Just for fun, I took 1/2 gallon of an uncarbonated 6% ABV beer and froze it a little. I skimmed off the ice and did it a couple more times until it was at 1/4 gallon. It tastes ok, sort of, but I'm wondering if I did a gravity reading will the ABV be accurate (assuming I take it at the correct temp). Or, does skimming off water change how the gravity reading thing works. My understanding is the gravity measures the water solution, and the pre-post fermentation comparison is how we get the ABV. So concentrating the alcohol might not really be reflected in the gravity reading since I removed water. Thanks.
Assuming that the final gravity of your beer was at 1.020 if you remove water/ice, that number should go up. However, since the alcohol is now more concentrated in the beer, and since alcohol is lighter than water, the removal of the water may be off-set by the greater amount of alcohol. I don't know if you can predict the effect by any sort of calculation without doing other calculations like a beginning weight and an ending weight of the liquid.
Why do you need to take a reading? Do it mathematically - close enough. Cutting volume in half while maintaining the same alcohol will result in doubling the percent by volume. No need for reading, you have 12% ABV beer.