JulianB1
Well-Known Member
Do these things get more complicated than just compound probabilities for satellites or whatever people are doing? I'm actually really intrigued.
Yeah it's actually very interesting (mathematically) and tricky, in fact I haven't fully solved it yet. I created a spreadsheet to list outcomes and the associated probabilities and expected values. There's an error somewhere because the total probability in the more complicated formulation of the game is only adding up to 99.5%, not 100%, so I'm either missing a possible outcome (an error I had yesterday but have since corrected), or I'm not calculating some of the probabilities correctly (most likely due to missing combination effects). But I'm close enough to a complete solution to answer the original question I was posed, which was whether or not there was an advantage to having 2 spots (and wagering twice as much) rather than 1. The answer (predictably) is no: the expected value of the game is always 0 since it's just money moving around a closed system. But having 2 numbers does (again, not surprisingly) increase the probabilities of various "big win" outcomes.
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