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

[dooglus]

//Dooglus' wizardry math

I'd love to give this a real-world try! I'm lost, though, on what the multiplier we bet on is (1%?) and how much to increase (is that 2%?) on each loss.

I'm betting at 1%, and setting the stake such that if we win, we get a balance of 2k.

When we win a 1% bet, the payout is 99x, so the profit is 98x, so if our balance is B, we need to calculate the stake S such that the profit, 98S is makes our balance go to 2000, ie. profit is 2000-B.

98S = 2000-B
S = (2000-B)/98

So when balance is 1000, stake is (2000-1000)/98 = 10.204081633
When balance is 989.79591836, stake is (2000 - 989.79591836) / 98 = 10.30820491
and so on.

I listed all the stake sizes in my previous post.

[romerun]

I'm seeing a strange problem. I always have my offsite = max. Once in a while, the percentage of my investment/site can change if I do [/offsite 0, then /offsite max]. For example, a few minutes ago I had like 0.17xx, then after doing these commands, now it is 0.18xx. Looks like a bug to me.

[SebastianJu]

snip

Thats really interesting. I really would have thought that betting one time has the bigger chance because the more you bet the more you should go near the statistical chance of losing and the house advantage gets more attention. So i didnt await your results.

But sorry for being not fully clear. What i wanted to do is winning a certain amount that is fixed in each bet. Lets say 1000 clams. Each played bet would have a target to win, so a profit of 1000 clams in the settings. So when i would have 10 clams to gamble, then i could bet all 10 clams and adjust the percent chance so that i will win 1000 clams with a bet size of 10 clams. The chance to win is 0.9801%, betsize 10 clams and profit 1000.1010101. So i could win the 1000 clams with this chance and this bet.

Though i could bet 1 clams 10 times with a chance of 0.0989% and a profit of 1000.01112235 clams each time. The chance looks slightly higher though the winnable amount is 0.09 clams lower too.

So what do you think, which one has the highest chance to win the 1000 clams at the end? Does your previous calculation apply so that small bets have a small advantage? I mean in theory one then could play thousands of bets with a chance of 0.0001% each, isnt it?

[SebastianJu]

I'm seeing a strange problem. I always have my offsite = max. Once in a while, the percentage of my investment/site can change if I do [/offsite 0, then /offsite max]. For example, a few minutes ago I had like 0.17xx, then after doing these commands, now it is 0.18xx. Looks like a bug to me.

No, thats normal. When you watch your stats check the multiplier. It shows 100x when offsite max. When you win then this value goes down. When you then do offsite 0 and offsite max again then you will have 100x again and in total you have invested more. Because your base investment ist more. And you dont have 99x offsite investment anymore but 100x.

[dooglus]

I'm seeing a strange problem. I always have my offsite = max. Once in a while, the percentage of my investment/site can change if I do [/offsite 0, then /offsite max]. For example, a few minutes ago I had like 0.17xx, then after doing these commands, now it is 0.18xx. Looks like a bug to me.

When you type "/offsite max", it sets your offsite amount to 99 times the value of your current onsite amount. And leaves it there. Your onsite amount will grow and shrink 100 times faster now and your offsite amount stays the same.

If the site has a run of bad luck, your onsite amount will decrease and so your offsite amount (which remains fixed) will be more than 99 times your onsite amount. There's no way of requesting such a state - it only happens if the site loses.

When you set it to 0 and then back to 'max', you're setting it to 99 times your *new* onsite amount, which is different than it was before.

[dooglus]

Thats really interesting. I really would have thought that betting one time has the bigger chance because the more you bet the more you should go near the statistical chance of losing and the house advantage gets more attention. So i didnt await your results.

Betting once has a much higher variance, but a lower expectation. Note that both strategies have negative expectation and so as a player you want high variance. If the variance was zero, you would always lose what you expect to lose. It's only variance that lets players profit from a -EV game.

