Question has no meaningful answer, since it depends on how strong one is, and even then on the type of position. Grandmasters can probably win most +.8 positions, and some that an enginge might rate as a much smaller edge, but many times top GMs can steer positions to ones that engines may think are significantly more than +.8, but the GMs know are not actually convertible into a win. There are specfic known positions that engines badly misevaluate, including a lot of totally closed positions. But in general, to go with your +1.5, thats generally a win for GMs or engines, unless your in a specific type of position that enginges misevaluate -- absent some type of surprise beyond the engine's search, which still happens even to top enginges running on ridiculous hardware.
How much evaluation advantage usually converts to a win in chess?
Generally you need an advantage of +1 pawn to win a game. The plan is to queen the pawn. Theoretically there are only 3 possible evaluations: =, +-, -+.
Those +/-, += essentially say: we do not know.
+/- means probably +-, but maybe =.
+= means probably =, but maybe +-
In chesssbase += is from 0.31 to 0.70, +/- is from 0.71 to 1.60 and +- starts at 1.61
For stockfish +1.50 is about 55% win / 44 % draw and 1% loss. At +2 it's about 80% winning chance
For humans it always depends on how difficult the position is.
As for me I usually minus .50 off any cpu evaluation when I am looking at my finished games in fact I have seen evaluation over 2.00 that then went to 0 and then a big plus score for the other player when looking at others finished games., its been my experience they tend to over evaluate,
For a human, Converting a advantage in the ruy lopez is VERY eazy.
Indeed eazier than for stockfish...
ArtNJ has it mostly right. The thing to remember is that the engine may evaluate the position at +5.00. but that evaluation depends on your finding a series of "only" moves in a complex position. In the same way, the engine may evaluate the position as 0.00, but only a series of "only" moves will draw, Everything else loses. So the engine evaluation often doesn't tell you what the practical chances are
Usually, how much advantage in a computer engine evaluation would generally convert to a win? For example, would +1.50 usually convert to a win for white?
Furthermore, how would you convert the evaluation advantage into standard notation? (eg what range of numbers would generally be +=, what range of numbers would generally be +/-, and what range of evaluations would generally be +-).