Combination with best win rate. I’d love you forever if you can solve my problem

[ethan9449]

I’ll explain all the details

Basically. On excel (please see image at end of post)

I have 40 cells going left to right

From bf9 to cs9. Or whatever but it’s 40 cells in a row.

Each cell will have 9 numbers between 1 to 10. They are all missing at least 1 number between 1 to 10

An example of a cell could be 1,2,4,5,6,7,8,9,10

Another could be 1,2,4,5,6,7,8,9,10

I have that going left to right for 40 cells.

On the left of these rows I then have a

2 or a -1

A 2 represents a win. A -1 represents a loss. Ive justed use those number but it doesnt matter what

I then have these 40 cells going down roughly 180,000 rows

What I want to do is find the best number combination with the best win rate

Best win rate being the wins to losses for each possible combination

So what is a number combination? A number combination is ONE number chosen from each of the 40 cells. (remember each cell contains 9 numbers seperated by commas)

I think I worked it out and there can be trillions of possibilities to mark each row

So if there is a 2 next to the first row with all those 40 cells of numbers. All the combinations in that row get chalked up with a win. Each row would have trillions of possibilities though because it’s 9 to the power of 40

And I basically need that done over and over again down 180,000 rows


And then I want the data of maybe the top 1000 combinations with the best win rates or something like that with at least a decent ammount of occurences

Is there a workaround this?

 

[mmm4444bot]

Thanks for posting the corrected thread. Members will have additional questions because it's not clear what your math background is, what your data represents, how you determine the "best" win/loss ratios and why you're doing this. Historically, in this forum, members are not very motivated to invest effort in projects lacking a clear end goal or methodology. Similar hesitations occur in situations where it's too confusing to determine whether a project's setup or methodology is valid. There are two, common types of error: mathematical errors and errors in logic. Mathematical error is math done incorrectly, and error in logic is when correct math doesn't provide useful results (eg: underlying assumption wrong, setup incomplete).

I've provided a suggestion, at the end of this post. First, I'll comment on two of your math claims.

what is a number combination? A number combination is ONE number chosen from each of the 40 cells.

In mathematics, it's not that simple. The order in which we write numbers does not matter in a combination. (If order does matter, then it's called a permutation instead of a combination.) Additionally, combinations and permutations may be formed with or without repeats. (Instead of the word 'repeats', we also see the words 'replacements' or 'repetitions' used.)

For example, consider choosing 3 digits from the first 3 positive Integers, without repeating digits.

123 132 213 231 312 321

If those are combinations, then they all represent the same combination (i.e., there is only one combination, since order makes no difference).

If those are permutations, then they represent different permutations (i.e., there are six permutations, since order makes a difference).

When repeated digits are allowed, then there are two additional cases.

Your combinations seem to allow repeated digits, and it seems like you're treating equal digits in different cells as distinct from one another (otherwise, why set up 40 cells), yet I'm not sure that you intend either of those. For example, let's assume that each cell in a particular row contains 1. Here's one possible 40-digit combination.

1111111111111111111111111111111111111111

And, if those ones are meant to be distinct from one another, then we would have 40 such combinations (and no way to distinguish them without changing the notation).

Is that valid, in your project? Here's one reason why I ask.

Each row would have trillions of possibilities though because it’s 9 to the power of 40

With repeated digits, and treating digits in one cell as distinct from equal digits in other cells, the number of possibilities is much greater than 9^40. Each row contains 40 cells, and each cell contains 9 digits. That's a total of 360 digits from which to form 40-digit combinations with repeats. In combinatorics theory, there is a formula to count those.

[n + k – 1]! / [k! (n – 1)!]

n is the number of digits from which to choose (360), k is the number of digits in each combination (40) and symbol ! denotes factorials.

That's 17,733,036,675,953,720,251,858,044,788,974,644,413,924,343,853,806,474,060 combinations, which is nearly 120 quadrillion times larger than 9^40.

That total seems ridiculous to me, so I must be misinterpreting some thing(s). Hence, my suggestion.

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Here's my suggestion. Create a much simpler version of your spreadsheet, as an example to help members understand what you're trying to accomplish. Perhaps, the following will work (I'm not sure): two rows with four cells each, where each cell contains three of the first four positive Integers.

-1 [1,2,4] [1,2,3] [2,3,4] [1,3,4]
-2 [2,3,4] [1,3,4] [1,2,3] [1,2,4]

Next, please explain your thinking as completely as you can. That is, form the 4-digit combinations with repeats, tell us how the -1 and 2 apply and show us what you consider the "top combinations with the best win rates" to be and why. Feel free to use a version that differs from what I posted, but strive for simplicity.

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