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

[dooglus]

So say there are two investors.  Investor A has invested 100 BTC. Investor B has invested 100 BTC also.

Right now the max profit is set to 0.5%.

If someone bets 0.1btc at 49.5%
Then they both are able to gain 0.05 btc. (or lose)

Now you implement your method.  Investor B decides to risk 1% instead.

So now if someone bets 0.1 btc,
Investor A can win ±.33 and investor B can win ±.67.

This doesn't seem fair.  Investor A is still okay with betting at this risk level.  Why does investor B take some of his bet?

Here's another analogy:

--
A and B both invest 100 BTC.  Someone wants to bet 0.1 BTC.  Both investors stand to gain 0.05 BTC.

Now investor B decides to double his risk by investing another 100 BTC.

So now if someone bets 0.1 btc,
Investor A can win ±.33 and investor B can win ±.67.

This doesn't seem fair.  Investor A is still okay with betting at this risk level.  Why does investor B take some of his bet?
--

In both cases investor B has doubled his risk, and as a result 'takes' some of investor A's action.  In both cases he has diluted the other investor's share by risking more.  In your analogy he did it by doubling his Kelly factor, and in mine he did it by doubling his investment.  In both cases he's doubling his exposure, and so doubles his reward.

[Peter R]

How many repeat bets does it it take to push a gambler's +1 sigma line negative?

It takes 4 X longer for a gambler's +1 sigma line to go negative at 1% than at 2% house edge.

What does that mean, a sigma line going negative?

I mean the curve 1 standard deviation above his expected profits.  Until this curve goes negative, it is really not that surprising at all for the gambler to keep popping up into profits.

If I remember correctly he took around 15,000 bets according to dooglus in the chat. In such case that is above the 9,999 bets you state, so in the negative curve line as you say. How high is the chance for that to happen according to your estimations/calculations?

Thanks for the question RationalSpeculator.  To calculate properly, we need an updated list of all Nakowa's bets (a new nakowa.txt file from dooglus).  Nakowa makes a mix of small and big bets, and we need to know the distribution to calculate the various "sigma lines" properly.  I intend to update my probability chart when I get the new data:



I bet that by now Nakowa is close to the "green zone."

Cheers,
Peter

[dooglus]

This is my proposal (same as before)
1) if bets are lower than the lowest percentile than everyone gets an equal piece of the pie based on holdings
2) if bets is between percentiles of the max profit then the lowest percentiles will risk as much as they can, then the remaining holders will split risk among themselves based on holdings.
3) if bets are the max profit then everyone invests there max risk
4)highRisk investors DO get higher profit share.  As you can see the high risk investor gets more action.

This method is exactly like what is implemented now.  Except for the fact that high risk investors increase the max profit even higher, and they will get profit off of this higher risk.

Suppose 99 investors invest 1 BTC each with 0.99% risk and one brave investor invests 1 BTC at 1% risk.

The 1% (highest risk) investor gets only 1% of all bets, except for the most dangerous max profit bets, of which he gets 100%.

So by being the only investor willing to risk the fully Kelly, he gets to experience very high variance because the lower risk investors take an unfair share of all the sub-max profit bets.

That's the problem with your proposal for me, Chris.

[integrity42]

Just an FYI, nakowa nearly bust today. He was down to just around 1,000 BTC left, and then went on to win another 8,000

[willphase]

Suppose 99 investors invest 1 BTC each with 0.99% risk and one brave investor invests 1 BTC at 1% risk.

The 1% (highest risk) investor gets only 1% of all bets, except for the most dangerous max profit bets, of which he gets 100%.

So by being the only investor willing to risk the fully Kelly, he gets to experience very high variance because the lower risk investors take an unfair share of all the sub-max profit bets.

That's the problem with your proposal for me, Chris.

but this higher risk investor also gets the profit when a whale comes in and loses.

I just don't see the point of implementing the simple fractional kelly system when you can get the same thing from just investing less.

Will

[mechs]

Suppose 99 investors invest 1 BTC each with 0.99% risk and one brave investor invests 1 BTC at 1% risk.

The 1% (highest risk) investor gets only 1% of all bets, except for the most dangerous max profit bets, of which he gets 100%.

So by being the only investor willing to risk the fully Kelly, he gets to experience very high variance because the lower risk investors take an unfair share of all the sub-max profit bets.

That's the problem with your proposal for me, Chris.

but this higher risk investor also gets the profit when a whale comes in and loses.

I just don't see the point of implementing the simple fractional kelly system when you can get the same thing from just investing less.

