Just-Dice.com : Invest in 1% House Edge Dice Game

[Lohoris]

If you play long enough to a -EV game, you will lose. Always. That's pure hard math, and anything else a delusion.

Only in the long run.
In the short run you may still win, if you get lucky.
And that's the point.

[dooglus]

Why don't I just get out completely?  Of at least go back to investing just a few thousand dollars?

You're free to.  The remaining investors would probably even thank you for increasing their share of future profits.

Please do whatever you feel is best for you.

[mechs]

Just a reminder, anyone interested in bidding on my J-D account which has 479BTC of commission free investment available (current value 47.9 BTC at current 10% rate), my auction ends tonight at 1AM est.  Last bid is 4BTC by Dooglus who also agreed to escrow for free to the winner.

https://bitcointalk.org/index.php?topic=355604.new#new

Auction ending 1am est 12/6

Thank you

[tucenaber]

Umm... you're right in the first part, but to the last paragraph I could add: given any fully specified Martingale (odds, betting size progression, ending conditions), I can construct an equivalent single bet strategy. The only reason to employ a Martingale over a single bet strategy is that the former seems easier to risk-manage intuitively for the human mind.

I disagree, but will allow you to prove me wrong...

Suppose I have 127 BTC and want 128.  I propose betting 1 BTC at 49.5% (2x payout).  If it wins, stop, else double and repeat until it wins.  So bet:

1, 2, 4, 8, 16, 32, 64

until one of them wins.  If none wins, I've lost all 127 BTC.  If any wins, I've got the 128 BTC I wanted.

This strategy will work so long as any one of the maximum of 7 bets wins.  ie. unless all 7 lose.  The probability of all 7 losing is 0.505^7 = 0.008376, so I have a 100 * (1 - 0.008376) = 99.1624% chance of success.

It's pretty likely that I'll end up betting less than the full 127 BTC.  My expected total stake is less than 127.  So my expected loss is less than 1.27 BTC.

What's your equivalent single bet strategy?  How much does it expect to risk?  How much does it expect to lose?

I would like t follow up on this since I think it is a very important point.

What this means is that a player can improve his expected return from -1% to -0.05% (!) using the above (truncated) martingale strategy.
This in turn means that the current 0.5% max winnings is at least 10 times the optimal Kelly bet against a martingaling player if I'm not mistaken. And that is dangerous.

[nicolaennio]

Umm... you're right in the first part, but to the last paragraph I could add: given any fully specified Martingale (odds, betting size progression, ending conditions), I can construct an equivalent single bet strategy. The only reason to employ a Martingale over a single bet strategy is that the former seems easier to risk-manage intuitively for the human mind.

I disagree, but will allow you to prove me wrong...

Suppose I have 127 BTC and want 128.  I propose betting 1 BTC at 49.5% (2x payout).  If it wins, stop, else double and repeat until it wins.  So bet:

1, 2, 4, 8, 16, 32, 64

until one of them wins.  If none wins, I've lost all 127 BTC.  If any wins, I've got the 128 BTC I wanted.

This strategy will work so long as any one of the maximum of 7 bets wins.  ie. unless all 7 lose.  The probability of all 7 losing is 0.505^7 = 0.008376, so I have a 100 * (1 - 0.008376) = 99.1624% chance of success.

It's pretty likely that I'll end up betting less than the full 127 BTC.  My expected total stake is less than 127.  So my expected loss is less than 1.27 BTC.

What's your equivalent single bet strategy?  How much does it expect to risk?  How much does it expect to lose?

I would like t follow up on this since I think it is a very important point.

What this means is that a player can improve his expected return from -1% to -0.05% (!) using the above (truncated) martingale strategy.
This in turn means that the current 0.5% max winnings is at least 10 times the optimal Kelly bet against a martingaling player if I'm not mistaken. And that is dangerous.

I reply since I was originally doubting it, maybe I can tell you how I see this point now.

The expected loss is less than 1.27BTC because on average you bet much less than 127BTC (in the above case it is roughly 7BTC on average). If you compute the average bet size, which is much smaller than the worst case one, you can see that the expected return is -1% and this is the only possible expected return. However, if you specify that your strategy can lose at maximum 127BTC and wins at maximum 1BTC, you can find different ways of betting the money with different average bet sizes and thus different expected losses. Betting all the 127BTC is probably the worst way :-)

[SebastianJu]

Hm... yesterday i tried investing 1BTC. I came back a hour later and it dropped... another hour later it dropped even more. The next day it had been dropped way more... at the evening its even way more now... I cant really see a house advantage of 1% here. With the mass of bets happening it simply makes no sense to me that this big amount of bets turn out to have this result.

