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

[dooglus]

When a player risks 1 unit at 33% for a 3x payout for example, the house is risking 2 units for a 1.5x payout with a 67% chance of winning. If you apply the Kelly Criterion on those numbers you'll see that it's still optimal to risk 1% of the bank.

f = (bp - q) / b

where f is the fraction to risk,
b is the payout multiplier minus 1
p is the probability of the house winning
q is the probability of the house losing

So in the 49.5% bet, where the payout is 2x,
b = 2-1 = 1
p = 0.505
q = 0.495
f = (1*0.505 - 0.495) / 1 = 0.505 - 0.495 = 0.01 = 1%

And in the 33% bet, where the payout (for the house) is 1.5x,
b = 1.5-1 = 0.5
p = 0.67
q = 0.33
f = (0.5*0.67 - 0.33) / 0.5 = (0.335 - 0.33) * 2 = 0.01 = 1%

And it's the same for every other bet:

If the player has probability q of winning, the payout to the player is 0.99/q
When the player risks 1 unit, the house risks 0.99/q - 1 unit
That's a payout multiplier for the house of 1 / (0.99/q - 1) + 1

b = 1 / (0.99/q - 1) + 1 - 1
f = (b*p - q) / b
  = (p/(0.99/q - 1) - q) * (0.99/q - 1)
  = (p*q/(0.99 - q) - q) * (0.99 - q)/q
  = (p/(p - 0.01) - 1) * (p - 0.01)
  = p - (p - 0.01)
  = 0.01
  = 1%

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[dooglus]

He won 12 times, came back the next day and 7 even bigger bets, then the next morning 7 more times. Then he waited 2 hours and played and lost it all. What was he thinking about in those 2 hours?

Did you see this log I made of his chat and his bets?

http://pastie.org/pastes/9252179/text

[boumalo]

20,651 average BTC wagered per day previous (June 20, 2013 - Feb 17,2014)
 2,386 average BTC wagered per day last 4 months (Feb 18, 2014 - Jun 17, 2014)

In the last 120 days the total amount wagered is 18.43% of the amount wagered in a single day on Sep 29,2013.

Expected return for investors (considering that it will stay as the last months) is going so low that I'm thinking about divesting. I really love Dooglus' idea, but I don't get why the website isn't advertised much more (to players, of course, he doesn't need nor want more money invested).

So am I correct in understanding that if it was your website you would favor raising the max profit back to 1% in order to attract someone like Nakowa again (or Nakowa himself). You would like the possibility of cashing in big as an investor vs another big loss.

Yes, of course, as 1% still isn't risky for investors, while we could encourage more betting.

If I take the statistic of 2386BTC wagered/day it gives an expected return of 18.67%/year

A player loosing 500BTC and nice profits brought thousands more in the bankroll

Hopefully for investors, big whales will come or players will divest, players will divest if a whale will big when it is actually a better time to invest more because the whale may come back to play and the bankroll is lower

[PacoMartin]

When a player risks 1 unit at 33% for a 3x payout for example, the house is risking 2 units for a 1.5x payout with a 67% chance of winning. If you apply the Kelly Criterion on those numbers you'll see that it's still optimal to risk 1% of the bank.

f = (bp - q) / b

where f is the fraction to risk,
b is the payout multiplier minus 1
p is the probability of the house winning
q is the probability of the house losing

So your saying these are the optimum bets for the player, and not the house?
edge   1%
1-'edge'   99%

b	1	2	0.5
p	49.5%	33.0%	66.0%
q	50.5%	67.0%	34.0%
q/b	50.5%	33.5%	68.0%
f	-1.0%	-0.5%	-2.0%

[dooglus]

When a player risks 1 unit at 33% for a 3x payout for example, the house is risking 2 units for a 1.5x payout with a 67% chance of winning. If you apply the Kelly Criterion on those numbers you'll see that it's still optimal to risk 1% of the bank.

f = (bp - q) / b

where f is the fraction to risk,
b is the payout multiplier minus 1
p is the probability of the house winning
q is the probability of the house losing

So your saying these are the optimum bets for the player, and not the house?
edge   1%
1-'edge'   99%

b	1	2	0.5
p	49.5%	33.0%	66.0%
q	50.5%	67.0%	34.0%
q/b	50.5%	33.5%	68.0%
f	-1.0%	-0.5%	-2.0%

Yes.  You need to consider how much the house should risk, considering the odds the house is getting.

