6 possible dice values log2 gives around 2.6 bits per roll. Naively you can spend 3 bits per roll, wasting .4 bits each time, or you can pack n bits into a sing

6 possible dice values log2 gives around 2.6 bits per roll. Naively you can spend 3 bits per roll, wasting .4 bits each time, or you can pack n bits into a single message to asymptotically approach 2.6 bits per roll on average. But you can't get under 12.9 bits for 5 dice rolls.