The winning end losing bets are really spread fairly about all invested coins or is there some early investor advantage or so?

Anyway... i will watch this some more days but with this amount of random calculations this result doesnt make sense anymore to me. You know... throwing a dice often enough you will get more near the result to having nearly the same amount of all 6 digits as a result. And there has to be thousands of bets in the last day.

Its strange at least...

@nicolaennio... no martingale doesnt work. You cant beat luck this way. I hope you wont try it to make a fortune since you only will lose at the end. If you dont believe me ask google for explainations.

[Rannasha]

Hm... yesterday i tried investing 1BTC. I came back a hour later and it dropped... another hour later it dropped even more. The next day it had been dropped way more... at the evening its even way more now... I cant really see a house advantage of 1% here. With the mass of bets happening it simply makes no sense to me that this big amount of bets turn out to have this result.

The winning end losing bets are really spread fairly about all invested coins or is there some early investor advantage or so?

Anyway... i will watch this some more days but with this amount of random calculations this result doesnt make sense anymore to me. You know... throwing a dice often enough you will get more near the result to having nearly the same amount of all 6 digits as a result. And there has to be thousands of bets in the last day.

Its strange at least...

@nicolaennio... no martingale doesnt work. You cant beat luck this way. I hope you wont try it to make a fortune since you only will lose at the end. If you dont believe me ask google for explainations.

If you take a look at the charts listed at http://bitcoinproject.net/just-dice-casino/just-dice-charts/profit-chart (especially the 2nd on that page) you will see that the profit follows the 1% of amount wagered curve reasonably well, but that there are spikes up and down when either the house or the gamblers get lucky. Right now, the site has not been very lucky for the last few days, causing loss to investors.

A 1% house edge is really small and while the numbers of bets on JD is very high, but most bets are dust-sized and the actual wager-amounts are often dominated by a handful of large gamblers. They can easily hit a good streak with such a small house edge.

[tucenaber]

I reply since I was originally doubting it, maybe I can tell you how I see this point now.

The expected loss is less than 1.27BTC because on average you bet much less than 127BTC (in the above case it is roughly 7BTC on average). If you compute the average bet size, which is much smaller than the worst case one, you can see that the expected return is -1% and this is the only possible expected return. However, if you specify that your strategy can lose at maximum 127BTC and wins at maximum 1BTC, you can find different ways of betting the money with different average bet sizes and thus different expected losses. Betting all the 127BTC is probably the worst way :-)

That is not correct I think. It is true that you can never turn a negative EV into a positive, but you can make it less bad. The average bet size is irrelevant. The martingale strategy dooglus used in his example has only two outcomes: either you win 1 or you lose 127. The probability of losing is q_m=(1-p)⁷ and therefore the expected return is EV=1*(1-q_m)-127*q_m.

Just as dooglus pointed out earlier, the surprising thing is that q_m is much smaller than the probability of losing a single bet with the same return, i.e. the following two strategies have exactly the same payoffs, but the probabilities are not the same:

Single bet with bet size 127:
p=0,982265625
EV=p*1 - (1-p)*127 = 0,982265625 - 0.017734375 * 127 = -1.27

Martingale starting at 1
p = 1-0.505⁷ = 0,99162394
EV = p*1-(1-p)*127 = 0,99162394 - 0,0083760574 * 127 = -0,0721353 !!!!

The martingale is clearly much better. The expected value is much closer to zero than the single bet.

@nicolaennio... no martingale doesnt work. You cant beat luck this way. I hope you wont try it to make a fortune since you only will lose at the end. If you dont believe me ask google for explainations.

Prove me wrong.

[dooglus]

What this means is that a player can improve his expected return from -1% to -0.05% (!) using the above (truncated) martingale strategy.
This in turn means that the current 0.5% max winnings is at least 10 times the optimal Kelly bet against a martingaling player if I'm not mistaken. And that is dangerous.

I just started writing an "oh my God you're right and it's even worse than that!" post:

Not only that, but as well as reducing the effective house edge, the martingale player is also doubling the effective max bet.  He's never betting more than 64 in my example, but is effectively betting 127 to win 1.  So he's almost doubled the effective max bet from 64 to 127.

But... we don't have a max bet.  We have a max profit.  Kelly tells us not to risk more than 1% of the bankroll per bet.  The "all-in 127 to win 1" bet profits by at most 1 BTC.  But the equivalent 7-step martingale bet profits by 64 units on the last step.  I think this factor of 64 difference means I need to scale down your statement, to:

This in turn means that the current 0.5% max winnings is at least 10/64 times the optimal Kelly bet against a martingaling player if I'm not mistaken. And that is safe.