That is different than considering how much the player should risk, considering their odds.

It's not symmetrical, which is somewhat counter-intuitive.

[PacoMartin]

Did you see this log I made of his chat and his bets?

So he was set to transfer it out, and then he said "ouch"?

[PacoMartin]

If I take the statistic of 2386BTC wagered/day it gives an expected return of 18.67%/year
A player loosing 500BTC and nice profits brought thousands more in the bankroll
Hopefully for investors, big whales will come or players will divest, players will divest if a whale will big when it is actually a better time to invest more because the whale may come back to play and the bankroll is lower

That sounds almost correct. The value 2386*.9%=21.5 BTC per day. Seems like 15.7% of 50K BTC.

My suggestion was to filter out all the bets in the first few months, and look for ones that profit was over 0.5% where the odds of winning were 49.5% or better (rule out the jackpot bets). If it turns out there is only a dozen, and they were all Nakowa. You could list the ones he lost and the ones he won.

So rather than go back up to 1% of Bank to entice a whale, just point out that Nakowa won 10,000 BTC and only broke the current rules a limited number of times. It could be all the motivation that will make a whale want to play.

Right now, he has a blog of Nakowa crying that they changed the rules on him mid-play and that is dishonest.

[maqifrnswa]

When a player risks 1 unit at 33% for a 3x payout for example, the house is risking 2 units for a 1.5x payout with a 67% chance of winning. If you apply the Kelly Criterion on those numbers you'll see that it's still optimal to risk 1% of the bank.

f = (bp - q) / b

where f is the fraction to risk,
b is the payout multiplier minus 1
p is the probability of the house winning
q is the probability of the house losing

So your saying these are the optimum bets for the player, and not the house?
edge   1%
1-'edge'   99%

b	1	2	0.5
p	49.5%	33.0%	66.0%
q	50.5%	67.0%	34.0%
q/b	50.5%	33.5%	68.0%
f	-1.0%	-0.5%	-2.0%

Yes.  You need to consider how much the house should risk, considering the odds the house is getting.

That is different than considering how much the player should risk, considering their odds.

It's not symmetrical, which is somewhat counter-intuitive.

Kelly criterion says that no players should ever play just-dice, nor should they go to vegas (except blackjack if you card count). However, Kelly criterion says casinos and Doog should allow players to play.

[dooglus]

Did you see this log I made of his chat and his bets?

So he was set to transfer it out, and then he said "ouch"?

There's a 2 hour gap after he asked for the coins to be sent back to him in which I did so and then he put them back into the gambling account again.

He moved the coins around a few times I think.

[PacoMartin]

f = (bp - q) / b

where f is the fraction to risk,
b is the payout multiplier minus 1
p is the probability of the house winning
q is the probability of the house losing

Yes.  You need to consider how much the house should risk, considering the odds the house is getting.
That is different than considering how much the player should risk, considering their odds.
It's not symmetrical, which is somewhat counter-intuitive.

So we have to make the transformation
p(house)=q(player)
q(house)=p(player)
b(house)=1/b(player)
which implies
f(house)==house edge

But for a player it is more optimal to wager at 3X payout instead of 2X payout.

---------------------
So if average play in bitcoin was 5X higher for your first 90 days vs your last 120 days, do you consider them about equal since bitcoin is now worth 5X more in dollars?

So daily play is just over a million dollars, which is what it was when you started.

Profit	Days	Average US$millions per day
1.00%	90	$1.11
1.00%	8	$14.75
0.25%	3	$3.23
0.50%	14	$15.87
0.50%	128	$3.95
0.50%	120	$1.27

                        

MaxProf	Days	Average	Minimum	Maximum	Sum
1.00%	90	11,722	644	124,771	1,055,016
1.00%	8	119,543	4,755	384,966	956,346
0.25%	3	25,741	15,904	33,064	77,223
0.50%	14	125,812	7,485	1,553,358	2,061,576
0.50%	128	6,782	1,448	70,669	868,111
0.50%	120	2,386	691	5,756	286,325

11% a year is a good return, but the risks involved in investing in a site like JD are absolutely huge.
Being realistic the stock market should return 7%, maybe more on average,

(like I said, personally I trust him, but after what has happened at other Dice sites people should be wary)

I guess I don't really see that. It's been 8 months since the last really high variation, and there has been a steady amount of return, on bitcoins which have increased in value against USD by 500%.

