Ask Haywire up north of calgary. He just clobbered a caribou with one on the caribou hunt out of a 300 ultramag. It went two feet straight down at around 400 yards. They are fine up to caribou size stuff but to thin a jacket for elk. Great deer bullet for your purpose.
The 162gr A-Max worked very well on whitetails when fired from my 7STW. Broadside shots or high shoulder shots both proved to be rapidly fatal.
I'm assuming that you are shooting one of the 300 mags; the 208 A-Max would be more bullet than needed but (IMO) would get the job done at almost any conceivable range.
I was going to use them in my 300RUM but the Berger 210VLD was producing tighter groups in this rifle. The A-Max is usually easier to find, less costly and just as accurate. Both are reliable at dispatching deer.
My dad uses the 162 grain Amax in his 7mm and has taken several white tails at 300 to 500 yards with no problem whatsoever! I have killed mule deere and elk with the 155 grain Amax close range though, out of a 300 win mag . I've also killed some yotes and white tails with the 208 out of my 300rum but I will say that I shoot the 210 grain berger now and I have tighter groups with it in my rifle (but) I haven't put the loading time into the Amax like I have the 210 berger. Bottom line is dead is dead and if you could ask the two white tails mule deere and elk that I have on the wall ,they would say that their firm believers in AMAXS