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Topic: Satoshi Dice -- Statistical Analysis - page 13. (Read 192896 times)

legendary
Activity: 1806
Merit: 1090
Learning the troll avoidance button :)
Been watching this thread for a couple weeks or so now, just joined so I had the ability to post. Great job on the charts and effort put in btw! I have around 400 usd invested in Satoshi Dice, but I think the site needs to expand or it will eventually die out. The problem with betting bitcoins is many who mine them use them as investments or flat out sell them to those who use them as investments. Imo bitcoin has become too expensive of a commodity and SatoshiDice needs to branch out with other coins like LTC or FTC for example. With the lack of places to use these coins, those who mine them have a lot less worth for them and have less of a problem gambling them away. The key to a site like Satoshidice is the law of averages which basically states the more bets taken results in a percentage closer to the 1.9% profit. This is just my two cents, but I strongly believe if satoshidice either mined a base amount of altcoins or bought them, then allowed people to play with them, the coin prices would not only go up (instant advantage for satoshidice), but monthly we would see more profit. This is just my opinion, but feel free to respond to it. Grin

Fair point trading the alt currencies might produce some revenue if they live long enough Smiley Maybe go to the main satoshidice thread and add it to the suggestion box for ever to check out Smiley
full member
Activity: 156
Merit: 100
If this is life , then I prefer death !
Been watching this thread for a couple weeks or so now, just joined so I had the ability to post. Great job on the charts and effort put in btw! I have around 400 usd invested in Satoshi Dice, but I think the site needs to expand or it will eventually die out. The problem with betting bitcoins is many who mine them use them as investments or flat out sell them to those who use them as investments. Imo bitcoin has become too expensive of a commodity and SatoshiDice needs to branch out with other coins like LTC or FTC for example. With the lack of places to use these coins, those who mine them have a lot less worth for them and have less of a problem gambling them away. The key to a site like Satoshidice is the law of averages which basically states the more bets taken results in a percentage closer to the 1.9% profit. This is just my two cents, but I strongly believe if satoshidice either mined a base amount of altcoins or bought them, then allowed people to play with them, the coin prices would not only go up (instant advantage for satoshidice), but monthly we would see more profit. This is just my opinion, but feel free to respond to it. Grin
sr. member
Activity: 294
Merit: 250
This bull will try to shake you off. Hold tight!
Yes, thanks for the update Smiley

Amount of bets is accelerating the past few days.

If this continues sdice might break the record of total amount of bets done in a month. That would confirm that growth is still strong.  
legendary
Activity: 1806
Merit: 1090
Learning the troll avoidance button :)
Thanks for the effort Smiley
legendary
Activity: 2940
Merit: 1333
Recent wins making over 100 BTC profit:

Quote
Sat May 18 00:36:01 2013 <2000  236686 2c9394f2cdc85fc7:0  1BDDDQ8VhXPF11m2rDoVJXj1BgWPazEttz BET     6.00000000 WIN    185.91940800
Sat May 18 03:17:03 2013 <8000  236696 f37bdd3e26be6a6b:2  1Cp7czVeWweLwf14evirmAvtvGJvD5AEyu BET    17.00000000 WIN    119.00666400
Sat May 18 04:17:00 2013 <1000  236703 22ee1ad305de5bcf:4  1Cp7czVeWweLwf14evirmAvtvGJvD5AEyu BET     5.00000000 WIN    314.84068000
Sat May 18 05:35:13 2013 <8000  236708 f9791ea0aeaf7e28:2  1Cp7czVeWweLwf14evirmAvtvGJvD5AEyu BET    17.00000000 WIN    119.00666400
Sat May 18 13:02:44 2013 <2000  236752 22f4a5d76673e4bd:3  1BDDDQ8VhXPF11m2rDoVJXj1BgWPazEttz BET     6.00000000 WIN    185.91940800
legendary
Activity: 2940
Merit: 1333
Is that really bad news?

Only if keeps happening...  Wink  But in general I think casinos like it when players win.  It's good publicity, and they generally win it back eventually anyway.

Quote
Total of 49 bets unaccounted for.

