Variance of coin flip how to#

even if you're being conservative nikkei type crashes happen (in many different market types, that's just an example).

Variance of coin flip how to#

it's not that simple, and most ppl who would take it have even less understanding of how to handle it. Y'all make it sound so easy to invest a million dollars without screwing it up. Your comment here that it's a subjective question is something I absolutely agree with, however I strongly disagree with your previous claim that Expected Value only has utility in the context of multiple trials is simply wrong. I thought it was pretty redundant to explicitly specify 'for me' at the end of every sentence in my previous post in a topic which is inherently about an entirely subjective and personal aspect I don't think I ever claimed it was an objective mathematical one (and attention was explicitly drawn to this through the use of emphatic quotes around correct). It's pretty obvious that what metric one uses to analyse the question is inherently going to be subjective and non-universal since the entire concept of some amount of money being life changing is subjective.

There is objectively a 'best' decision depending on the metric which you use to analyse the question that doesn't mean it's universal or every metric is going to result in the same 'best' decision. Just as one can use expected utility to claim one is correct. Just as standard deviation is an objective measure one can use to claim one is correct. The italicised is incorrect it actually explicitly is an objective measure which one can use to claim one is 'better'. I thought it was pretty clear that this was an aspect being considered given that I specifically drew attention to the fact that I one expected value is a 5000% increase over the other rather than simply being higher. 25 which I don't agree is 'particularly high' nor does it need to be stated. Lowering the guaranteed amount - that could change my mind, however.Ĭlick to shrink.Well first of all I don't agree that it leaves out a lot of info the variance of a single coin flip is pretty trivially. Also, a higher prize doesn't even matter that much, the decision would be the same for 1 bil and up. Yeah, for me the question boils down to if I'm ready to gamble a sum away. Your answer is 'the expected value is more important to me' which is totally fine, but that's not a 'correct' answer, that's just your choice. 'One option has higher expected value' is an implication, not an answer.

'Would you choose a higher expected value with high variance or a lower expected value with 0 variance?' is the question of the thread if we translated it into probability terms. And that's a purely personal subjective decision, not an objective mathematical one. The result of comparing these distributions is entirely dependent on what you decide to measure (again, 1 mil choice is infinitely better if you measure by variance). 'Means nothing' may be a bit hyperbolic but the point is that the expected value is not a singular objective measure by which we can claim that one choice is 'correct'. By choosing only one, you've made an choice that left a lot of info (variance) out of the picture. The problem with comparing theoretical expected values as mathematical characteristics of distributions is that it's not the only measure to characterize a distribution.