Ralph-looping a math paper to (attempt to) win a pub argument

A while back a friend and I played a variant of Texas hold'em. In short: four players, cooperative, no betting. Each street (pre-flop, flop, turn, river) the four dice in the centre (faces 1, 2, 3, 4) get distributed across the players via a take-or-steal protocol that ends the moment the fourth centre die is taken. Each player ends a round with one die. The team wins iff every player's river die matches their final placement at showdown. The dice are the only communication channel. The tabletop argument was simple: should the die mean "how strong is my hand right now" or "where do I think I'll finish at showdown"? I had a strong intuition for the second. My hunch was that the information conveyed by the 'current state' is strictly less than the information available by taking future cards up until the river into account, and therefore, we can share a larger amount of information by using that as our communication anchor. My friends were unconvinced. So I did the obvious 2026-thing…