[dragonwriter]

> Prop 13 limits property tax to the value of the house when you bought it

No, it restricts increases in the basis value to which the tax rate is applied to a maximum of the value after purchase (or other qualifying event) + 2% per annum.

> unlike most places where you pay property tax on the current value.

A number of other states have Prop 13 like limits to the annual increase in tax basis value, and some others do full market valuation but split the increases over a several year period so that the tax basis value lags the increase, and other places just have fairly infrequent reassessment except at purchase (which, in effect, also causes tax basis value to, on average, trail behind increases.)