I also would reccomend something besides the game king. I have shot 3 texas hill country whitetail bucks(relatively small deer) with 150 gr. game kinds relatively slowly from a 30-06. They werefrom 50 to 150 yards and all pretty much broadside shots which were behind the shoulder in all cases but one. I never had a significant peice of the bullet exit. A couple had small holes where tiny gragments of the bullet exited but no real penetration of the bullet, and definately not an exit wound that would leave sufficient blood trail for easy recovery. In all cases there were tiny fragments of lead inside the body cavity. In my opinion a bullet that is of an appropriate weight for the hunted game that will not expand reliably AND hold together and penetrate, even at low velocities by todays standards(30-06 factory ammo out of 22" barrel) does not offer acceptable performance on big game, or anything bigger than varmints. The jacket of the game king is just too thin and had is not bonded to the core, nor does it have any type of locking ring, jacket wall or partition, or even a thick base.
You dont need a premium bullet to get good performance on deer though. Try hornady interlock bullets, SST(basically interlock but with plastic tip, or my personal choice the nosler ballistic tip. The interlock and SST both have an interior ring built into the jacket to control expansion and the ballistic tip has a jacket that gets thicker toward the thick solid base. The ballistic tip is reputably the most accurate hunting bullet in production. I have no experience with the ballistic tip 25-06, but my dad is shooting 100 gr. hornady interlock out of his sako(23 3/8" barrel) and getting well over 3300 fps and really really good accuracy with RL 22, win cases, and fed match 210 primers. Hes also working on a load with the 117 gr. SST with the same powder, primer, and i belive federal cases and it looks to be pretty accurate so far. Im trying to get him to try ballistic tips.
Hope this helps.