Data keeps flowing in

2402 samples now.

First, I want to thank one reader, MaienM, for making a wonderful little AddOn that records the time and ItemID of my flips automatically. It's a really handy tool that makes my data gathering a lot smoother and less tiring. Thanks MaienM!

As for the data, I think I'm at a point where I have enough data to do a little more detailed analysis. I didn't want to get into too much analysis there were so few data points, as it would have been pretty much useless. I'm mostly just curious to see if some of the assumptions that we all make, like the independence of each flip, are actually supported by the data so far. Let's see what I can dig up in the next few days.

Cumulative stats summary:

Total Samples: 2402
Current total prize money won: 6155.5 g
Current estimated fair price: 2 g 56 s 27 c

Prize (gold)	Count	Percentage	Bootstrap Error (1-sigma)
0.1	1275	53.08%	1.01%
0.5	476	19.82%	0.81%
1	385	16.03%	0.75%
5	209	8.70%	0.58%
20	43	1.79%	0.27%
50	6	0.25%	0.10%
200	6	0.25%	0.10%
1000	2	0.08%	0.06%
5000	0	0.00%	NA

Here's a plot of the distribution:

Raw data page is updated.

Patch 4.0.6, New Rules to Play By?

2202 samples now.

Been very busy lately... real life can be a bitch.

In a brighter (!?) news, we finally have the arrival of patch 4.0.6. This is the first time that I've taken data since the patch. I'm really hoping that they didn't screw around with the odds of the prize cards. I have pretty much no data as of now (only 100 new data points) to make any inferences, so I'm just going to have to keep on doing what I've been doing.

Cumulative stats summary:

Total Samples: 2202
Current total prize money won: 5961.1 g
Current estimated fair price: 2 g 70 s 71 c

Noticed how winning another 1000g card only increased the fair value by 40 silver? The end is closer...

Prize (gold)	Count	Percentage	Bootstrap Error (1-sigma)
0.1	1171	53.18%	1.06%
0.5	434	19.71%	0.85%
1	347	15.76%	0.78%
5	196	8.90%	0.61%
20	40	1.82%	0.29%
50	6	0.27%	0.11%
200	6	0.27%	0.11%
1000	2	0.09%	0.06%
5000	0	0.00%	NA

Here's a plot of the distribution:

Raw data page is updated.

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.