For a few weeks there, wagering was more than twice the value of the bank in a day. But don't forget that if someone tries it again, they could lose next time creating a bonanza for the investors.

Biggest Wagering Days since October 12, 2013
Fri, Nov 15, 13   70,669 BTC
Tue, Jan 7, 14   29,185
Fri, Feb 14, 14   25,835
Sun, Jan 26, 14   25,306
Sat, Dec 14, 13   24,720
Tue, Jan 21, 14   24,156
Sat, Jan 25, 14   15,531

[blizeH]

The wagered per day hasn't broke 10k for months now, crazy looking back that it was at one point a regular occurrence

[jarlelin]

Is there any good way I can easily find the wagered per day stats? Historical and up-to-date?

[eltopo]

Is there any good way I can easily find the wagered per day stats? Historical and up-to-date?

https://bitcoinproject.net/justdice.php

[PacoMartin]

The wagered per day hasn't broke 10k for months now, crazy looking back that it was at one point a regular occurrence

Yes, in my summary table the peak 5,756BTC in the last 120 days. It broke 10K only 16 days out of the last 250.

There is no question that wagering has calmed down, but expressed in millions of USD per day, it still is averaging about the same as the first 90 days.


Sometimes casinos get calm.

That one peak day in September averaged over 1000BTC per second for a 24 hour day.
When wagering was averaging $15-$16 million per day (nearly twice the value of the Bank) then you are going to get variance. If you think about what was wagered Nakowa winning 10K BTC or ($1.25 million at the time) is not particularly shocking.

Profit	Days	Average US$millions	MAX US$millions
1.00%	90	$1.11	$11.34
1.00%	8	$14.75	$47.37
0.25%	3	$3.23	$4.16
0.50%	14	$15.87	$197.93
0.50%	128	$3.95	$29.51
0.50%	120	$1.27	$3.77

                                                

This table convinces me that it would be a grave error to up the MaxProfit back to 1% to stimulate whales. There was a huge amount of play for a 14 day period at 0.5%.

[21pilot]

maybe there is a simple explanation for the decreasing turnover at just-dice.
In the northern hemisphere it´s summer and that means people spend more time away from their computers
and are busy with other stuff.

The same phenomenon also happens in other gambling markets (simply look at the player pools
of the biggest poker networks on pokerscout.com ...).

[PacoMartin]

maybe there is a simple explanation for the decreasing turnover at just-dice.
In the northern hemisphere it´s summer and that means people spend more time away from their computers
and are busy with other stuff.

Possibly, but it was pretty calm over the winter though. But if it's still averaging over $1.2 million per day, that is not much different than the first 90 days. The bank has over 51K BTC and the rate of return is decent.

I look at all these work pools throwing away hundreds of dollars every week on powerball, lured by the promise of multimillion dollar payoffs. I think they would be better off at JD playing 500:1 odds for $150K, and not having the lottery soaking them with a 50% house edge.

[dooglus]

Is there any good way I can easily find the wagered per day stats? Historical and up-to-date?

Yes, go to JD, click on 'stats' and then 'wagered per day'. 

[dooglus]

That one peak day in September averaged over 1000BTC per second for a 24 hour day.

That sounds very unlikely.  With a max bet of 500 BTC that's 2 bets per second for 24 hours.

I don't think he was playing that long, or that fast, or that large.

>>> 1553357.82296363 / 24 / 60 / 60
17.978678506523497

That's 18 BTC per second, which while still crazy sounds more plausible.

Edit: maybe you meant $1000 per second?

[dooglus]

maybe there is a simple explanation for the decreasing turnover at just-dice.
In the northern hemisphere it´s summer and that means people spend more time away from their computers
and are busy with other stuff.

I think the simplest explanation is that there are a limited number of people who:

a) have a lot of Bitcoins
b) are willing to risk them on a gambling site
c) know about Just-Dice

Most of those people already lost their coins.

In the early days we had a number of people who came to the site to bankroll it and who ended up gambling instead. It's a kind of natural selection that the people who held on to their coins are the people who are able to resist that temptation; the strongest survived and are less willing to take risks with their share of the bankroll.

We still get some who do it, but less than we used to.

[PacoMartin]

That sounds very unlikely.  With a max bet of 500 BTC that's 2 bets per second for 24 hours.

Mea Culpa
That one peak day in September averaged over 1000 BTC per MINUTE for a 24 hour day.