Will

I agree, it will make things worse and more complicated, not better.  Just stay at 0.5%, we are getting more than enough variance with that judging by today;s swings between +6000 profits and -5000 loss ending at -3100

[chriswen]

This is my proposal (same as before)
1) if bets are lower than the lowest percentile than everyone gets an equal piece of the pie based on holdings
2) if bets is between percentiles of the max profit then the lowest percentiles will risk as much as they can, then the remaining holders will split risk among themselves based on holdings.
3) if bets are the max profit then everyone invests there max risk
4)highRisk investors DO get higher profit share.  As you can see the high risk investor gets more action.

This method is exactly like what is implemented now.  Except for the fact that high risk investors increase the max profit even higher, and they will get profit off of this higher risk.

Suppose 99 investors invest 1 BTC each with 0.99% risk and one brave investor invests 1 BTC at 1% risk.

The 1% (highest risk) investor gets only 1% of all bets, except for the most dangerous max profit bets, of which he gets 100%.

So by being the only investor willing to risk the fully Kelly, he gets to experience very high variance because the lower risk investors take an unfair share of all the sub-max profit bets.

That's the problem with your proposal for me, Chris.

I must have explained what I meant wrong.  This is what I'm trying to say.

99 investors invest 1 BTC with 0.99% risk.  1 investor invest 1 BTC at 1% risk.

Max profit = 0.9901 = 99*1*.0099 + 1*1*0.01

What you're mistaking is what happens for the max profit bets.

For the low profit bets the higher risk investor gets only 1% of all bets, this is what is happening now.
-if bet <= 0.99 (100*.0099) the risky person gets 1% share (this is what happens now)

For bigger bets let's say a bet of 0.9901
Each small investor gets 0.0099 BTC (.99% of their bankroll, 0.999899% of the bet) All low risk investors now get only 98.99% of bet
The risky investor gets to risk 0.01 BTC (1% of his bankroll, 1.001% of the bet) (not 100%)

So by being the only investor willing to risk the full Kelly he gets to experience more variance on bigger bets.

And just because he is willing to risk a bit more to extend the bankroll doesn't mean he gets to take an unfair share of the sub-max profit bets.

[dooglus]

No link, apparently nakowa at one point told dooglus that. I heard it in chat.

This puts his lower bound at 10,000 and his potential higher bound at 100,000.

Also he was into bitcoin 2011 or 2010 so he is an early adopter and could have acquired that many.

It's something he told me via IM when he first invested:

Wed 26th June 2013
(10:10:57 PM) squiggles: btw, this investment is not from me, [redacted], in fact, I myself have more than 6 digits of bitcoin, it’s pointless for me to earn more coins.

[willphase]

I haven't been keeping up with all the proposals but FWIW I'm interested in being able to set my personal max bet e.g. 0.1% of bankroll - any bets below this, I get action on, any bets above, I get neither profit nor loss.

I don't think this is unfair on those people willing to risk more (e.g. full 1% kelly) because they get all the profits when a whale comes in and loses big.  I just look at the times when there are no whales playing and I guess that maybe there's around 5,000 BTC a day being bet below 0.1% of bankroll (below 3BTC) - aside: I wish I had numbers on this! - and I"m happy with 50 BTC profit a day split across investors - that still works out more than any other interest I can earn anywhere else.

Will

[dooglus]

There's absolutely NOTHING that indicates he is cheating. The wild swings he is experiencing looks 100% legit. Look at how he plays, its just a completely random walk.

Here's a chart of the site's profits for the day, with the expected profit (minus 20k, to bring them closer together!) overlayed.

The random walk goes horizontally, whereas the expectation goes up at 30 degrees to the horizontal.  How?  And why?

[chriswen]

I haven't been keeping up with all the proposals but FWIW I'm interested in being able to set my personal max bet e.g. 0.1% of bankroll - any bets below this, I get action on, any bets above, I get neither profit nor loss.

I don't think this is unfair on those people willing to risk more (e.g. full 1% kelly) because they get all the profits when a whale comes in and loses big.  I just look at the times when there are no whales playing and I guess that maybe there's around 5,000 BTC a day being bet below 0.1% of bankroll (below 3BTC) - aside: I wish I had numbers on this! - and I"m happy with 50 BTC profit a day split across investors - that still works out more than any other interest I can earn anywhere else.

Will

Except for the fact that your investment doesn't increase the max profit.  All you do is help decrease the variance of low bets for other high risk investors.  And that is not needed.

