PhilK:
Personally, I always prefer sting to thud, so for me the ideal thickness is about 3/8" - the exact thickness of my much-prized (but now very hard to find) 'Cracker Barrel' paddle. It's seven-ply birchwood, so pretty well unbreakable - and, as quite a few young ladies will ruefully attest, very much a 'real' spanking paddle.
Well, ideally my paddlings start out with 'sting' (a lighter wooden implement) then eventually produce more 'thud' (via the spanker switching to a thicker, heavier one), but of course I'm on the opposite side of the (wife-administered) swats.
Anyway, I also possess a "Cracker Barrel" paddle, purchased close to two decades ago at a novelty/souvenir shop in Arcade, New York, purportedly the town where such paddles are (or at least were) produced--it was originally attached by an elastic string to a small rubber ball, as a single-user paddywhacking exercise testing and presumably improving hand-to-eye coordination.
Its dimensions are about 11 1/4" x 5 3/8" x 1/4" with a mildly oval-shaped head and a round-tipped handle, somewhat like a smaller, lighter version of a Jokari paddle, but a bit less oval-headed, apparently made out of tightly-compressed plywood. It is indeed overwhelmingly 'sting' in its impact, and quite effective when employed with enthusiasm. (Given its relative lightness, obviously the less protection the targeted behind has the more convincing the smacks will be--it's pretty much pointless to deploy it atop a bluejean-covered rear end.)
I'm imagining a game with two such paddles, one of them detached from the flexible string and ball but the second one not. The spanker assigns the spankee a certain amount of bare-bottom swats with the first paddle (let's say an even one hundred), minus the number of times the spankee can bounce the ball off the second one before missing, for a chosen number of attempts (let's say three).
So if the spankee were to manage six consecutive hits the first time, ten the next time and eighteen the third time (assuming practice resulting in improvement), he/she would have reduced his/her walloping with the first paddle to 76 smacks (100-34). To help the spanker also improve his/her coordination though, he/she could be allowed a set number of consecutive-hit attempts to lengthen the spankee's paddling.
For switches, both could start at zero and take turns with a specified number of attempts, with the winner, i.e. whoever ends up with more overall hits, giving the loser the difference in whacks. So if one person gets say 12+15+24 (51 total) over three attempts, while the other gets say 7+13+17 (37 total), the first one would end up giving the second person 14 spanks with the other paddle--or possibly a multiplied number thereof, by mutual agreement.
"I'm just spitballing here" (to quote Colonel Nathan Jessip) about spankophile-style possibilities with "Cracker Barrel" seat-smackers...

--C.K.
P.S. : "Never strike a child across his face, Mother Nature provides a more suitable place," that's the version of that paddle-inscription saying which I'm most familiar with.