Having Two Sets of Frequency Results, How Do I Check if They are Significantly Different? I modeled a game using a program and it generated two sets of data that look similar to this after iterating the game 10 million times:
A:
1100 | 5
1000 | 7
900 | 11
800 | 15
700 | 20
600 | 43
500 | 55
400 | 99
300 | 67
200 | 62

B:
1100 | 9
1000 | 24
900 | 55
800 | 99
700 | 143
600 | 90
500 | 56
400 | 43
300 | 22
200 | 15

(I know the frequencies don't add up to 10 mill, this is just a snippet)
The number on the left represents the amount of money the 'player' ended with after the iteration of the game was completed. The number on the right side represents the frequency of the money.
I was wondering what statistical test I could use to compare these two sets of data to see if they were statistically different. I have research the chi squared test, but I cannot figure out what to use for the expected value.
Any other ideas?
Tim.
 A: As written you're apparently asking about general differences in distribution rather than some specific alternative.
It depends on what kind of deviations you're most interested in identifying but with that sort of sample size even something relatively low power* like a $k\times 2$ chi-squared test would probably suffice
If you particularly care to pick up particular kinds of deviation like a higher mean, say, and less about a pattern of differences that went +,-,+,-,+,- then I'd suggest something different to that.
* (because it ignores the bin-ordering) 
Are those values on the left of each data set actual values or centers of bins?
A: I'm assuming you're interested in finding out if program A was better than program B at playing the game as measured by how much "money" it made during different runs.
For this, it would be preferable to:


*

*Use similar no. of observations from both experiments.

*Use individual values for this test as opposed to binning these and rounding off to nearest 100 units.


Using the data you've provided, if we plot this data, its frequency distribution looks like this (blue lines plot frequencies of sample B and red lines plot sample A):

Expanding the frequency distribution to individual observations (assuming the "money" value is representative of the bin) a 2 sample t-test gives this result:
        Welch Two Sample t-test

data:  sampleA and sampleB
t = -16.197, df = 785.57, p-value < 2.2e-16
alternative hypothesis: true difference in means is not equal to 0
95 percent confidence interval:
 -241.6868 -189.4358
sample estimates:
mean of x mean of y 
 452.6042  668.1655

Here, x is sample A and y is sample B.
So it appears that program B performed much better at playing the game than program A.
