the penalty for making a wrong guess,

是猜错了的惩罚
and you were forced at the beginning to say,

在一开始就被迫要说
"What guess would you like to make for how the dice is

骰子最后得到的数是什么
going to turn out-- how the dice is going to turn out

骰子将怎么得出结果
and if you're wrong,

如果你们预期错了呢
we'll penalize you by this measure of error?"

我们将用误差作为惩罚
Well, if you were just taking the absolute error,

要是只考虑绝对误差
your best guess would be any number between 3 and 4.

最好的猜测应该是3或4
You could say 3 and 1 half, but you could also say 3 and 1 quarter,

可以是三又二分之一或三又四分之一
because if you said 3 and 1 quarter,

因为如果你说三又四分之一
you'd become closer on all the low rolls of the dice,

就接近骰子的小点数
and be a little further off on all the high rolls,

离大点数就远了点