I've run a few simulator tests on a simple deck with chapel, 3 silvers, grand markets, go green when you have all/enough grand markets. The win rate drops slightly for each platinum it buys, even the first platinum. Perhaps someone can check through Jomini's maths in more detail.
The math is fairly straight-forward. The odds of getting a non-Gm in the first card is 5/14, the odds of the next card then being a non-Gm is then 4/13, so on and so forth. This means that we end up with a 120/240240 chance of drawing a straight dead 5 card hand, this simplifies down to .05%.
So what are the odds that you will draw your entire deck? Consider if the bottom card of the deck is a non-Gm, this means you have 5 cards in hand, only 4 can be non-Gm and everything else in the deck is a Gm - ergo you MUST be able to draw & play the entire deck if the bottom card is a non-Gm. So odds that the bottom card is not a Gm are 5/14 or ~35.7%. Conversely, this means that ~64.3% of the time you DO have a Gm on the bottom so it doesn't get played.
We can now repeat this exercise with one fewer Gm. If we have 8 Gm and a 5 card hand we will play the entire deck if we have a non-Gm on the bottom (5/13). So 5/13ths of the time when we have a Gm on the bottom, we will have a non-Gm second from bottom (thus we only fail to play one Gm this turn). Thus we can so .643 x 5/13 = .247 or 27.4% of the time you will hit 21. Add these two probabilities (35.7 + 24.7) and you get the odds for hitting $21 or greater. We could continue this for a third iteration and calc the odds that all three of the bottom cards are Gm, but that doesn't seem to be worth the time.
Note: I did the initial calculations in a different manner, it shouldn't have an impact, but I wasn't rigorous with decimals so things may not calc out exactly the same.
Unequivocally, you have a higher expectation value of points you can buy after the plat over the Gm. Unequivocally, the value of adding the Gm to the deck is exactly 2 coin.
So why does DG's simulator have the plat lose? Because we don't care about just one turn's worth of expected cash output. Sure for the first plat, you get a higher expected cash value, but as you buy more dead cards, you have less and less draw. It is only very near the "draw your whole deck, reliably" point where +1 card starts to lose value. His sim
starts at the reliable whole deck draw point and promptly moves away from it. After the 3rd colony, he has much better odds of using the +1 card from Gm to chain more Gm (totaling more coin than a Plat). If we are buying 8 or even 4 colonies, this just hammers the Plat.
So why not just forgot about the corner case if it doesn't last that long? In a word: megaturn. If you only buy VP on your final turn or two, it can be far more efficient to do something like smithy/village/plat/plat (total cost 25) than Gm x5 (total cost 30); both leave you with +10 coin, but the latter only gives +1 card and of course the +buy. This becomes particularly acute with things like - being able to get more coin by playing coppers or using Border Village/Smithy to only pay 24. You can get to double colony a half turn sooner and that can be a much bigger deal than +1 card, particularly if you over bought components because of copper concerns.
After all, Plat vs Gm is just a closer set of numbers than Gold vs Market. Somewhere there is a point where the advantages of treasure (e.g. purchase efficiency) outweigh the consistency of +1 card. Gm is closer to plat on those advantages, but it still isn't quite there. Most people don't rave about how +1 card from market just destroys gold in engines, clearly the value of +1 card is fluid and at some point on its relative value, we reach a tipping point where treasure is more effective. For Market vs Gold, this is early on with plenty of use left for the draw. For Gm vs Plat, it is a lot later in the curve, but nonetheless, still there.
Dondon:
Actually, I think that depends on your likelihood of dead draw. A Fishing village/Oracle engine will almost never draw the Gm dead, on the other hand a Hunting grounds/Bandit camp engine is much more likely to make a dead draw. Even with either of those specified, I don't think the math obviously favors Plat or Gm - small changes in deck composition can easily swing it one way or the other.