[...] So what do you think, which one has the highest chance to win the 1000 clams at the end? Does your previous calculation apply so that small bets have a small advantage? I mean in theory one then could play thousands of bets with a chance of 0.0001% each, isnt it?

OK, so you're asking whether it's safer to make a single bet of 1000 at 49.5% to profit by 1000, or to make 1000 bets of 1, each aiming to make 1000 profit? Or is each bet aiming to make 2000 profit? (1000 to keep as profit, and 1000 to cover the 1000 stakes)?

Note that if you bet 1 CLAM 1000 times, each one aiming to make a profit of 1000, and only 1 on them wins, your net profit is only 1 CLAM, since one bet profited by 1000 but the other 999 all lose 1 CLAM each. If that's the case, then the 1000 bets is more likely to be successful, because you're aiming to profit by 1 overall, whereas the single large bet is aiming to profit by 1000.

[SebastianJu]

Thats really interesting. I really would have thought that betting one time has the bigger chance because the more you bet the more you should go near the statistical chance of losing and the house advantage gets more attention. So i didnt await your results.

Betting once has a much higher variance, but a lower expectation. Note that both strategies have negative expectation and so as a player you want high variance. If the variance was zero, you would always lose what you expect to lose. It's only variance that lets players profit from a -EV game.

[...] So what do you think, which one has the highest chance to win the 1000 clams at the end? Does your previous calculation apply so that small bets have a small advantage? I mean in theory one then could play thousands of bets with a chance of 0.0001% each, isnt it?

OK, so you're asking whether it's safer to make a single bet of 1000 at 49.5% to profit by 1000, or to make 1000 bets of 1, each aiming to make 1000 profit? Or is each bet aiming to make 2000 profit? (1000 to keep as profit, and 1000 to cover the 1000 stakes)?

Note that if you bet 1 CLAM 1000 times, each one aiming to make a profit of 1000, and only 1 on them wins, your net profit is only 1 CLAM, since one bet profited by 1000 but the other 999 all lose 1 CLAM each. If that's the case, then the 1000 bets is more likely to be successful, because you're aiming to profit by 1 overall, whereas the single large bet is aiming to profit by 1000.

1000 clams to win 1000 clams doesnt make so much sense. I try to be lucky and win a bigger amount. So lets say 1000 clams is the win amount with all bets. It does not get changed regardless of the size of the bet or the lost amounts.

So when i use 1 clam as a start, its more near what i want, then i could bet 1 clam one time with a low chance. Chance to lose is huge. Though i could bet 0.1 clams 10 times or 0.01 clams 100 times. In these runs the chances are 10 time and 100 times lower. It doesnt matter that the chance to win is low, the profit of 1000 clams is never changed until the luck was exceptional or the clam is eaten away.

Is there a difference in these approaches?

[dooglus]

So when i use 1 clam as a start, its more near what i want, then i could bet 1 clam one time with a low chance. Chance to lose is huge. Though i could bet 0.1 clams 10 times or 0.01 clams 100 times. In these runs the chances are 10 time and 100 times lower. It doesnt matter that the chance to win is low, the profit of 1000 clams is never changed until the luck was exceptional or the clam is eaten away.

Is there a difference in these approaches?

OK, so let me check that I have it right:

You have 1 CLAM and want to get to 1000 CLAMs.

You can either do:

a) 1 * 1 CLAM bet at 1,000x or
b) 10 * 0.1 CLAM bet at 10,000x
c) 100 * 0.01 CLAM bet at 100,000x

If (a) wins, you end up with 1000 CLAMs. That happens with probability 0.00099

If any of (b) win, you end up with at least 1000 CLAMs. Maybe 2 or more win. You win at least once with probability 0.000989559.

If any of (c) win, you also end up with at least 1000 CLAMs. You win at least once with probability 0.000989515

So the probability of losing the whole CLAM goes up a little as you make more, smaller bets. But that is balanced by an increased chance of winning more than once.