Results: 2013-May-19 02:08pm (up to block 236968)

   Address  Target   Should Win |    #Bets |        Win        |   Lose  | Refunds |   BTC In   |  BTC Out   |  Refund  |   Profit  |   RTP 
----------------------------------------------------------------------------------------------------------------------------------------------
 1dice9wVt   64000      0.97656 |    23969 |   21643 (0.97857) |     474 |    1852 |   25549.25 |   25123.20 |   241.34 |    426.05 |  98.332
 1diceDCd2   60000      0.91553 |   147630 |  134299 (0.91574) |   12357 |     974 |   80040.59 |   78838.05 |     2.42 |   1202.53 |  98.498
 1dicegEAr   56000      0.85449 |    94484 |   80275 (0.85685) |   13411 |     798 |   85913.81 |   85139.93 |   401.34 |    773.88 |  99.099
 1dicec9k7   52000      0.79346 |    99286 |   78254 (0.79395) |   20309 |     723 |   67619.30 |   65924.91 |  1188.23 |   1694.38 |  97.494
 1dice9wcM   48000      0.73242 |   432513 |  317051 (0.73475) |  114459 |    1003 |  316410.10 |  308626.83 |  6173.32 |   7783.27 |  97.540
 1dice97EC   32768      0.50000 |   780259 |  389029 (0.49977) |  389386 |    1844 |  723346.00 |  705858.66 |  6524.01 |  17487.33 |  97.582
 1dice8EMZ   32000      0.48828 |  1302037 |  634575 (0.48814) |  665409 |    2053 |  934742.92 |  915859.73 |  2926.58 |  18883.19 |  97.980
 1dice7W2A   24000      0.36621 |   307358 |  112674 (0.36745) |  193964 |     720 |  599799.64 |  591078.71 |  1013.81 |   8720.93 |  98.546
 1dice7fUk   16000      0.24414 |   316094 |   76952 (0.24405) |  238358 |     784 |  384195.33 |  369780.11 |  2323.31 |  14415.22 |  96.248
 1dice7EYz   12000      0.18311 |   131664 |   24067 (0.18373) |  106921 |     676 |  183057.56 |  184589.80 |  3315.43 |  -1532.23 | 100.837
 1dice6YgE    8000      0.12207 |   232567 |   28512 (0.12294) |  203406 |     649 |  104620.51 |  104217.37 |   101.13 |    403.14 |  99.615
 1dice6wBx    6000      0.09155 |    62279 |    5643 (0.09143) |   56078 |     558 |   17617.03 |   19358.76 |     7.69 |  -1741.73 | 109.887
 1dice6GV5    4000      0.06104 |    40426 |    2485 (0.06212) |   37517 |     424 |    8048.51 |    7962.82 |    31.47 |     85.68 |  98.935
 1dice6gJg    3000      0.04578 |    32973 |    1505 (0.04636) |   30957 |     511 |   10215.53 |   11231.52 |    25.47 |  -1015.99 | 109.946
 1dice6DPt    2000      0.03052 |   103040 |    3130 (0.03051) |   99453 |     457 |   45474.75 |   40586.88 |     9.59 |   4887.86 |  89.251
 1dice61SN    1500      0.02289 |    27968 |     642 (0.02329) |   26925 |     401 |    8126.68 |    8715.85 |    15.23 |   -589.17 | 107.250
 1dice5wwE    1000      0.01526 |   160513 |    2465 (0.01542) |  157364 |     684 |   44387.53 |   39597.30 |     2.67 |   4790.22 |  89.208
 1dice4J1m     512      0.00781 |    41456 |     324 (0.00797) |   40335 |     797 |    8525.02 |    6965.53 |    10.36 |   1559.49 |  81.707
 1dice3jkp     256      0.00391 |    27858 |     117 (0.00427) |   27315 |     426 |    6118.23 |    8664.72 |    13.31 |  -2546.49 | 141.621
 1dice37Ee     128      0.00195 |    22864 |      42 (0.00188) |   22302 |     520 |    2450.38 |    1583.25 |    48.58 |    867.13 |  64.612
 1dice2zdo      64      0.00098 |    31524 |      35 (0.00113) |   30931 |     558 |    2211.46 |    1740.52 |   117.14 |    470.93 |  78.705
 1dice2xkj      32      0.00049 |    31002 |      13 (0.00043) |   30532 |     457 |    1682.16 |    1831.03 |     1.60 |   -148.86 | 108.850
 1dice2WmR      16      0.00024 |    25027 |       5 (0.00020) |   24529 |     493 |     889.90 |     606.68 |    22.21 |    283.22 |  68.174
 1dice2vQo       8      0.00012 |    25844 |       5 (0.00020) |   25285 |     554 |     618.29 |     433.94 |    14.66 |    184.34 |  70.185
 1dice2pxm       4      0.00006 |    15072 |       2 (0.00014) |   14534 |     536 |     216.63 |     320.41 |    18.48 |   -103.77 | 147.904
 1dice1Qf4       2      0.00003 |    13293 |       0 (0.00000) |   12708 |     585 |     182.73 |       0.50 |    28.56 |    182.23 |   0.276
 1dice1e6p       1      0.00002 |   146695 |       3 (0.00002) |  144143 |    2549 |    1866.02 |    3843.83 |   175.81 |  -1977.80 | 205.991
----------------------------------------------------------------------------------------------------------------------------------------------
           small (bets < 4 BTC) |  4549797 | 1857124           | 2670381 |   22292 |  884297.63 |  868709.20 |   347.68 |  15588.43 |  98.237
            big (bets >= 4 BTC) |   125898 |   56623           |   68981 |     294 | 2779628.36 | 2719771.76 | 24406.21 |  59856.59 |  97.847
----------------------------------------------------------------------------------------------------------------------------------------------
                                |  4675695 | 1913747           | 2739362 |   22586 | 3663925.99 | 3588480.97 | 24753.90 |  75445.02 |  97.941
----------------------------------------------------------------------------------------------------------------------------------------------

