, and that's OK too.

There are betting limits because we live in a finite universe, and the house has a finite bankroll.

Kelly tells us how to set those limits, but they exist for bigger reasons.

Are you bearing in mind that the max profit per bet is *always* 1% of the total bankroll, and so it decreases as the bankroll decreases?

I don't think you can really put a number on "risk of bankruptcy" in such a situation.  You can work out the chance of someone taking half the bankroll - say it's 10%.  But then the chance of them taking half of what's left, taking it down to 25% of the starting roll is another 10%, making it 1% overall.  And so on.  The chance of halving it again to 12.5% is another 10%, for a 0.1% chance overall, etc.

At which point do you consider "bankruptcy" when all they can do is keep halving the bankroll?

(Note that the 10% here is completely made up - I've no idea what the real number is.  But nakowa was incredibly lucky and "only" took us down 14% one week and 12% the next.  I expect your 8% is far too high).

Hey it's you!

You might be able to help me with this...

If someone was to say "ha there's no way there's ever been a losing streak of 28 or more bets on any dice site ever at 49.5%" and I say "oh yeah?  I bet it has happened on Just-Dice alone!" and then someone else says "I bet you 49 BTC that it didn't happen" and I say "OK then!"...

What are my odds of winning?

Suppose that there are 357,937,388 bets at 49.5% and that they were all made by the same person.

What's the odds that it contains a losing streak (p(loss) = 0.505) of length 28 or more?

We know that the odds of a losing streak of length 28 happening in your first 28 rolls are 1 in 1/0.505**28 = 203,161,501.  That makes me think I have a greater than 50% chance of winning.

I'm told that the expected number of rolls before you see a 28 loss streak is around 514 million, but I don't know why.  That makes me think I have a lesser than 50% chance of winning.

So what are the odds of winning?

"Some of this actually happened."

Is it just me or is your signature barely legible?

That's a good idea!  The website could do the hashing client-side, using a client-side randomly generated seed.

Or see https://lbaat.net/ , particularly the ability to "Send message to the future".  I guess that just moves the trust from you to them (the people running lbaat can read the messages ahead of time), however.


You can keep the secret in the browser's local storage, and have a button to "reveal guesses" or something which sends the cached secret to the secret.  That hashing itself needn't be done by the user, just by his browser.  This is the same kind of trust the blockchain.info wallet has - you trust its client-side javascript to know your private key and not to share it unencrypted with the central server.

For a forum game, the players are going to have to do the hashing and secret-caching themselves.  But the kinds of people wanting to play such a geeky game are probably capable of that if you link them to a site that does sha256 for them...

You only need enough for one more bet once you reach the bottom of your chart (by definition, pretty much).

He could have been down to his last 45.5 BTC, and managed to make it all back from there.

But since people seem to care, here's his list of deposits and withdrawals:


The deposits sum to 8450.29159284 BTC.  So he was pretty close to busting at -8k.

As I said in the JD chat where you mentioned it, the biggest problem with this kind of a game is that somebody (presumably but not necessarily you) gets to see all the entries early, and can use that information to win.

I don't see how such a game can be made provably fair, which might make it difficult to get people to play.

The same as every other account: 0.

Edit: but as you can see the chart nearly touches -8000 BTC at one point - so it's safe to say he had at least that many coins to play with.

One last one for now - the biggest of them all - nakowa.

It's hard to plot a complete chart of his play because he switched accounts constantly, and I think he tended to try to disassociate himself from any losing accounts.  But here's just one of his accounts at play:



And a (particularly lucky) sample of the bets that made up that session:

https://bitcointalk.org/index.php?topic=631601 

It was around the end of September 2013 so a little over $100.

And here's Diablo.  Not such a classic martingale, and dominated by a single lucky 500 BTC win...