Your expectation is the same in all 3 cases. You're risking 1 CLAM and so expect to lose 0.01 CLAMs (1%).

Here's the math for a, b, and c respectively:

>>> 1 - (1 - 0.99/1000) ** 1
0.00099

>>> 1 - (1 - 0.99/10000) ** 10
0.000989559

>>> 1 - (1 - 0.99/100000) ** 100
0.000989515

[SebastianJu]

So when i use 1 clam as a start, its more near what i want, then i could bet 1 clam one time with a low chance. Chance to lose is huge. Though i could bet 0.1 clams 10 times or 0.01 clams 100 times. In these runs the chances are 10 time and 100 times lower. It doesnt matter that the chance to win is low, the profit of 1000 clams is never changed until the luck was exceptional or the clam is eaten away.

Is there a difference in these approaches?

OK, so let me check that I have it right:

You have 1 CLAM and want to get to 1000 CLAMs.

You can either do:

a) 1 * 1 CLAM bet at 1,000x or
b) 10 * 0.1 CLAM bet at 10,000x
c) 100 * 0.01 CLAM bet at 100,000x

If (a) wins, you end up with 1000 CLAMs. That happens with probability 0.00099

If any of (b) win, you end up with at least 1000 CLAMs. Maybe 2 or more win. You win at least once with probability 0.000989559.

If any of (c) win, you also end up with at least 1000 CLAMs. You win at least once with probability 0.000989515

So the probability of losing the whole CLAM goes up a little as you make more, smaller bets. But that is balanced by an increased chance of winning more than once.

Your expectation is the same in all 3 cases. You're risking 1 CLAM and so expect to lose 0.01 CLAMs (1%).

Here's the math for a, b, and c respectively:

>>> 1 - (1 - 0.99/1000) ** 1
0.00099

>>> 1 - (1 - 0.99/10000) ** 10
0.000989559

>>> 1 - (1 - 0.99/100000) ** 100
0.000989515

So there is a slightly higher chance of winning when betting the whole 1 clam in one run instead spreading bets over more runs with lower chance? I didnt await that either.

Thanks for your explaination.

[dooglus]

So there is a slightly higher chance of winning when betting the whole 1 clam in one run instead spreading bets over more runs with lower chance? I didnt await that either.

Yes. I think it's fairly intuitive:

When you roll once, your expected payout is P1_1 * 1000 where P1_1 is the probability of winning the single roll.

When you roll ten times, your expected payout is the sum from N=1 to 10 of all the (PN_10 * N * 1000) where PN_10 is the probability of winning N of the 10 bets.

We know the expected payout is the same in both games, so:

P1_1 = sum(PN_10 * N) > sum(PN_10)

ie. the chance of winning the single roll is bigger than the chance of winning any non-zero number of the 10 rolls.

[dooglus]

I often update the "recent profit" chart, and usually keep it to just the last week or two. But for a long time now we've been struggling to stay over the 100k profit line, and so I've been letting the recent profit chart get longer and longer.

Now it is time to move on. So here's the "recent profit" chart going back a little over 6 weeks:



Posted here for the record. Now I can go back to only showing the last week or two of "recentness".

It's also been a while since I posted the weekly return figures for the 1x and 100x investor:

