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The PFS boons purchasable with Playtest Points now list a cost increase after the first purchase, which is a good update. The listed increase, though, doesn't match the actual increase, at least for the one I've purchased thus far. The 'Experienced Adventurer' boon (start a character at 2nd level) says the starting price is 12 points and that it doubles after each purchase. After purchasing one, however, there is now a listed price of 48 points, 4x the starting price.

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The description is a bit misleading-- boon prices can have "added values" or "multipliers", but multipliers don't actually multiply them by the same amount each time. Instead, they turn the cost into:
base cost + (multiplier * base cost * number of previous purchases)
My understanding is that we now want multipliers to work the way you'd expect, and the way the description indicates. I'll check in with OPF to see how they would prefer things to work.

NielsenE |

The two boons that I spot and was able to spot check:
River Kingdom Excavation says 'May purchase more than once, but cost increases 50% at each purchase' It starts at 4 PTP, but shows 12 PTP for a second purchase. That's not a 50% increase. 50% Increase would suggest 6PP for the second one.
Experienced Adventurer says 'May purchase more than once, May purchase more than once, but price doubles at each purchase.' starts at 12, lists 48 for a second purchase. Double would suggest 24.
If we used the equation you list:
RKE: 4 + (.5 * 4 * 1) = 4 + 2 = 6 as expected
EA: 12 + (1 * 12 * 1) = 24 as expected
Both are off by a factor of two.
It looks like what you're doing is either:
base cost + (multiplier * base cost * number of times purchased counting the next purchase)
or
(base cost + (multiplier * base cost * number of previous purchases) x2
Either way it looks like the equation you thought it should use would give the same results as the text and people expected. It sounds like developers and OPF have the same understanding of what the algorithm is, its just implemented incorrectly.