The problem comes with reading comprehension, and an actual factual understanding of a concept, something HA is incapable of. All he can do is spit out wikipedia quotes that he doesnt even begin to attempt to comprehend.
Tom's post a little bit ago explained things fairly well. The problem comes in when you try to treat a die like it a continuous variable, when in fact it is discrete. An expected value would be the most likely value you'd get by rolling a die. In rolling a die, you get a flat line distribution of all possible outcomes. rolling a 1 = a 2 = 3 = 4 = 5 = 6. So how is 3.5 the expected outcome? Its the AVERAGE, not the expected. There is NO expected value for rolling 1 die, because all 6 possibilities have an equal chance of being rolled. (1/6) Case in point: I have a die with sides cat, dog, bird, mouse, horse, and pig. Whats the expected outcome for THAT die? mouse.5?
Things DO make sense when rolling multiple die, however. If i roll 2 dice, i get a distribution of possible outcomes, where the most likely (highest percentage) outcome is 7. (6/36) So 7 is the expected outcome for a roll of 2 dice. Also, it IS possible to roll a 7 by rolling 2 die. But you cant just say that since 7 is expected for 2 die, then 3.5 is the expected for 1 die, because 1 die does not have the same distribution as rolling 2 die.
Mathematically, if you roll a die thousands of times, and calculate the AVERAGE value of each die roll, you will get 3.5. Thats a mathematical definition of average. By rolling a die multiple times, you've turned a set of discrete variables into a system of continuous variables. But you cannot back extrapolate that onto 1 die roll. 1 roll has equal probabilities of getting a 1,2,3,4,5,or 6. Therefore it has no "expected" value, and you cannot claim that the "expected roll" is 3.5, and that any other roll is "error".
This level of reading comprehension and basic understanding of mathematical concepts is what gets HA in trouble with his each and every post.