The difference here is that you're talking about a competitive zero-sum game when the difference between two PCs, one with a +1 and one without, is not. You're also setting the terms of the number of coin flips. If I had the choice of whether to continue after each flip, as a gambler would have in a casino, I might well take up the offer even with this arrangement, hoping for a streak and a chance to stop before losses caught up. That's why games with even worse payoffs for the player can still work in a casino environment.
They certainly do work -- for the casino.
The difference between the stats of two PCs is the difference between two different zero-sum
combat games. The PC with lower stats gets hit more often (lower defenses), has fewer HP, and his fight takes longer to win because he hits less often and deals less damage when he hits.
In 3.x, it's worse than that, because of the geometric nature of power by level. If your Con is 4 lower than mine at 1st level, that's only +2 HP difference. By 20th level, it's a difference of +40 HP. Now, that +2 HP is nothing to sneeze at because you have them for every single fight, but the +40 HP is staggering.
Same deal with 3.x spells. Sure, +1 to attacks and +1 (or +1.5) damage is nice, but the real power of higher stats is more high-level spell slots each of which has a higher save DC (so you're at least +2 more likely to "hit", and your spell deals more damage or imposes a worse condition than a lower-level spell could... AND you get to keep the lower-level spell just in case this one didn't work).
But at any particular snapshot in time throughout those 1000 die throws, would an observer be able to easily tell you have an edge over me based on the piles of money we've amassed? That's really what the question of statistical significance is about. What + do you have to have for the observer, looking at our money piles, to be confident he's correctly identifying which of us has the better odds of making the money.
I think you're saying that if a player has such a poor attention span that he can't recall how well a fight has gone so far, then the effect of a +1 bonus tends to be lost on him. If you're saying something else, you should re-phrase, because your scenario is irrelevant to any game I've seen.
The players aren't outside observers with anterograde amnesia. They get to watch everyone's history of success and failure play out. They can see that one guy hits on a 9 and the other guy misses on a 10.
In the end, the +1 is a nice benefit, but it's not a game breaker. Missing one or two +1s in character development compared to your peers isn't likely to make a huge difference in any particular encounter. Each +1 is likely make the difference between success and failure for only 5% of the rolls. If you happen to roll the (success number-1) a lot in a fight, then the +1 is a huge benefit. But that's not likely to happen. It's far more likely for any single roll, given 19 other numbers on the die, that the +1 has no effect whatsoever.
In my experience, players are aware of the effect of their exact bonuses 10% of the time: when they hit by one, and when they miss by one.
Here's a trick: never tell your players the AC of a monster, and see how long it takes them to figure it out amongst themselves. In my experience, it's about 2-3 rounds of attacks before they've got it. (This is a mini-game one of my players enjoys, so I got to observe this process.)
That's the exact same information as would be required to know who is
better than whom. So you've got 2-3 rounds of "statistical equality" in life before reality sets in and everyone knows how much you suck.
Cheers, -- N