i assumed same probability of success (although i did not say so explicitly, since as you said it was so fucking obvious) thus the expectation is only dependent on pay-off. Downside is same in both. Upside is way bigger in SPA. Hence the expected return on SPA is much larger
But there is absolutely no justification for believing that the probabilities are the same.
You can't say 'look at the math' if you have just made up the numbers to give the correct result.
And the downside probabilities aren't the same either. There is much more likelihood than random alt-coin X will lose 90% of its value than that a mainsteam stock will.
those of use who actually make a living off of financial markets make things called models. They are simulacra that we accept from the outset are not reality. We also accept that the underlying process generating the bids/asks/trades that we observe is unknown to us and incredibly complex... but that is exactly why we use models: it reduces the dimension of the problem we are trying to solve and allows us to make meaningful conclusions to guide our decisions as profitably as possible given what we know.
the model you are taking such issue with is admittedly simplistic, but can still be used to guide our thinking in powerful ways (in trading, simple rules are usually better than incredibly complex ones, i.e. the return for every added complexity had better be gigantic to counteract the opportunity cost of implementing it)
you're missing your own point about mathematical expectation: the probabilities don't have to be equal for SPA to be a better bet, SPA can even have a
much lower probability of success if the payout is high enough. If the payout on SPA is 4x and tech is 2x, then probability of SPA success can be up to 1/2 of the tech stock and still be a better bet.
since your living under a bridge troll ass will probably point out there are many combinations that don't make SPA a better investment, you and everyone can calculate them yourself with the following formula:
P_spa = (P_tech * Payout_tech) / Payout_spa
where:
P_spa = the breakeven probability of success in SPA (ie where its equally as good an investment as the tech stock)
P_tech = the probability of success you assume in the tech stock (or really, ANY alternative investment to SPA)
Payout_x = the payout associated with each outcome
plugin youre own thoughts, combinations, and ponder. feel free to share your results ;-)
in the example above
payout_tech = 2.0 (as in 2x your initial investment, a doubling of capital)
payout_spa = 4.0
assume 50/50 in tech stock i.e. p_tech = 0.5
p_spa = ( 0.5 * 2.0 ) / 4.0 = 0.25
so as long as p_spa is > 0.25 its still a better bet than tech stock
if expectation is all your considering