Sunday, January 30, 2011

2100+ Flips, Anger at Sqrt(N)



2102 samples now.

This is about the time where I start to hate the nature of random numbers. It turns out, the uncertainty of the estimate of expectation values (i.e., the mean) scales as 1/sqrt(N), where N is the number of samples one has observed. In other words, to reduce the uncertainty by a factor of two, one has to increase the number of observations by a factor of four.

Right now, we have a roughly 1% 1-sigma confidence on our sample. So, we know the odds of each prize to about 1% with a confidence of about 68%. To improve the uncertainty to 0.5%... it would take about 8000 flips total. That's about 6000 flips to go. Ouch.


Cumulative stats summary:

Total Samples: 2102
Current total prize money won: 4871 g
Current estimated fair price: 2 g 31 s 73 c


Prize (gold) CountPercentageBootstrap Error (1-sigma)
0.1 111052.81%1.09%
0.5 41819.89%0.87%
1 33115.75%0.80%
5 1929.13%0.63%
20 381.81%0.29%
50 60.29%0.12%
200 60.29%0.12%
1000 10.05%0.05%
5000 00.00%NA


Here's a plot of the distribution:




Raw data page is updated.

Tuesday, January 25, 2011

Another milestone: 2000+ flips



2002 samples now.

And yet, no 5000 gold card.

Imagine that the actual chance of getting the winning card is 1/1000. Then, the chance of me not drawing the grand prize in 2000 draws (assuming iid) is 13.52%. If the chance is 1/800, then that same percentage drops to 8.2%. I think I can now pretty safely claim that the chance of winning is smaller than 1 out of 800.

And yet, I can't stop gambling...

Cumulative stats summary:

Total Samples: 2002
Current total prize money won: 4761.6 g
Current estimated fair price: 2 g 37 s 84 c


Prize (gold) CountPercentageBootstrap Error (1-sigma)
0.1 105652.75%1.12%
0.5 39419.68%0.88%
1 31915.93%0.82%
5 1849.19%0.65%
20 361.80%0.30%
50 60.30%0.12%
200 60.30%0.12%
1000 10.05%0.05%
5000 00.00%NA


Here's a plot of the distribution:




Raw data page is updated.

Saturday, January 22, 2011

Gambling Some More



1802 samples now.


Cumulative stats summary:

Total Samples: 1802
Current total prize money won: 4571 g
Current estimated fair price: 2 g 53 s 68 c


Prize (gold) CountPercentageBootstrap Error (1-sigma)
0.1 95352.89%1.18%
0.5 35619.76%0.94%
1 27815.43%0.85%
5 1689.32%0.68%
20 341.89%0.32%
50 60.33%0.14%
200 60.33%0.14%
1000 10.06%0.06%
5000 00.00%NA


Here's a plot of the distribution:



Raw data page is updated.

Tuesday, January 18, 2011

More Flips!



1602 samples now.

Lately, I've been wondering whether there are any factors that can affect the outcome of a flip. Is every flip completely fair and independent of each other? Or does the outcome of a flip depend on, say, your location, level, gear, stats, race, etc...? Those potential sources of skew are not too worrisome though. I've been using the same character at the same level, location, and more or less the same gear.

What does worry me, though, is the potential that the outcome depends on the state of my server. Maybe there's a limit on how many 5000g that can be in game at the same time? That sort of limits, if there is one, is totally out of my control. What can I do...

Cumulative stats summary:

Total Samples: 1602
Current total prize money won: 4345.7 g
Current estimated fair price: 2 g 71 s 27 c


Prize (gold) CountPercentageBootstrap Error (1-sigma)
0.1 84752.87%1.24%
0.5 31219.48%0.98%
1 24515.29%0.90%
5 1569.74%0.74%
20 291.81%0.33%
50 60.37%0.15%
200 60.37%0.15%
1000 10.06%0.06%
5000 00.00%NA


Here's a plot of the distribution:




Raw data page is updated.

Sunday, January 16, 2011

Quick Update



1502 samples now.

I'm somewhat surprised by the fact that I haven't flipped a single 5000 gold prize yet. But, life goes on. What I am not surprised about is the fact that the cards are still selling way above their estimated fair value. Gambling is in our blood.

On a totally different note... GO BEARS! WOOT!

Cumulative stats summary:

Total Samples: 1502
Current total prize money won: 4019.6 g
Current estimated fair price: 2 g 67 s 62 c


Prize (gold) CountPercentageBootstrap Error (1-sigma)
0.1 79653.00%1.33%
0.5 29419.57%1.05%
1 22815.18%0.96%
5 1459.65%0.79%
20 271.80%0.35%
50 60.40%0.14%
200 50.33%0.16%
1000 10.07%0.07%
5000 00.00%NA


Here's a plot of the distribution:




Raw data page is updated.

Saturday, January 15, 2011

Quick Data Update



1402 samples now.

Work is exhausting...

Cumulative stats summary:

Total Samples: 1402
Current total prize money won: 3803.6 g
Current estimated fair price: 2 g 71 s 30 c


Prize (gold) CountPercentageBootstrap Error (1-sigma)
0.1 74653.21%1.33%
0.5 27219.40%1.05%
1 21315.19%0.96%
5 1369.70%0.79%
20 251.78%0.35%
50 40.29%0.14%
200 50.36%0.16%
1000 10.07%0.07%
5000 00.00%NA


Here's a plot of the distribution:



Raw data page is updated.

