Margaret - I have found something I believe will interest you. I requested the article through my library system at Walden University. They could not obtain the copy but sent me this information that I pass to you:

Thank you for contacting the library for assistance finding the following:

Kretzschmar, Fritz ; Heinsius, Elli: Über einige Darstellungen altrömischer Rechenbretter. - S. 96-108, Taf. 3-4

I am not able to locate this for either free or for purchase online. From what I can tell the only library that owns this item is Zentralinstitut fur Kunstgeschichte, Bibliothek, Munchen, 80333 Germany. Unfortunately this is not one of the libraries that we are able to borrow from. You could try to email them to see if they would be able to send you a photocopy. Whether they can or not will likely be based on their policies and possible copyright issues. If you want to email them to ask about getting the article the address is [email protected].

I hope this information helps. Please let us know if you would like further assistance with this or anything else.

Best,

Nykol Eystad

Reference Librarian

Walden University Library

[email protected]

1-855-764-4433 (toll free) 

I anticipate that you will be able to acquire your copy by e-mail and if it's not too much trouble and doesn't conflict with your University's policies, I would also like a copy for my records. Thank you so much.  

There's a small chapter on the Abacus (and finger counting) used in the Roman Imperial period in Artifacts from Ancient Rome by James B. Tschen-Emmons, pp. 3 - 7, including in the arena and the law courts.  The references cited therein may be of some help to you.

https://books.google.com.au/books?id=SziaBAAAQBAJ&pg=PA72&lpg=PA72&dq=gambling+in+ancient+rome&source=bl&ots=KacLShuWNS&sig=Z0ex5kXUYWlm_Q7VX-UerWrqJd4&hl=en&sa=X&ved=0CEAQ6AEwBzgUahUKEwiF9Pygo4_GAhVOM7wKHRp7AKE#v=onepage&q=abacus&f=false

Thanks, Kathleen. I have known Catullus 5 since high school days, and the connection is again interesting on this occasion. 

Margaret,

          Your question was very interesting to me so that I did a quick and dirty search with some positive results. Unfortunately, most of the material I found lacked scholarly credence, however, the information hopefully can lead to better data. There is an excellent thesis on the abacus by a young lady named Laura Gobbi who studied at the University of Bologna. She tells of the use of a marble table type abacus and other smaller versions. Of interest is that the table type had to do with the representation of the numbers with letters, a practice passed from the Greeks, and possibly before. I am sending her thesis which I hope will be of use. I can help with a translation if you need.

          There seems to be quite a concurrence regarding betting at the coliseums, certainly among the Italians. Sadly, one of the most well-referenced articles I found was on Wikipedia. The Italian version was the first with practically no citations, just a bibliography of substantial worth. I found the English version which contained internal citations at https://en.wikipedia.org/wiki/Chariot_racing. A Roman tour guide provided a reference to betting at the games and the Website for the city of TIvoli tells of the Roman proclivity for gaming and gambling in various contexts. I hope these will be of use to you. I lived and worked in Italy for about five years in Sicily, Naples, Florence, and other locations so these issues are dear to me. Let me know how I can help. 

References 

Claudio, O. (2015). Colosseum. Ancient Rome. Retrieved from http://www.ancientrome.it/tour/roma-antica/colosseo?jjj=1435796661298

Gobbi, L. (2011). Storia dell’abaco: Una Introduzione. Bologna, Italy: L’Universita di Bologna. Retrieved from http://amslaurea.unibo.it/3094/1/gobbi_laura_tesi.pdf

Tivoli e Intorni. (2014). Il tempo libero: passeggiate, giochi, e giocattoli.  Retrieved from http://www.tibursuperbum.it/ita/note/romani/TempoLiberoGiochi.htm

Wikipedia.org. (2015, Maggio) Corsa dei Carri. Retrieved from https://it.wikipedia.org/wiki/Corsa_dei_carri

Wikipedia.org. (2015, May) Chariot Racing. Retrieved from https://en.wikipedia.org/wiki/Chariot_racing

 I will continue to look for Latin or other classical references.

