What's the best shot size? It's a good question, and the answer isn't really that straight-forward. Because a lot of factors come into play, not the least of which is what type of shot you'll be using.
This question has been around a long time. Lovett Williams in his book Wild Turkey Hunting and Management dedicates a few pages to this question. Perhaps counterintuitively to new hunters asking the question, he says that bigger is not better. He says, "If you use [lead] 4s by force of habit, testing [lead] 5s, 6s and 7-1/2s will be enlightening - the smaller shot size has greater effective killing range." And based on my personal testing, I'd tend to agree with him, generally speaking.
To some folks, that may be counterintuitive. But to those who have spent much time at the range, I don't think it will be. And the reason for this is what I tend to call the pattern/penetration gap, for lack of a better term.
In his book Williams has an illustration on page 168 that goes a long way to help us visualize it. He compares lead #6s with lead #2 (but don't get hung up on his opinion of what constitutes a "good pattern"):
You can see that in his opinion lead #6s are better than lead #2s, because you have longer effective killing range based on pattern density, while at the same time you have a shorter range at which the pattern is too sparse for effective killing. But yet individual pellets still retain enough energy to harm the turkey without killing it immediately so you as a hunter can recover it.
That gap between sufficient pattern density and range at which individual pellets still retain a sufficient penetration energy is what I'm calling the pattern/penetration gap. IMO, in order to maximize your shotshell's effectiveness, the hunter should consider his combo's pattern/penetration gap, and take that into consideration when he's deciding what to shoot at live turkeys.
So, what is the optimal shot size for turkeys? Well, of course the first piece of information we need to know in order to answer that is what type of shot you are shooting. Because the answer will vary greatly depending on that.
Everybody knows I prefer to shoot the 18g/cc shot, but what size 18g/cc shot I prefer varies depending on what kind of payload and gauge I'm shooting. For the twelve gauge, I lean towards 8-1/2s as being about optimal for heavy 2 oz loads. If I'm shooting a lighter 12 gauge load or 20 gauge, I tend to lean towards #9s. And if I'm shooting a small bore (28 or .410), I like 9-1/2s. In each of these cases the reason my shot size preference varies is due to the pattern/penetration gap. Any pattern that has sufficient density but lacks sufficient pellet penetration energy, is wasting potential. And any pellet size that has has sufficient penetration energy but lacks sufficient pattern density, is wasting potential.
So, what shot size is optimal for turkey? Here's my 2 cents, assuming a typical heavy 12 gauge load unless otherwise noted, and keeping in mind that the effective killing performance of the "optimal" sized pellets will vary greatly from one shot type to another:
steel shot: #3
lead shot: #5-#6
Hevi shot: #6
Heavyweight: #7 (#7-1/2 or #8 if they had it)
TSS: #8-1/2 (heavy 12 gauge); #9 (light 12 and 20 gauge); #9-1/2 (28 ga and .410)
Pattern density can be easily and objectively measured at the range. And pellet penetration energy is easily made known with the available ballistics programs like KPY. So, in order to make the choice, it's just a matter of deciding on the minimum standard for both pattern density and pellet penetration energy, and you're ready to go.
There you have it - brought to you by the pattern/penetration gap.