Tuesday, January 11, 2011

Cataclysm Bubble Crash?



1302 samples now.

I've noticed that my server's economy has taken a hit as of late. Herbs that used to see for 7g+ are now selling for a little over 4g. The Mysterious Fortune Cards are now selling for somewhere south of 30g and at times are near 20g each. Worse yet, my primary money maker, [Inferno Ink] price is also under pressure. Has the Cataclysm bubble burst?

Of course, I'm only looking at a small subset of the overall server economy. There may well be some flavor of the month that is selling like hot cake...

Cumulative stats summary:

Total Samples: 1302
Current total prize money won: 3495.1 g
Current estimated fair price: 2 g 68 s 44 c


Prize (gold) CountPercentageBootstrap Error (1-sigma)
0.1 69653.46%1.38%
0.5 24919.12%1.09%
1 19615.05%0.99%
5 1299.91%0.83%
20 231.77%0.36%
50 40.31%0.15%
200 40.31%0.15%
1000 10.08%0.08%
5000 00.00%NA


Here's a plot of the distribution:



Raw data page is updated.

Sunday, January 9, 2011

Another quick data update



1202 samples now. Gods of Warcraft were generous tonight. Three 200 gold cards. Woot!

Now, if I could just win the grand prize... grrrr...

Cumulative stats summary:

Total Samples: 1202
Current total prize money won: 3387.6 g
Current estimated fair price: 2 g 81 s 83 c


Prize (gold) CountPercentageBootstrap Error (1-sigma)
0.1 64653.74%1.44%
0.5 22818.97%1.13%
1 17914.89%1.03%
5 1189.82%0.86%
20 221.83%0.39%
50 40.33%0.17%
200 40.33%0.17%
1000 10.08%0.08%
5000 00.00%NA


Here's a plot of the distribution:



Raw data page is updated.

Saturday, January 8, 2011

Data update



1102 samples now. Another day, another new prize. This time the 200 gold card. I'm sleepy... so I'll put some more thoughts into the data another day.

Cumulative stats summary:

Total Samples: 1102
Current total prize money won: 2709.9 g
Current estimated fair price: 2 g 45 s 91 c


Prize (gold) CountPercentageBootstrap Error (1-sigma)
0.1 59954.36%1.50%
0.5 21019.06%1.18%
1 15514.07%1.05%
5 1109.98%0.91%
20 222.00%0.42%
50 40.36%0.18%
200 10.09%0.09%
1000 10.09%0.09%
5000 00.00%NA


Here's a plot of the distribution:




Raw data page is updated.

Wednesday, January 5, 2011

1000 gold fortune card!



902 samples now. I finally got an epic prize card, worth 1000 gold! After so many losing draws, I'll gladly take the second prize.

The 1000g card increased the fair value of the fortune card to a whopping... 2.5 gold or so. And people are still buying this card for 40g!

A little side note. The payout ratio of a typical US lottery is around 50%. That is, for a $1 lotto ticket, the fair price of the ticket is about 50 cents. The empirical payout ratio of [Mysterious Fortune Card] found so far (given the 40g street price) is 6.3%! Talk about getting rinsed.

Cumulative stats summary:

Total Samples: 902
Current total prize money won: 2240.5 g
Current estimated fair price: 2 g 48 s 39 c


Prize (gold) CountPercentageBootstrap Error (1-sigma)
0.1 49054.32%1.66%
0.5 17519.40%1.32%
1 12413.75%1.14%
5 889.76%0.99%
20 222.44%0.51%
50 20.22%0.16%
200 00.00%NA
1000 10.11%0.11%
5000 00.00%NA


Here's a plot of the distribution:





Raw data page is updated.

Tuesday, January 4, 2011

More data



802 samples now.

Cumulative stats summary:

Prize (gold) CountPercentageBootstrap Error (1-sigma)
0.1 43454.11%1.77%
0.5 15819.70%1.40%
1 10913.59%1.21%
5 8110.10%1.06%
20 182.24%0.53%
50 20.25%0.18%
200 00.00%NA
1000 00.00%NA
5000 00.00%NA


Here's a plot of the distribution:



Total Samples: 802
Current total prize money won: 1096.4 g
Current estimated fair price: 1 g 36 s 71 c

Raw data page is updated.

Monday, January 3, 2011

Another 50g Card!



702 samples now. Won another 50g prizes. Maybe the tide is turning?

(Don't be fooled... a human being is really good at "seeing" patterns in complete randomness)

Must... flip... more... cards...

Cumulative stats summary:

Prize (gold) CountPercentageBootstrap Error (1-sigma)
0.1 37953.99%1.88%
0.5 14120.09%1.52%
1 9413.39%1.28%
5 709.97%1.13%
20 162.28%0.56%
50 20.28%0.20%
200 00.00%NA
1000 00.00%NA
5000 00.00%NA


Pay attention to how the error estimates shrink over time. More samples = less uncertainty!

Here's a plot of the distribution:



Total Samples: 702
Current total prize money won: 972.4 g
Current estimated fair price: 1 g 38 s 52 c

I'lll be placing the raw data on its own page from now on. I didn't really want to make the main post page too long and heavy.