Not really, it was mostly luck. Don't confuse my skills with a bull market. 2009 to 2024 has been one of the longest and best bull markets in history. Anyone who bet long with leverage would make a killing. Most likely won't happen again after this presidential election and I will have to try something else, perhaps day trading stocks?
Just prove it, if you can... Is time t (ie. DTE) not needed? IMO w/o t it's not possible. Or is there maybe a math trick to solve it w/o t ? I doubt. And what about r and q? Ie. the interest rate and dividend rate? Facts please, no BS talk anymore!
p > 1 is impossible I guess you rather mean "prob. of expiring ITM > 0.5" (actually meaning "prob. of expiring OTM > 0.5", ie. the rest probability). And yes, your #2 as a goal makes very well sense
For those looking for a formula: IMO, the easiest method is using the "d1" (also known as "d+"; I call it "p1") of the Black-Scholes formula. It's our famous Greek friend named "Delta"! But then the above statement of 2rosy becomes dubious to understand, b/c Delta already gets understood by many as the p for expiring ITM. Maybe 2rosy can clarify what he means. I think 2rosy just means "Look for where abs(Delta) is > 0.5", ie. take those options with abs(Delta) > 0.5. Ie. collect Premiums from options with abs(Delta) > 0.5; the higher Delta the better, b/c for it becoming ITM is the rest probability, ie. pITM = 1 - abs(Delta). abs(x) is the absolute function, ie. makes a negative number positive. B/c for Put options Delta is negative (range 0.0 to -1.0). For Call options Delta is 0.0 to +1.0. Since an options seller does not want the option become ITM, then a small pITM as possible is desirable for the seller, meaning to sell Call options with high Delta towards 1.0 (or towards -1.0 for Put options), if found any. Those options usually have a higher IV than normal...
Also deep ITM strikes (DITM) and DOTM strikes have usually a much higher IV than the ATM strike, due to the effects of volatility smile. They usually have also a higher abs(Delta) since they are much far away from ATM (ie. the current stock price).
Correction of the last statement above: DITM strikes usually have also a higher abs(Delta) (ie. > 0.5) since they are much far away from ATM (ie. the current stock price). Remember: due to Put/Call parity, it follows that Call.Delta + Put.Delta = 1.0 . Ie. DOTM strikes have a low abs(Delta), ie. less than 0.5.