Thought experiment. If Terezi tossed, instead of a coin, a golfball-shaped hundred-sided die she nicked from Vriska, would that create 99 doomed Daves? What if she rigged a situation where Dave has a 1/∞ chance of succeeding in his quest, with instructions for every doomed Dave to reverse back to the alpha timeline? Would that create INFINITE Daves out of nothing? Also infinite boondollars, obviously. And infinite grist, if you can recycle the items they have.
But it doesn't matter what Terezi uses on her end. She could use a coin, an eight sided die, or the decibel level of Karkat's voice.
The result of the toss doesn't matter, because that's always going to be the same, because there's nothing Dave can do to change the outcome of the flip. What Dave chooses to do based on the result is what splits the timeline.
I.E.,
Terezi flipped a coin. It ended up bad heads.
Doomed Dave picked bad heads to learn about the god tiers now.
Alpha Dave picked bad heads to wait to learn about the god tiers.
If Terezi had flipped good heads instead the result would be exactly the same. There'd still be a doomed Dave lying on the bed and Alpha Dave would be standing before him with a sword held in his hand.
Even if Terezi rolled an infinite sided die, the result would be the same, because there will always be a doomed Dave who decided to choose opposite what Alpha Dave did.
The result doesn't matter at all. Terezi doesn't even need to flip a coin at all, just pretend like she does. Only what Dave decides to do on the result splits the timeline.