Being lucky is not being rational. However it is undoubtable that winning in a lottery is mostly a positive outcome and that it requires for you to have purchased the ticket which is a decision. Something that looks only at outcomes would applaud the decision to buy the ticket (perhaps unconditionally).
The definiton of instrumental rationality is most commonly invoked when critisiing those that employ a complex methodology of choosing correctly while the methodolody can be criticed or the agent had evidence that could have been construed to be a reason to abandon the methodology. The critism "before" "instrumental rationality would focus on making an error in applicaiton of a methodology or not having any methodology at all to make the decision. The common sentiment from these can seem like "have a methodology and apply it correctly". And it seems clear that there are better and worse methodologies and one should try to apply the best available. And it seems "I had a methodology and applied it" doesn't make one to be "rational" (more like "dogmatic").
It seems one coudl have a reasonable chance of being "rational" if one had bad methodologies if one actively upswitches and upgrades their "carry on" methodology whenever they encounter new ones. It seems also that as the argument goes on the focus on metacognition increases. This can be seen also to frame the previous critisms in a new light. Its not that unmethodological decisions are "unrational" per se but doing so means likely that you missed to pick up a good methodology before that where you here could have applied to great success. So rather than "having" an methodology its more important to "pick up" methodologies with it being less essential whether you currently have or do not have a good methodology. With consistent pickups you should in the future have a great quality methodology. but rather than being the means its the effect.
Eliezer defines rationality as such:
Extrapolating from the above definition, we can conclude that an act is rational, if it causes you to achieve your goals/win. The issue with this definition is that we cannot evaluate the rationality of an act, until after observing the consequences of that action. We cannot determine if an act is rational without first carrying out the act. This is not a very useful definition, as one may want to use the rationality of an act as a guide.
Another definition of rationality is the one used in AI when talking about rational agents:
A precept sequence is basically the sequence of all perceptions the agent as had from inception to the moment of action. The above definition is useful, but I don't think it is without issue; what is rational for two different agents A and B, with the exact same goals, in the exact same circumstances differs. Suppose A intends to cross a road, and A checks both sides of the road, ensures it's clear and then attempts to cross. However, a meteorite strikes at that exact moment, and A is killed. A is not irrational for attempting to cross the road, giving that t hey did not know of the meteorite (and thus could not have accounted for it). Suppose B has more knowledge than A, and thus knows that there is substantial delay between meteor strikes in the vicinity, and then crosses after A and safely crosses. We cannot reasonably say B is more rational than A.
The above scenario doesn't break our intuitions of what is rational, but what about in other scenarios? What about the gambler who knows not of the gambler's fallacy, and believes that because the die hasn't rolled an odd number for the past n turns, that it would definitely roll odd this time (after all, the probability of not rolling odd
). Are they then rational for betting the majority of their fund on the die rolling odd? Letting what's rational depend on the knowledge of the agent involved, leads to a very broad (and possibly useless) notion of rationality. It may lead to what I call "folk rationality" (doing what you think would lead to success). Barring a few exceptions (extremes of emotion, compromised mental states, etc), most humans are folk rational. However, this folk rationality isn't what I refer to when I say "rational".
How then do we define what is rational to avoid the two issues I highlighted above?