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)	Count	Percentage	Bootstrap Error (1-sigma)
0.1	1110	52.81%	1.09%
0.5	418	19.89%	0.87%
1	331	15.75%	0.80%
5	192	9.13%	0.63%
20	38	1.81%	0.29%
50	6	0.29%	0.12%
200	6	0.29%	0.12%
1000	1	0.05%	0.05%
5000	0	0.00%	NA

Here's a plot of the distribution:

Raw data page is updated.

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)	Count	Percentage	Bootstrap Error (1-sigma)
0.1	1056	52.75%	1.12%
0.5	394	19.68%	0.88%
1	319	15.93%	0.82%
5	184	9.19%	0.65%
20	36	1.80%	0.30%
50	6	0.30%	0.12%
200	6	0.30%	0.12%
1000	1	0.05%	0.05%
5000	0	0.00%	NA

Here's a plot of the distribution:

Raw data page is updated.

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)	Count	Percentage	Bootstrap Error (1-sigma)
0.1	953	52.89%	1.18%
0.5	356	19.76%	0.94%
1	278	15.43%	0.85%
5	168	9.32%	0.68%
20	34	1.89%	0.32%
50	6	0.33%	0.14%
200	6	0.33%	0.14%
1000	1	0.06%	0.06%
5000	0	0.00%	NA

Here's a plot of the distribution:

Raw data page is updated.

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)	Count	Percentage	Bootstrap Error (1-sigma)
0.1	847	52.87%	1.24%
0.5	312	19.48%	0.98%
1	245	15.29%	0.90%
5	156	9.74%	0.74%
20	29	1.81%	0.33%
50	6	0.37%	0.15%
200	6	0.37%	0.15%
1000	1	0.06%	0.06%
5000	0	0.00%	NA

Here's a plot of the distribution:

Raw data page is updated.

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)	Count	Percentage	Bootstrap Error (1-sigma)
0.1	796	53.00%	1.33%
0.5	294	19.57%	1.05%
1	228	15.18%	0.96%
5	145	9.65%	0.79%
20	27	1.80%	0.35%
50	6	0.40%	0.14%
200	5	0.33%	0.16%
1000	1	0.07%	0.07%
5000	0	0.00%	NA

Here's a plot of the distribution:

Raw data page is updated.

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)	Count	Percentage	Bootstrap Error (1-sigma)
0.1	746	53.21%	1.33%
0.5	272	19.40%	1.05%
1	213	15.19%	0.96%
5	136	9.70%	0.79%
20	25	1.78%	0.35%
50	4	0.29%	0.14%
200	5	0.36%	0.16%
1000	1	0.07%	0.07%
5000	0	0.00%	NA

Here's a plot of the distribution:

Raw data page is updated.

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)	Count	Percentage	Bootstrap Error (1-sigma)
0.1	696	53.46%	1.38%
0.5	249	19.12%	1.09%
1	196	15.05%	0.99%
5	129	9.91%	0.83%
20	23	1.77%	0.36%
50	4	0.31%	0.15%
200	4	0.31%	0.15%
1000	1	0.08%	0.08%
5000	0	0.00%	NA

Here's a plot of the distribution:

Raw data page is updated.

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)	Count	Percentage	Bootstrap Error (1-sigma)
0.1	646	53.74%	1.44%
0.5	228	18.97%	1.13%
1	179	14.89%	1.03%
5	118	9.82%	0.86%
20	22	1.83%	0.39%
50	4	0.33%	0.17%
200	4	0.33%	0.17%
1000	1	0.08%	0.08%
5000	0	0.00%	NA

Here's a plot of the distribution:

Raw data page is updated.

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)	Count	Percentage	Bootstrap Error (1-sigma)
0.1	599	54.36%	1.50%
0.5	210	19.06%	1.18%
1	155	14.07%	1.05%
5	110	9.98%	0.91%
20	22	2.00%	0.42%
50	4	0.36%	0.18%
200	1	0.09%	0.09%
1000	1	0.09%	0.09%
5000	0	0.00%	NA

Here's a plot of the distribution:

Raw data page is updated.

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)	Count	Percentage	Bootstrap Error (1-sigma)
0.1	490	54.32%	1.66%
0.5	175	19.40%	1.32%
1	124	13.75%	1.14%
5	88	9.76%	0.99%
20	22	2.44%	0.51%
50	2	0.22%	0.16%
200	0	0.00%	NA
1000	1	0.11%	0.11%
5000	0	0.00%	NA

Here's a plot of the distribution:

Raw data page is updated.

More data

802 samples now.

Cumulative stats summary:

Prize (gold)	Count	Percentage	Bootstrap Error (1-sigma)
0.1	434	54.11%	1.77%
0.5	158	19.70%	1.40%
1	109	13.59%	1.21%
5	81	10.10%	1.06%
20	18	2.24%	0.53%
50	2	0.25%	0.18%
200	0	0.00%	NA
1000	0	0.00%	NA
5000	0	0.00%	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.

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)	Count	Percentage	Bootstrap Error (1-sigma)
0.1	379	53.99%	1.88%
0.5	141	20.09%	1.52%
1	94	13.39%	1.28%
5	70	9.97%	1.13%
20	16	2.28%	0.56%
50	2	0.28%	0.20%
200	0	0.00%	NA
1000	0	0.00%	NA
5000	0	0.00%	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.