I’m not sure I see what you’re suggesting instead, though I will point out I believe there is an error in that section- the point of this problem is to figure out what is wrong with the calculation suggesting you should defect.
I calculated the expected values for bytes with the bit-level analysis- that is, the bit-level analysis has done the “okay, you’re a decider” updating but is still dealing with numbers on the scale of bytes. So $21 comes from 1⁄8 * $21 + 7⁄8 * $21=$21.
The justification for that is, if you sent in a byte of identical bits, all bits know that they are clones and so whatever they decide, all the others will decide as well.
I’m not sure I see what you’re suggesting instead, though I will point out I believe there is an error in that section- the point of this problem is to figure out what is wrong with the calculation suggesting you should defect.
I calculated the expected values for bytes with the bit-level analysis- that is, the bit-level analysis has done the “okay, you’re a decider” updating but is still dealing with numbers on the scale of bytes. So $21 comes from 1⁄8 * $21 + 7⁄8 * $21=$21.
The justification for that is, if you sent in a byte of identical bits, all bits know that they are clones and so whatever they decide, all the others will decide as well.