Dreidel conjecture on the average number of spins

Let $Dr(a,p,b)$ denote the average number of spins in the full two-player Dreidel game starting with $a$ nuts for the first player, $p$ coins, and $b$ nuts for the second player, and set

$$Q(a,b):=Dr(a,2,b).$$

Dreidel conjecture. The average number of spins is approximately

$$Q(a,b)\approx \widetilde{Q}(a,b)=2.21814151862618181904832628843\cdot ab-1.09709667033405910669478639669\cdot a-0.447079544643588135688652268182\cdot b+2.83880783734231869675987135868.$$

This conjecture extends the authors' approximation method from the simplified Dreidel game, where only two outcomes can occur, to the full game with all four outcomes. The preceding discussion reports numerical evidence that the increments in the two starting nut counts converge to constants, but no proof of this approximation is given.