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Averaging Bernoulli Processes Averaging Bernoulli Processes

08-28-2020 , 04:34 PM
Hey guys, I'm trying to write a program to determine a gambler's luck on a standard deviation scale over time, similar to this picture here:



You'll see the player's actual performance relative to their surmised luck superimposed on itself.

I'm stuck on one part though: For a gambler that uses many different bet sizes or gambling outcomes (i.e. betting at 2:1, 5:1, 1:5 and so forth), how do you average these Bernoulli processes? Is it as simple as taking a weighted average of everything or is there something else to it?
Averaging Bernoulli Processes Quote
08-30-2020 , 05:22 PM
https://stats.stackexchange.com/ques...-probabilities

Had to do a lot of digging but found most of the answer on that link up above on the off chance anyone cares or searches this type question in the future.
Averaging Bernoulli Processes Quote
09-06-2020 , 01:27 PM
It's probably easiest to just use a variant of bootstrapping for this:

For each bet randomly choose the outcome based of p_i. Repeat this many times and then use the quantiles as your estimate.

Juk

Edit: See this thread for an example:

https://forumserver.twoplustwo.com/2...d-not-1410413/

Edit2: Pretty sure I used the same method for the "SNG luck analyser" I wrote years ago, so might be worth looking in that thread too.

Last edited by jukofyork; 09-06-2020 at 01:35 PM.
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