Jud,
As I am at pains to remind people every day in my line of work, reality and a person's idea of reality are related but quite separate entities. And one much always keep in mind which is operating in a given situation.
If I step out in front of a speeding bus at lunch time, what matters at that moment is reality. It hits me or doesn't. My injuries are fatal or not. It hits me square-on or just clips my leg.
If I'm deciding whether to cross the street against the light, reality is not in play. I am not in that moment doing a decades-long scientific investigation of the probabilities associate with a bus coming or not, how fast it is moving, how good I am at dodging if it does. I am making that decision based on the version of "reality" that exists in my at that moment in time. And our personal "reality" for most things is highly unstable across varied situations.
If I'm late to a meeting, walking fast and still thinking about the presentation I just left which pissed me off by running a half-hour long I absolutely guarantee you I will assess the probability of a bus hitting me while crossing against the light as lower than if I'm killing time on my lunch hour and perfectly relaxed. It's human nature for emotional and biochemical arousal states to influence our perception of the odds of various outcomes. Unavoidable, really. Although in certain contexts people can discipline themselves to take such factors into account and not go too far astray.
The decision about putting or picking up on the last hole of a tight match is totally based on subjective "reality" perceptions. There is no information available during a speculative bull session to inform an estimate of "the right decision". The whole thing is totally dependent on factors that can only be assessed while you're standing on that green at that moment. And that's not a time when Dave Pelz is available to come do a study, any decision reached is gong to be subject to the vagaries of the mental, emotional and arousal state of the players involved.
Which is why it's perfectly sensible to stick to general principles and not engage in obviousness arguments predicated on understanding the scientific probabilities that obtain. Because they don't. A general principle that seems quite defensible for golfers is not to forgo attempting a putt which will will the match. I personally have a hard time seeing any argument against that which would be persuasive as a general principle. And I reject references to objective probability charts are irrelevant.
Jim C,
The whole point of Vegas' existence is that the games are contrived such that there is no conceivable situation in which the odds favor the player. Me and you having a putting contest is not analogous to me and you each pulling a slot machine lever.
If Dave Pelz draw a graph of the likelihood of a 15-handicapper making a first putt under such and such specified conditions, that is a post hoc description of a bunch of observations in which all manner of things are assumed to "average out". If Dave Pelz draws a graph of how likely the next coin flip is to come up heads, that is probabilistic in a way that the Dave Pelz putting data is not. The odds are exactly 50/50 with each toss, they aren't 10/90 sometimes and 80/20 other times but if you flip enough you can get an average number. There is a probabilistic component to putting but it is rather small in importance compared to the non-random factors at play. Vegas is constructed by giving the appearance that non-random factors are much more (relatively) important than they are while assuring that the probabilistic effects in fact dominate the outcome.