I agree w/ Shivang re: what might have happened had Krishna rolled the dice for the Pandavas. It would have been a tit-for-tat to Shakuni, it would have undone the gains of the Kauravas, and even the punishment part of the vows of Bhima could have been retained as a part of the deal if the Pandavas won. Also, when Balarama played Rukmi, the goal on the end of Rukmi & his allies was to humiliate Balarama, but Krishna didn't prevent that game, and let it proceed to its logical end - Balarama slaying Rukmi and battering his allies.
If the game allowed 4 players, another thing Krishna could have done would have been to be the partner of the Pandavas and let the Kauravas play the remaining 2 colors. Then Krishna wouldn't have been throwing for the Pandavas, but would have been a fully legitimate player in his own right, and could have played both his own pieces, as well as that of the Pandavas.
Speaking of which, in all the games of dice I've read about, I've never read about >2 players. Does anyone know of such an instance where 2 or more people participated in such a contest?