Ah yes, the backgame geniuses from the middle east. Well I think we all know how well they do against modern players! It is I grant you a recognisable style, much as a vertical kamikaze dive is a recognisable method of landing an aircraft. Rarely seen on Fibs, never on the Grid and never in this era on live tournament tables. Cubeless in single games, ie Mediterranean cafe style, it can be quite effective. In match play, no.
I look forward to playing you one day. Thanks for the chat, enlivened a dull rainy day for me.

Name one expert who doesn't use a computer to analyse.
Falafel plays in exactly the same way as a bot, as his astonishing PR rates shows. He can of course revert to a back game when he has to do so, but to nominate him as an example of an arab back game stylist is just about as far from the truth as it is possible to get. He is the very model of a modern player, aided of course by his great individual powers of analysis. When he does play a back game, he will play it in the much the same way as XG does.

If you were in court and had to prove that a sequence of dicerolls that were rolled during a match came from a RNG and not from manually rolled dice, HOW would you prove it?

Excellent question. There is a lot of talk about dice sequences that are "truly random" as opposed to those that aren't. But when the challenge is posed to describe the difference between random and non-random, it quickly becomes apparent that it is unclear what kind of answer could possibly satisfy. The problem is compounded by false and misleading notions such as "any pattern will occur if only you roll often enough" (a widespread erroneous conclusion from the "law of large numbers").

Is 123456123456 a non-random sequence? How many times does the pattern have to repeat until it becomes non-random? Questions like these have no answer because they are confused: It is conceptually impossible to attribute randomness (or non-randomness) to finite sequences of rolls. (Which will yet not prevent us from disposing of a dice generator that repeats 123456 fifty times.)

See also

http://www.fibsboard.com/general-chit-chat/the-old-dice-controversy/msg28741/#msg28741
http://www.fibsboard.com/general-chit-chat/the-old-dice-controversy/msg28758/#msg28758

These are some of the reasons why the random dice debate revolves in an eternal circle.

For our purposes, the appearance (or non-appearance) of sequences is of no consequence. All we need to know is that on the next roll we can't predict what that roll will be with any greater accuracy than probability.

This is confused. The predictability or non-predictability of rolls is inextricably bound up with the appearance of sequences. In order to determine whether a dice generator's next roll is predictable or not, one has no choice but to examine the sequences it produces.

We have to remember that probability represents knowledge: With no prior knowledge of what a number generator has come up with in the past, all options of prediction become the same. Suppose a dice generator named DG_1 only ever rolls the number 1 and one named DG_123456 rolls a more or less even distribution of all numbers between 1 and 6. Suppose further that we have no knowledge (yet) of what either DG does. Then DG_1 will initially be just as unpredictable as DG_123456. Obviously that doesn't make the two generators equal with regard to predictability in the long run. After DG_1 has produced 11111111111, we can hypothesize about its future rolls and successfully predict them. With DG_123456 this may be harder (unless it comes up with 123456123456123456 or some other easily discernible pattern). Whatever happens, the analysis of sequences is crucial to the question of predictability.

Even if the next roll is not predictable from the previous one, it may yet be predictable from longer sequences of previous rolls. I gave an example of a sequence with this property in http://www.fibsboard.com/general-chit-chat/the-old-dice-controversy/msg28741/#msg28741

11 12 13 14 15 16
21 22 23 24 25 26
31 32 33 34 35 36
41 42 43 44 45 46
51 52 53 54 55 56
61 62 63 64 65 66
<repeat from beginning>

(For simplicity, only one die is being rolled here, the corresponding sequence for two dice is a 36x36 matrix.)

In this sequence, the distribution of the next roll is perfectly even with respect to the previous one: Every number n is followed by every number m exactly twice. Hence it is impossible to predict the next roll from its predecessor with "greater accuracy than probability" (with greater accuracy than p = 1/6 for any number). But it obviously does not follow that the sequence is random, meaning that it is entirely unpredictable. For example, knowing that I rolled 444 previously will allow me to predict the next roll to be a 5 with 100% accuracy. Knowing that I rolled 44 will give me a 50/50% predictability of a 4 or a 5 coming up next, and so on.

What the phrase "with greater accuracy than probability" means is exactly what the question of what constitutes randomness (= predictability) is about. It contains the entire complexity of that question. The phrase "all we need to know ..." seems to promise that the issue of randomness can somehow be reduced to something very simple, namely, the predictability of the next roll. But the predictability of the next roll continues to be a very big deal, namely, to show patternlessness in the generated dice sequence. Only the absence of patterns can guarantee unpredictability (= randomness).

You are leaving out one very important variable! Dice that OTHER players take out of the sequence.
And that in and of itself adds another level of randomness!

That's true, but I wasn't writing about rolls in an actual FIBS match. The only purpose of the example sequence I gave was to show that the concept of predictability is a complex and difficult one.

The perspective you were considering was from inside the server (the actual roll generator) where it would be impossible for us to observe.

You still misunderstand. I wasn't talking about FIBS at all. I was countering the notion that an examination of predictability can be decoupled from analysing dice sequences, as dorbel seemed to suggest.

That is true, but when trying to predict rolls, the point of observation is critical.

For the purpose of prediction, the only critical data are the actual rolls that I am handed. That is the only "point of observation" there is.

If anybody wanted to prove or disprove that FIBS rolls are random (which was not my purpose), they could of course not resort to assumptions about the inner workings of the FIBS software. Again, the only data needed are the dice as handed to the players, by whatever machinery is going on in the background.

We're talking about different things really. The only point that I was making is no technique available to a player on Fibs or the Grid will enable you to predict the next roll. Thats it really