I soon will present the results of my research on the problem of this topic in this thread. Spoiler: all 3 probability results are correct at the same time: 88%, 66%, 53% It's about the correct interpretation of what each exactly means & describes! As said the devil is in the details...
Solution to the problem in the OP (p for CC payoff at expiration). There are at least 3 probabilities, each having a different meaning: Code: 1) pWin_BEP = 0.659665 (66%) --> R3 = 1.938281 2) pWin_BEP+Pot = 0.539563 (54%) --> R3 = 1.171849 3) pWin_BEP+Pot+Weighted = 0.882536 (88%) --> R3 = 7.513246 All 3 operate right of the Break/Even Sx point (BEP). R3 ("Reward Risk Ratio") means reward expectancy for every $1 risked. Formula: R3 = p / (1 - p). R3 replaces all the many different (and wrong) Expectancy formulas out there in the wild. Pot is the money that was on the table (depends on the # of simulation runs, but we are interested only in the percentages). The case #3 is the most advanced method, but also complicated to calculate (requires a numerical integration method). It interprets the payoff curve as "probability-weighted": payoffs near the initial S have a higher p than those further away. IMO, the R3 of it is the most realistic one. Attached also pgm output, but for experts only. Uses long lines --> use "less -Sn filename.txt" when viewing in Linux terminal.
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