1x
--
Dec 12 2014     0.00%   100.00%
Dec 15 2014     3.64%   103.64%
Dec 22 2014     5.02%   108.85%
Dec 29 2014     2.09%   111.13%
Jan  5 2015     8.16%   120.20%
Jan 12 2015     5.28%   126.55%
Jan 19 2015     3.55%   131.04%
Jan 26 2015     2.10%   133.79%
Feb  2 2015     2.10%   136.60%
Feb  9 2015     1.94%   139.24%
Feb 16 2015     1.93%   141.93%         100x
Feb 23 2015     1.95%   144.70%         ----
Mar  2 2015     1.81%   147.32%         Mar  7 2015     0.00%   100.00%
Mar  9 2015     1.77%   149.93%         Mar  9 2015     0.64%   100.64%
Mar 16 2015     1.73%   152.53%         Mar 16 2015     2.53%   103.18%
Mar 23 2015     1.74%   155.18%         Mar 23 2015     4.01%   107.32%
Mar 30 2015     1.67%   157.78%         Mar 30 2015     2.06%   109.53%
Apr  6 2015     1.65%   160.38%         Apr  6 2015     2.51%   112.27%
Apr 13 2015     1.63%   162.99%         Apr 13 2015     2.48%   115.05%
Apr 20 2015     1.58%   165.57%         Apr 20 2015     1.42%   116.69%
Apr 27 2015     1.64%   168.28%         Apr 27 2015     3.43%   120.69%
May  4 2015     1.60%   170.98%         May  4 2015     0.52%   121.32%
May 11 2015     1.56%   173.65%         May 11 2015     0.94%   122.46%
May 18 2015     1.48%   176.22%         May 18 2015     0.37%   122.91%
May 25 2015     1.59%   179.03%         May 25 2015     5.65%   129.86%
Jun  1 2015     1.55%   181.81%         Jun  1 2015     4.59%   135.83%
Jun  8 2015     1.49%   184.52%         Jun  8 2015     4.12%   141.42%
Jun 15 2015     1.41%   187.13%         Jun 15 2015     2.00%   144.25%
Jun 22 2015     1.42%   189.78%         Jun 22 2015     3.48%   149.28%
Jun 29 2015     1.30%   192.24%         Jun 29 2015    -3.45%   144.13%
Jul  6 2015     1.38%   194.90%         Jul  6 2015     1.81%   146.73%
Jul 13 2015     1.33%   197.49%         Jul 13 2015     0.72%   147.79%
Jul 20 2015     1.42%   200.31%         Jul 20 2015    10.40%   163.16%
                                                                      
Jul 20 2015     0.21%   200.73%         Jul 20 2015     2.31%   166.92%

[superbit]

What is the very bottom row? Average?

[Keyser Soze]

I believe the bottom figure is a partial period (not a full week) and in this case is only part of a day. Since the weekly cutoff was the 20th, it would be the returns between the weekly cutoff and when he pulled the report.

[dooglus]

What is the very bottom row? Average?

Oh, each line other than the last is from mightnight Sunday/Monday. The last line is "right now", ie. the return so far this week. In this case I generated the report on a Monday, so the last two lines ave the same date, and the last line represents less than 24 hours.

On December 12th, CLAM was trading at 0.004 BTC, and BTC was ~$350.
Now, CLAM is at 0.01 BTC and BTC is at ~$275.

If you bought into CLAM on Dec 12th and invested at 1x on JD, your USD value will have increased by a factor of:

>>> 0.01 / 0.004 * 200.73/100 * 275/350
3.94291

about 4.

[chriswen]

Yeah price has actually increased even with stake inflation.

[SebastianJu]

Dooglus, can you tell how much bandwith just-dice is taking per hour when you are in the chat tab? I assume its not so much but it might pile up.

Occassionally i have to use my smartphone internet and i didnt find a way yet to measure the bandwith usage per tab in firefox.

So can you give an estimate number for hourly bandwith usage?

[dooglus]

Dooglus, can you tell how much bandwith just-dice is taking per hour when you are in the chat tab? I assume its not so much but it might pile up.

Occassionally i have to use my smartphone internet and i didnt find a way yet to measure the bandwith usage per tab in firefox.

So can you give an estimate number for hourly bandwith usage?

Great question, as always.

I just lost the whole morning trying to figure out an answer. I was hoping that the socket.io module would provide a way of keeping track of bytes sent and received, but it doesn't appear to. Even worse, I don't think it would even be able to, because the data that goes over the websocket is compressed using the 'deflate' algorithm, and that happens transparently in the browser and isn't even visible to the application level. So with some code changes I could get the site to tell you how much data it is sending and receiving per hour, but that would be the uncompressed amount, which isn't what you care about when you look at your phone bill.

