I have a different concept of value to your good self, EC1, and I think I can see why DG and others might struggle with it.
I don't get the idea that if a horse has a 10% chance of winning a race it means that if the race is run ten times it will one of those runnings, to me that is counter-intuitive. At this time of year it's hard to imagine wide margin winners being overturned if the race is run again, I don't see it as equivalent to rolling dice.
Sure, luck in running is needed, horses get baulked, boxed in, intimidated and all the rest of it. Over jumps there can be falls, mid-air collisions, horses falling in front of you, etc. So it's true that in many races the best horse on the day doesn't win because of some misfortune, but barring accidents in most races at this time of year the margins are not very fine and there is a clear cut winner.
To me the uncertainty derives from what Slim would describe as 'guessing'. Evaluating form and estimating a horse's chances requires the use of assumptions which may be right or wrong. Will the horse improve, will the race be run to suit, will it go on the ground?
For these reasons I tend to regard percentage chance mainly in terms of degree of confidence that I've identified the most likely winner and the size of the margin it appears to hold over its opposition. From this I have an idea of the odds I will be prepared to accept, having built in an added margin to allow for luck in running.
If I don't like the odds I will let it pass, but I would find it very hard to go and back another horse in the race to beat what I consider to be the most likely winner.