How to Perdict Gravity?

For my first all grain beer I will be brewing an English Ordinary Bitter. I am using the recipe from John Palmer which includes British Invert Sugar.

Since this is my first all grain I computed my grain bill using 65% eff. My concern is if things go better than that.

I have been reading tons of threads, books, etc about efficiency, all grain techniques and I will be mashing in a cooler with a SS braid.

Since the invert sugar isn't added until the boil I will leave it out if my gravity is high enough - but if it isn't what is the formula for figuring out how much of x substance will give you the gravity addition you want?

I have been looking all over for this but have come up empty handed...

Also one more question I haven't been able to find an answer for: at what point in the mashing and lautering process do you want to take hydrometer readings?

Thanks

Table sugar will add 45 points per gallon per pound, so you have to take that figure and calculate your addition based on wort density. Papazian has a calculation for it, I think.

Or you could sit down with some brewing software, get your numbers to where you're at your current gravity, then slowly add sugar in amounts to the recipe until it hits your target gravity, then add that amount of sugar.

I think the math on this is pretty tricky, so I'd probably do it trial and error with the software.

as soon as your kettle is full take the reading, this gives you your mash efficency. For a 10 gallon boil, if you are going to boil off 2 gallons over an hour, you will have 12 gallons in your brewpot which will be concentraited down to 10 gallons by the end of the boil. Do some simple algebra to figure out how much more concentraited the wort will be. If you are shooting for an og of 1.05 and are going to have the same amount of sugar but only 10/12ths of the liquid you would shoot for a 1.041 pre boil gravity.

I did a horrible job explaining this, but hopefully it makes sense, there are all kinds of pretty formulas in several homebrew books.