The referee rolls two unbiased dices: one of the dices outcome is a score and the other dice outcome is the number of times that the first dice should be rolled.

For instance, if the second dice outcome is 4, then the referee will roll 4 times the first dice, and the result will be the sum of the 4 outcomes.

The players never know the second dice outcome; theu are only informed of the first dice outcome.

In my example, (first dice will be rolled 4 times) the players would only be informed of each outcome of the first dice. Imagine that the outcomes will be 2, 6, 3, 3 (total 14).

You must put your bets before the result of each outcome.

In the begining, without any information, you would place a bet for a total outcome.

After you know the first outcome (in our example, 2) you can revise your bet.

Then, after knowing the second outcome (6), you can revise your bet again. And so on.

What is the best strategy for this game (not using brut force...)?