I don't have a good idea at all of the bandwidth usage, which is why I was hoping to be able to tell you "just type /bandwidth and it will tell you" - but I can't. Yet. If ever.

Also I guess the bandwidth usage would vary a lot depending on how many big bets are being made, and how much people are chatting.

[itod]

Dooglus, can you tell how much bandwith just-dice is taking per hour when you are in the chat tab? I assume its not so much but it might pile up.

Occassionally i have to use my smartphone internet and i didnt find a way yet to measure the bandwith usage per tab in firefox.

So can you give an estimate number for hourly bandwith usage?

Great question, as always.

I just lost the whole morning trying to figure out an answer. I was hoping that the socket.io module would provide a way of keeping track of bytes sent and received, but it doesn't appear to. Even worse, I don't think it would even be able to, because the data that goes over the websocket is compressed using the 'deflate' algorithm, and that happens transparently in the browser and isn't even visible to the application level. So with some code changes I could get the site to tell you how much data it is sending and receiving per hour, but that would be the uncompressed amount, which isn't what you care about when you look at your phone bill.

I don't have a good idea at all of the bandwidth usage, which is why I was hoping to be able to tell you "just type /bandwidth and it will tell you" - but I can't. Yet. If ever.

Also I guess the bandwidth usage would vary a lot depending on how many big bets are being made, and how much people are chatting.

Probably the keyword in the question is "estimate". Can you use that same "deflate" algorithm to compress 1MB of chat log? That precision would be more than enough IMHO.

[dooglus]

Updated week-by-week profit stats, for a 1x investor and a 99x investor:

1x
--
Dec 12 2014     0.00%   100.00%
Dec 15 2014     3.64%   103.64%
Dec 22 2014     5.02%   108.85%
Dec 29 2014     2.09%   111.13%
Jan  5 2015     8.16%   120.20%
Jan 12 2015     5.28%   126.55%
Jan 19 2015     3.55%   131.04%
Jan 26 2015     2.10%   133.79%
Feb  2 2015     2.10%   136.60%
Feb  9 2015     1.94%   139.24%
Feb 16 2015     1.93%   141.93%         99x
Feb 23 2015     1.95%   144.70%         ---
Mar  2 2015     1.81%   147.32%         Mar  7 2015     0.00%   100.00%
Mar  9 2015     1.77%   149.93%         Mar  9 2015     0.64%   100.64%
Mar 16 2015     1.73%   152.53%         Mar 16 2015     2.53%   103.18%
Mar 23 2015     1.74%   155.18%         Mar 23 2015     4.01%   107.32%
Mar 30 2015     1.67%   157.78%         Mar 30 2015     2.06%   109.53%
Apr  6 2015     1.65%   160.38%         Apr  6 2015     2.51%   112.27%
Apr 13 2015     1.63%   162.99%         Apr 13 2015     2.48%   115.05%
Apr 20 2015     1.58%   165.57%         Apr 20 2015     1.42%   116.69%
Apr 27 2015     1.64%   168.28%         Apr 27 2015     3.43%   120.69%
May  4 2015     1.60%   170.98%         May  4 2015     0.52%   121.32%
May 11 2015     1.56%   173.65%         May 11 2015     0.94%   122.46%
May 18 2015     1.48%   176.22%         May 18 2015     0.37%   122.91%
May 25 2015     1.59%   179.03%         May 25 2015     5.65%   129.86%
Jun  1 2015     1.55%   181.81%         Jun  1 2015     4.59%   135.83%
Jun  8 2015     1.49%   184.52%         Jun  8 2015     4.12%   141.42%
Jun 15 2015     1.41%   187.13%         Jun 15 2015     2.00%   144.25%
Jun 22 2015     1.42%   189.78%         Jun 22 2015     3.48%   149.28%
Jun 29 2015     1.30%   192.24%         Jun 29 2015    -3.45%   144.13%
Jul  6 2015     1.38%   194.90%         Jul  6 2015     1.81%   146.73%
Jul 13 2015     1.33%   197.49%         Jul 13 2015     0.72%   147.79%
Jul 20 2015     1.42%   200.31%         Jul 20 2015    10.40%   163.16%
Jul 27 2015     1.30%   202.90%         Jul 27 2015     3.62%   169.07%
Aug  3 2015     1.26%   205.45%         Aug  3 2015     2.59%   173.44%