SD Profit before fees:      75445.02892822 BTC (2.059%)
Cumulative Fees Paid:        3921.12217500 BTC
SD Profit after fees:       71523.90675322 BTC (1.952%)
Pending Liabilities:           -0.21907916 BTC
Final SD Profit:            71524.12583238 BTC (1.952%)
Profit This Month:            -79.28251224 BTC
----
Since Satoshi Dice started, there have been:
Blockchain Tx: 15219484  :  SatoshiDice Tx:  8587114  (56.4%)
Blockchain MB:   6683.8  :  SatoshiDice MB:   3542.1  (53.0%)



sr. member
Activity: 294
Merit: 250
This bull will try to shake you off. Hold tight!
So what was the good news?

good news: whale is back
bad news: he's kicking our ass

Is that really bad news?

True it can destroy the dividend temporarily but at the same time the whale is raising expected profit still dramatically.

Expected profit is much more important than actual profit, as expected profit tells the true story about future profits.

The whale being back is very valuable confirmation for me that whales are not a one time event but will continue to come.

Him having temporary luck is exactly why they will continue to come back. It just feels so good Smiley and that's exactly what sdice offers. A temporary high!  
 
legendary
Activity: 2940
Merit: 1333
So what was the good news?

good news: whale is back
bad news: he's kicking our ass
sr. member
Activity: 294
Merit: 250
This bull will try to shake you off. Hold tight!

The whale seems to be back...


That is great news. Smiley

Historically this meant expected profit tripled in only 1 month. Let's see how it plays out now.
legendary
Activity: 1078
Merit: 1002
Bitcoin is new, makes sense to hodl.
whale is back
member
Activity: 74
Merit: 10

Anyway, what do you want first, the good news or the bad news?  Wink


So what was the good news?
donator
Activity: 2058
Merit: 1007
Poor impulse control.
If half the families have no girls, of the remainder less than half have one girl. Some have two or three. The median is the "midway" number, the number that has an equal number of results on either side. Since half the families have no girls,  the median number is 0.

Edit: Oh, I see what you mean. That was a dumb thing to write, eh? I'll fix it .... and fixed.

I still don't like it.  If half the families have 0 girls, and half the families have 1 or more, then isn't the median 0.5?  The median is half-way between the highest value in the lowest half (0) and the lowest value in the highest half (1).

The way I work it out:

The median is when the CDF = 0.5 (ie 50th percentile).

The probability of any family being complete after the next birth:

p * (1 - p)^(n + 1)

where p = prob(girl) and n = nth child


so the CDF P(X > x) will be sum[p * (1 - p)^(n + 1)] from 0 to x

Using wolfram alpha, you get p (1-p)^x-(1-p)^x+1, or 1 - (1 - p)^(x + 1).


