First, let's define 'tautology'. In logic, a tautology is a proposition that is true under all possible conditions of the variables. So, here it comes:
ExpectedValue(EV) = ProbabilityOfWin(POW) * ExpectedPayoff(EP)
But, before we get down to the real nitty-gritty, do you think it's possible to refute that proposition? If so, tell us what we've missed.
OK, then. It's pretty simple, isn't it? Just choose the bet with the maximum EV. Works in roulette, blackjack, jai-alai - you name it. Let's look at the elements of the equation:
Exactly what it says - there is NOTHING ambiguous here. You should be willing to admit that such a probability EXISTS. Post position, player abilities, partnership affinities, service advantage, hotness/coldness (and as many other factors you can think of) are all in play here. Whether you are able to CALCULATE it, however, is a totally different story.
You should be willing to admit that there IS such a value. How, or if, you are able to CALCULATE it is a totally different story. Means, medians, outliers, standard deviation, attendance, game #, 'Joe Sixpack' effects, the 'Goikostorza factor' - what else could influence the payoff? Sound familiar?
Please note that an inability to compute the two variables
accurately in no way diminishes the truth of the proposition.
So, what kind of calculations do you with these two variables? If you don't try to maximize EV, then, pray tell, what DO you do?
For simplicity, please confine the discussion to pari-mutuel Win betting, though the same concept applies to any jai-alai bet (you Texas hold'em fans can try another forum)
This is a STATISTICAL question, so "I always play 6-8" or "I always bet the hot hand", though interesting, doesn't really advance the discussion.
Anyone care to take a crack at this?