I'm not convinced - and you did have me worried for a minute there, but I think the fact that the equivalent martingale sequence needs a much higher max profit than the single large bet it's replacing means that Mr. Kelly is still satisfied despite the reduction in effective house edge.

[zipmaster]

Hey Doog,

would it be possible for users to query the betting history of specific users? I'm referring to something analogous to the "My Bets" tab where one can type in a specific user ID and see the betting history of that user.

Thanks!

[tucenaber]

What this means is that a player can improve his expected return from -1% to -0.05% (!) using the above (truncated) martingale strategy.
This in turn means that the current 0.5% max winnings is at least 10 times the optimal Kelly bet against a martingaling player if I'm not mistaken. And that is dangerous.

I just started writing an "oh my God you're right and it's even worse than that!" post:

Not only that, but as well as reducing the effective house edge, the martingale player is also doubling the effective max bet.  He's never betting more than 64 in my example, but is effectively betting 127 to win 1.  So he's almost doubled the effective max bet from 64 to 127.

But... we don't have a max bet.  We have a max profit.  Kelly tells us not to risk more than 1% of the bankroll per bet.  The "all-in 127 to win 1" bet profits by at most 1 BTC.  But the equivalent 7-step martingale bet profits by 64 units on the last step.  I think this factor of 64 difference means I need to scale down your statement, to:

This in turn means that the current 0.5% max winnings is at least 10/64 times the optimal Kelly bet against a martingaling player if I'm not mistaken. And that is safe.

I'm not convinced - and you did have me worried for a minute there, but I think the fact that the equivalent martingale sequence needs a much higher max profit than the single large bet it's replacing means that Mr. Kelly is still satisfied despite the reduction in effective house edge.

Thank god, you're right I'm convinced.

[nicolaennio]

Martingale starting at 1
p = 1-0.505⁷ = 0,99162394
EV = p*1-(1-p)*127 = 0,99162394 - 0,0083760574 * 127 = -0,0721353 !!!!

The martingale is clearly much better. The expected value is much closer to zero than the single bet.

The average bet size of the martingale is 7.21B and the average return is -0,0721353, so there is no change in Kelly or more expected return or whatever problem of any sort. However that idea that with a Martingale I can better use my money (achieving a profit with a smaller average bet size) is interesting for a theoretical speculation.

[TheJacob]

The thing that concerns me about this is the weekly 10% off the top with no make up.

Depending on volume, spread of bets,etc its possible for this to be a loser for investors.

Dooglus has what we call a freeroll. No ill will toward him, but I'm hesitant towards this as I don't see any reason the commission needs to be taken out every week or not carry losses forward.

Just to be 100% clear here is the issue. You get 90% of the profits over X time period and 100% of the losses over X time period. Is that a good bet on 10 seconds? Absolutely not.

At what point does it become a good bet? I don't know precisely, but its certainly possible its a time period longer than 1 week.

[nicolaennio]

The thing that concerns me about this is the weekly 10% off the top with no make up.

Depending on volume, spread of bets,etc its possible for this to be a loser for investors.

Dooglus has what we call a freeroll. No ill will toward him, but I'm hesitant towards this as I don't see any reason the commission needs to be taken out every week or not carry losses forward.

Just to be 100% clear here is the issue. You get 90% of the profits over X time period and 100% of the losses over X time period. Is that a good bet on 10 seconds? Absolutely not.

At what point does it become a good bet? I don't know precisely, but its certainly possible its a time period longer than 1 week.

If you can code I suggest you to run some simulations and "see". If people bet a number of BTC comparable to the max bet that time can be quite long and if whales betting so much appear at this low rate, once every two months or so, it can be a lifetime. But if people make frequent small bets also one month would be enough.

[Rannasha]

The thing that concerns me about this is the weekly 10% off the top with no make up.

Depending on volume, spread of bets,etc its possible for this to be a loser for investors.

Dooglus has what we call a freeroll. No ill will toward him, but I'm hesitant towards this as I don't see any reason the commission needs to be taken out every week or not carry losses forward.

Just to be 100% clear here is the issue. You get 90% of the profits over X time period and 100% of the losses over X time period. Is that a good bet on 10 seconds? Absolutely not.

At what point does it become a good bet? I don't know precisely, but its certainly possible its a time period longer than 1 week.

Losses are carried forward. You only pay commission over actual profits. If your investment goes down X% in week one and then grows back to your original amount in week two, you can withdraw the investment without having paid a single satoshi in commission.

[TheJacob]

Losses are carried forward. You only pay commission over actual profits. If your investment goes down X% in week one and then grows back to your original amount in week two, you can withdraw the investment without having paid a single satoshi in commission.

Yeh, I reread the explanation. Makes more sense now. Only profit over peak matters.