From here you need to calculate the quantile function, and I'm going to let wolfram alpha do the heavy lifting again:

P = 1 - (1 - p)^(x + 1), So
x = log((P-1)/(p-1))/log(1-p)

In this case, we want to find the median, where P(X > x) = 0.5

log((P-1)/(p-1))/log(1-p) = log(1)/log(0.5) = 0

So the median value is zero.

However, you could still be correct. If you read wikipedia, there's a formula for the median of a geometric distribution, and a statement that if part of the result is an integer then the median is "not unique". In this case that's true, but I don't know why or what it means.
legendary
Activity: 2940
Merit: 1333
If half the families have no girls, of the remainder less than half have one girl. Some have two or three. The median is the "midway" number, the number that has an equal number of results on either side. Since half the families have no girls,  the median number is 0.

Edit: Oh, I see what you mean. That was a dumb thing to write, eh? I'll fix it .... and fixed.

I still don't like it.  If half the families have 0 girls, and half the families have 1 or more, then isn't the median 0.5?  The median is half-way between the highest value in the lowest half (0) and the lowest value in the highest half (1).
hero member
Activity: 756
Merit: 522
Good luck with your pooled baby mining.

I lolled.
donator
Activity: 2058
Merit: 1007
Poor impulse control.
there will be far more families without girls than with

Isn't it equal?

Half the families have a boy first and quit while they're ahead, and so have no girls.  The other half have a girl first, and so have a girl.


That's the mean. If half the families have no girls, of the remainder less than half have one girl. Some have two or three. The median is the "midway" number, the number that has an equal number of results on either side. Since half the families have no girls,  the median number is 0.

Edit: Oh, I see what you mean. That was a dumb thing to write, eh? I'll fix it .... and fixed.
legendary
Activity: 2940
Merit: 1333
there will be far more families without girls than with

Isn't it equal?

Half the families have a boy first and quit while they're ahead, and so have no girls.  The other half have a girl first, and so have a girl.
donator
Activity: 2058
Merit: 1007
Poor impulse control.
If anyone's still not getting the boy / girl problem, it's a Bernoulli trial, just like pooled bitcoin mining.

Think of it this way - a family keeps submitting babies until it submits a boy and the family is solved (the difference is that in pooled bitcoin mining all shares that are submitted are counted, not just the girls - so pooled bitcoin mining is a "shifted" geometric distribution).

Once you understand that, then you can estimate the various parameters of the number of girls submitted per solved family.

So, without providing proof,

p = 0.5     (a 50 - 50 chance of boy or girl per submission attempt, or to push the mining analogy way too far, baby mining difficulty = 2)

mean for girls submitted per solved family = (1-p)/p = 1

The reason that I think people might be confused is that since there will be far more families without girls than for any other number "n' of girls per family, the median girls per family is zero. (As dooglus points out below, half the families should have no girls).

median for girls submitted per solved family = ceiling(-1/log2(1-p)) - 1 = 0

and as you'd expect the variance is quite large:

variance for girls submitted per solved family = (1-p)/p^2 = 2

Good luck with your pooled baby mining.


hero member
Activity: 784
Merit: 1000
0xFB0D8D1534241423
50% of the country has one male child.
25% of the country has one male and one female child.
12.5% ... 2 females, one male
6.25% ... 3 females, one male
3.125% ... 4 females, one male
etc etc

Or you can look at it this way:

50% of the country has at least 1 girl - contributing P/2 to the girl population
25% of the country has a 2nd girl - contributing P/4 to the girl population
12.5% of the country has a 3rd girl - contributing P/8 to the girl population
...

so the total number of girls is P(1/2+1/4+1/8+ ...) = P.
Or, you can fall back to the axioms: there are n trials, and on average n/2 of them will be girls. The trial conditions are irrelevant to the probability. This is just a bit hard to grok.
newbie
Activity: 56
Merit: 0
It's going to be a bad month for dividends

Works for me. People will start panic selling as they always do and give me a chance to buy in super low Wink

Yeah true but the overall amount bet also seems to be going down. I think the site has lost quite a bit of its original popularity.
legendary
Activity: 1064
Merit: 1001
It's going to be a bad month for dividends

Works for me. People will start panic selling as they always do and give me a chance to buy in super low Wink
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