Aug  8 2015     1.03%   207.57%         Aug  8 2015     2.17%   177.21%

The 2nd column is the weekly profit, and the 3rd column is the cumulative return.

[Enzyme]

Updated week-by-week profit stats, for a 1x investor and a 99x investor:

1x
--
Dec 12 2014     0.00%   100.00%
Dec 15 2014     3.64%   103.64%
Dec 22 2014     5.02%   108.85%
Dec 29 2014     2.09%   111.13%
Jan  5 2015     8.16%   120.20%
Jan 12 2015     5.28%   126.55%
Jan 19 2015     3.55%   131.04%
Jan 26 2015     2.10%   133.79%
Feb  2 2015     2.10%   136.60%
Feb  9 2015     1.94%   139.24%
Feb 16 2015     1.93%   141.93%         99x
Feb 23 2015     1.95%   144.70%         ---
Mar  2 2015     1.81%   147.32%         Mar  7 2015     0.00%   100.00%
Mar  9 2015     1.77%   149.93%         Mar  9 2015     0.64%   100.64%
Mar 16 2015     1.73%   152.53%         Mar 16 2015     2.53%   103.18%
Mar 23 2015     1.74%   155.18%         Mar 23 2015     4.01%   107.32%
Mar 30 2015     1.67%   157.78%         Mar 30 2015     2.06%   109.53%
Apr  6 2015     1.65%   160.38%         Apr  6 2015     2.51%   112.27%
Apr 13 2015     1.63%   162.99%         Apr 13 2015     2.48%   115.05%
Apr 20 2015     1.58%   165.57%         Apr 20 2015     1.42%   116.69%
Apr 27 2015     1.64%   168.28%         Apr 27 2015     3.43%   120.69%
May  4 2015     1.60%   170.98%         May  4 2015     0.52%   121.32%
May 11 2015     1.56%   173.65%         May 11 2015     0.94%   122.46%
May 18 2015     1.48%   176.22%         May 18 2015     0.37%   122.91%
May 25 2015     1.59%   179.03%         May 25 2015     5.65%   129.86%
Jun  1 2015     1.55%   181.81%         Jun  1 2015     4.59%   135.83%
Jun  8 2015     1.49%   184.52%         Jun  8 2015     4.12%   141.42%
Jun 15 2015     1.41%   187.13%         Jun 15 2015     2.00%   144.25%
Jun 22 2015     1.42%   189.78%         Jun 22 2015     3.48%   149.28%
Jun 29 2015     1.30%   192.24%         Jun 29 2015    -3.45%   144.13%
Jul  6 2015     1.38%   194.90%         Jul  6 2015     1.81%   146.73%
Jul 13 2015     1.33%   197.49%         Jul 13 2015     0.72%   147.79%
Jul 20 2015     1.42%   200.31%         Jul 20 2015    10.40%   163.16%
Jul 27 2015     1.30%   202.90%         Jul 27 2015     3.62%   169.07%
Aug  3 2015     1.26%   205.45%         Aug  3 2015     2.59%   173.44%

Aug  8 2015     1.03%   207.57%         Aug  8 2015     2.17%   177.21%

The 2nd column is the weekly profit, and the 3rd column is the cumulative return.

Hi dooglus,

I'm thinking of investing in your website but I'm unsure about the table above.
Is 207.57% the profit, or return? If so, investing with a risk looks pretty safe lately.

Thanks