I must confess this is beyond what I remember from my school days many decades ago so I am hoping for some help.
I found an equation on-line for win rates and probabilities and added to it to get loss rates as well, that was simple enough. Ultimately I was able to get a list of probabilities such what are the odds to win or lose 2,3,4,5... times in a row.
I put this in a spreadsheet which is here. I made it publicly editable and it's just a copy so do whatever you like to it.
The equation goes like this:
Losing Odds = 1-(1-R^L)^((T-L)*(1-R)+1) . (G4 to G18 in the spreadsheet).
where:
L = Length of run of losses e.g.: 1,2,3,4,5... (E4 to E18 in the spreadsheet)
R = Lose rate e.g.: 20% etc. (C6 in the spreadsheet)
T = Tries: e.g. 100 (C4 in the spreadsheet)
What I want to do is rearrange this so I can solve L (Length of run of losses) given the rest. So in English:
If I know my losing odds to be 20 % over 100 tries then what will my length of run be at a probability of say 1% or less. I hope I worded that well but just in case my wording is muddy, the answer is obvious when looking at the spreadsheet, somewhere between 5 and 6, that being between cells E8 and E9.
With L, (the Length of the Run of Losses) being both in the normal part and the bracketed exponent part of the equation I don't really know how to rearrange this with the little I remember from my school days so help would be very much appreciated.
I found an equation on-line for win rates and probabilities and added to it to get loss rates as well, that was simple enough. Ultimately I was able to get a list of probabilities such what are the odds to win or lose 2,3,4,5... times in a row.
I put this in a spreadsheet which is here. I made it publicly editable and it's just a copy so do whatever you like to it.
The equation goes like this:
Losing Odds = 1-(1-R^L)^((T-L)*(1-R)+1) . (G4 to G18 in the spreadsheet).
where:
L = Length of run of losses e.g.: 1,2,3,4,5... (E4 to E18 in the spreadsheet)
R = Lose rate e.g.: 20% etc. (C6 in the spreadsheet)
T = Tries: e.g. 100 (C4 in the spreadsheet)
What I want to do is rearrange this so I can solve L (Length of run of losses) given the rest. So in English:
If I know my losing odds to be 20 % over 100 tries then what will my length of run be at a probability of say 1% or less. I hope I worded that well but just in case my wording is muddy, the answer is obvious when looking at the spreadsheet, somewhere between 5 and 6, that being between cells E8 and E9.
With L, (the Length of the Run of Losses) being both in the normal part and the bracketed exponent part of the equation I don't really know how to rearrange this with the little I remember from my school days so help would be very much appreciated.
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