[tucenaber]

Martingale starting at 1
p = 1-0.505⁷ = 0,99162394
EV = p*1-(1-p)*127 = 0,99162394 - 0,0083760574 * 127 = -0,0721353 !!!!

The martingale is clearly much better. The expected value is much closer to zero than the single bet.

The average bet size of the martingale is 7.21B and the average return is -0,0721353, so there is no change in Kelly or more expected return or whatever problem of any sort. However that idea that with a Martingale I can better use my money (achieving a profit with a smaller average bet size) is interesting for a theoretical speculation.

You are correct. The expected value will always be 1% of wagered amount regardless of strategy so everything is fine. This is of course in accordance with our intuition. (Mathematically it's still not quite obvious to me but this is not the math forums so let's drop that)

Regarding the paradox where a martingale strategy is both better and no better at the same time, I think the answer lies in a trade off between expected value and variance. In one case the bet size is fixed and in the other case the bet size is a random variable. The latter thus has a higher variance.

[pascal257]

2) While the Martingale system is a for sure loser on paper things get much more cloudy when you allow 1 satoshi bets and virtually no maximums. There's no way you haven't looked into this and I'm sure the conclusion is "but they'll be winning dust" which may be true but the right person could put a real hurt on a casino with this kind of spread and such favorable odds even if it were 25 cents at a time.

1 satoshi != 25 cents. If you run a martingale with a reasonable amount to start with, you'll hit max bet pretty fast.

[organofcorti]

2) While the Martingale system is a for sure loser on paper things get much more cloudy when you allow 1 satoshi bets and virtually no maximums. There's no way you haven't looked into this and I'm sure the conclusion is "but they'll be winning dust" which may be true but the right person could put a real hurt on a casino with this kind of spread and such favorable odds even if it were 25 cents at a time.

1 satoshi != 25 cents. If you run a martingale with a reasonable amount to start with, you'll hit max bet pretty fast.

And if you start at one satoshi, you'll make only one satoshi per loss-win sequence.

[itod]

2) While the Martingale system is a for sure loser on paper things get much more cloudy when you allow 1 satoshi bets and virtually no maximums. There's no way you haven't looked into this and I'm sure the conclusion is "but they'll be winning dust" which may be true but the right person could put a real hurt on a casino with this kind of spread and such favorable odds even if it were 25 cents at a time.

1 satoshi != 25 cents. If you run a martingale with a reasonable amount to start with, you'll hit max bet pretty fast.

I am well aware of how the Martingale works and I only mentioned one satoshi because it is the minimum bet. If you want to get down to it someone could have 10,000 bots winning 1 satoshi at a time with virtually no risk in about 2 hours. Of course they would increase that regularly as needed.

I brought up quarters because if you start at 25 cents you would be wagering a mere $128 bet on the 10th loss. The odds of losing 10 in a row if you set the odds to exactly 50% are 1:1024. On just-dice you could, with a large bankroll, get to the 20th bet before reaching the maximum profit per hand. The odds of losing 20 hands in a row set at 50% are one in a million.

In addition, there are ways to adjust the martingale so that you change the distribution of wins and losses in ways beneficial to you. This is especially true when you can adjust the odds to anything you want, from 0.01% up to 99.9%. I'm not interested in getting into the math involved but go look up how you can effect win distributions with gambling strategies for a good place to start.

You shake all that up and mix in a 1% edge, a lot of major BTC holders that are extremely well versed in mathematics (comes with the territory) and a very forgiving bet spread and it can lead to extensive losses for the "house that can't lose".

Once you start getting to numbers like 1 in a million, where it is more likely you win a small lottery than lose your bet on a gambling site, it's not a giant leap to think someone ballsy enough to sit on 10k or so BTC might decide to give it a shot. If the 1 in a million hits then the casino looks golden, but with those kinds of odds it wouldn't be unusual too far outside of a standard deviation for 10's of millions of iterations to go by without it ever happening. And you have to remember, the person "beating the odds" will be accumulating bankroll all along the way making it even harder to "bust" them.

Edit: And the fact that the 1 in a million hitting wouldn't even bust some of those that have graced the tables of just-dice makes it that much worse. Now you need that 1 in a million to come around on schedule every time and the player to not take his wins and go home. With that kind of betting system one could religiously beat the house for months and months on end and in the world of computers he could do so with a bot.

1 in a million is nothing, it's a certainty it will happen if you start with 1 satoshi and you want to gain 1 BTC, because you need 100 million martingale wins to achieve that. Much bigger loosing streak than loosing 20 in a row is almost a certainty when you chase a whole BTC as a reward.

There's obviously something counter-intuitive about the fact martingale will always loose. But it will, it's a proven fact as long as there's limited maximum bet.