[nrd525]

Contrary to common wisdom, if you increased the bet limit you would attract more people to the website and it is possible that one or more whale is motivated by the idea of winning your bankroll.

I know I'm more interested in just-dice because of the risks involved.

The downside is that you could lose your bankroll, but with the massive publicity from this a new bankroll could be built up and you might well do better in the longterm as you'd attract a lot of betters.

[jonitas]

What does the chart of the entire life of the site now looks like Doog?

[dooglus]

Ok...
eventually, after many bets, the number of times he guess HI or LO will (not including the rolls between 49.5 and 50.5) will converge to exactly 50%.   However, the losses on rolls between 49.5 and 50.5 will be permanently lost.

His stats from this session:

user 161188 -- wagered: 1482007.05642997; bets: 15360; balance: 9614.07834057; profit: 1163.78674773; losses: 7689; wins: 7671

And in detail:

mysql> select count(*), sign(profit), chance/1e4 from bets where uid = 161188 group by chance, sign(profit) order by chance;
+----------+--------------+------------+
| count(*) | sign(profit) | chance/1e4 |
+----------+--------------+------------+
|        2 |           -1 |       48.5 |
|        3 |            1 |       48.5 |
|     7686 |           -1 |       49.5 |
|        1 |            0 |       49.5 |
|     7661 |            1 |       49.5 |
|        4 |            1 |       50.5 |
|        3 |            1 |      98.99 |
+----------+--------------+------------+
7 rows in set (0.06 sec)

mysql> select 100 * 7661 / (7661 + 7686 + 1);
+--------------------------------+
| 100 * 7661 / (7661 + 7686 + 1) |
+--------------------------------+
|                        49.9153 |
+--------------------------------+
1 row in set (0.00 sec)

49.9153% of his "49.5%" bets won.  There was a single bet of 0 BTC, which lost:

bet #143904532: 0 BTC @ 49.5% hi: lucky:168905 profit:0.00000000

[chriswen]

Contrary to common wisdom, if you increased the bet limit you would attract more people to the website and it is possible that one or more whale is motivated by the idea of winning your bankroll.

I know I'm more interested in just-dice because of the risks involved.

The downside is that you could lose your bankroll, but with the massive publicity from this a new bankroll could be built up and you might well do better in the longterm as you'd attract a lot of betters.

Yeah, but I don't really care if a new bankroll is built up.  I'd rather keep the interests of the bitcoins I have invested right now.

And if you weren't online today, the max profit is at 0.5% and variance was very chaotic.

[Peter R]

There's absolutely NOTHING that indicates he is cheating. The wild swings he is experiencing looks 100% legit. Look at how he plays, its just a completely random walk.

Here's a chart of the site's profits for the day, with the expected profit (minus 20k, to bring them closer together!) overlayed.

The random walk goes horizontally, whereas the expectation goes up at 30 degrees to the horizontal.  How?  And why?

Hi doog, if you also plot the curves 1 standard deviation above and below your green expectation line, then perhaps it will show that what happened today was not that unlikely after all.

I think you can calculate variance of the i_th bet as

     V_i = B_i^2 (1-E)^2 (1-p_i) / p_i

where B = bet size, E = house edge and p = chance of win. 

The accumulated variance up to bet N is then

     V_total_N = V_0 + V_1 + ... + V_N

The standard deviation at bet N is then

     stdev at bet # N = Sqrt(V_total_N).

Cheers,
Peter



 

[dooglus]

This is a great day for investors, as the number of max bets grows, the variance decreases.... we're seeing nak doing thousands of bets at 171... i doubt we'll see -5000 again.

at the same time, 3 whales are playing.

enhpad (43175)
berathea (161188)
FFs Ownz (105829)

All making large bets

Lifetime charts for each account:

[nrd525]

I haven't read this whole thread, but has anyone considered the impact of both investing and betting?  Eg. if the whale had 90% of the bankroll, the bet limit would essentially be 5% (0.5%) or 10% (1%) of the real bank roll.

[dooglus]

Is it true FF Ownz went from 4 BTC all the way to 2000 BTC??

Not really.  I think he deposited 50 BTC, lost it all, deposited another 50 BTC, lost 46 BTC, then took the remaining 4 BTC balance up from there.  There were lots of withdrawals and deposits along the way.  I think the "from 4 BTC" rumour started from the fact that his balance was 4 BTC at one time.

[theskillzdatklls]

Doog:

Is it possible to get a lifetime graph of AIEV vs Actual rather than just the one day?  That would be interesting to look at.

Thanks!