This joke was supposed to be funny:
A Roman walks into a bar, holds up two fingers and shouts "Five beers, please!"
But disregarding the funniness, it made me actually think about the real system or systems that they did use. The evidence I found so far is from quite old sources and inconclusive, only pointing at reconstructions at what they might have used. Roman numerals are even said to have originated from hand-gestures for counting, according to one hypothesis.
Alfred Hooper has an alternative hypothesis for the origin of the Roman numeral system, for small numbers. Hooper contends that the digits are related to hand gestures for counting. For example, the numbers I, II, III, IIII correspond to the number of fingers held up for another to see. V, then represents that hand upright with fingers together and thumb apart. Numbers 6–10, are represented with two hands as follows (left hand, right hand) 6=(V,I), 7=(V,II), 8=(V,III), 9=(V,IIII), 10=(V,V) and X results from either crossing of the thumbs, or holding both hands up in a cross.
Another possibility is that each I represents a finger and V represents the thumb of one hand. This way the numbers between 1–10 can be counted on one hand using the order: I=P, II=PR, III=PRM, IV=IT, V=T, VI=TP, VII=TPR, VIII=TPRM, IX=IN, X=N (P=pinky, R=ring, M=middle, I=index, T=thumb N=no fingers/other hand). This pattern can also be continued using the other hand with the fingers representing X and the thumb L. (WP)
But that does not seem to match this description:
Finger numerals were used by the ancient Greeks, Romans, Europeans of the Middle Ages, and later the Asiatics. Still today you can see children learning to count on our own finger numerical system. The old system is as follows: ()
This seems to be generally correct depiction, however I do not see how well this could have worked on the one hand. and on the other:
The evidence seems to be against the assumption that the ancient Greeks and Romans had a system of representing higher numbers by placing the hands with palm or back exposed against various parts of the body as described by Bede. […] At this point we shall leave Bede for the reasons stated at the beginning of this section and consider some earlier evidence which shows that despite the general continuity of tradition, a change had taken place in the way 10 and 30 were represented.
(J. Hilton Turner: "Roman Elementary Mathematics: The Operations", The Classical Journal, Vol. 47, No. 2 (Nov. 1951), 63‑74 and 106‑108.)
Which seems to imply that apart from a seemingly arbitrary system in large parts to start with an even as randomly appearing change happened?
A couple of ancient sources that touch the subject:
Plautus, Miles Gloriosus, 204‑206; Pliny, Hist. Nat. 34, 33 (cf. Macrobius, Saturnalia 1, 9, 10); Suidas s.v. Ἰᾶνος; Cicero, Ad Att. 5, 21, 12‑13; Quintilian, Instit. Orat. 1, 10, 35.
But it is not without good reason that some of the greatest men have devoted special attention to this science. Geometry has two divisions; one is concerned with numbers, the other with figures. Now knowledge of the former is a necessity not merely to the orator, but to any one who has had even an elementary education. Such knowledge is frequently required in actual cases, in which a speaker is regarded as deficient in education, I will not say if he hesitates in making a calculation, but even if he contradicts the calculation which he states in words by making an uncertain or inappropriate gesture with his fingers.
How did the Romans use hand gestures to signal numerical values, did that system change over time, and is any of those steps conducive to the theory that written representation evolved from these finger signals?
While the connection between calculations, means thereof and written number representation is interesting as well indeed: The main focus here is specifically concentrating on counting, use of fingers and visual communication (body language, like it's used today). If simple counting with fingers should be an aid in (learners'?) arithmetics that should be most interesting as well.