 That is all incredibly helpful - thank you so much. Although not quotable and sometimes misleading, Wikipedia can often start off a search in the right direction, can't it?

Margaret,

I found something that I wanted to share. Is it possible that those marks were not associated with gambling at all? What if they were a counting system to keep track of jars or bowls? I am not familiar with the marks on your pottery, suggested dates of manufacture, or place of origin. There are curious vessels in a cache found in Upper Egypt and Northern Sudan that may hold the possibility of another use for the marks depending what they look life. Take a look at this document and let me know what you think. See https://www.britishmuseum.org/pdf/Breand_a.pdf. I have not researched how widespread this practice occurred nor during what time period, but it holds an interesting variable. 

Margaret,

I found an interesting article that shows a continuation of the incised marks some would say represented a counting system. This practice continued in Egypt until the 15th dynasty or about 1550 B.C.E. I continue my search. See attachment.

I am assuming the epigraphist has ruled out the possibility of the marks representing “maker’s stamps” (Peña, 2007, Apr, p. 37) but I wonder if they are simple marks, could they represent dated material that came in the jars with identifying or numerical markers, possibly noting packaging origins or due dates of the contents, that is, "tituli picti" (Peña, 2007, Jan) Oops, I may have wrongly assumed this is regarding amphorae. I gather the pottery is simple and for storing if found in an amphitheatre. What type of distinguishing marks or unique pattern indicated to the epigraphist that this could have been an abacus?

References

Gallorini, C. (1998, Jun). Incised marks on pottery and other objects from Kahun: Systems of communication in Egypt during the late middle kingdom. [thesis]. Volume 2. University College of London. Retrieved from http://discovery.ucl.ac.uk/1317898/

Peña, J. (2007. Jan). Two groups of tituli picti from Pompei and environs: Sicilian wine, and not hand-picked olives. Journal of Roman Archaeology, (20), pp. 233-254. doi: http://dx.doi.org/10.1017/S1047759400005390

Peña, J. (2007, Apr 30). Roman Pottery in the Archaeological Record. Cambridge: Cambridge University Press.

John - the marks were made post cocturam. They are fragmentary, but were very precisely ruled and incised on part of a shallow and very flat-based dish in samian ware [terra sigillata].

We also have several small counters of exactly the right size from the site. I'm not able to say too much/post a photo online before publication of the site report and the other specialist reports, but the excellent epigraphist at Oxford University gave his reasoning for suggesting the likelihood of its being a make-shift abacus. This raises in my mind various possibilities: an individual's betting records being only one possibility.  Any other ideas for taking your ersatz abacus, ruled on a dish, to the games?

One reference that may help, but I've not yet got hold of is Kretzchmer, F. and Heinsius, E. 1951 ‘Über einige Darstellungen altrömischen Rechenbretter’, Trierer Zeitschrift 20, 96–108

Margaret - I think the idea of accounting makes the most sense to me. Perhaps they kept tabs on the ups and downs of betting. I found an article that tells they used the loose tessere of the counting board to tally accounts. Are your marks the typical four lines of the counting board? I find the word "calculate" or "to pebble" an interesting historical concept. I am going to see if we can find a copy of your "out of print" article from the Trierer Zeitschrift. Funny, I used to live close to Trier in Baumholder.

Here is the account of tessere for the abacus used to tally accounts. p.519.

https://books.google.com/books?id=mmsdAQAAMAAJ&pg=PA519&lpg=PA519&dq=abacus+tessere+samian&source=bl&ots=sJ1ypHRtSa&sig=qsRWXvLFoL6Km6wqH2zvlnS_wNI&hl=en&sa=X&ei=cU-ZVdTIFMjX-QH59JrADA&ved=0CC4Q6AEwAg#v=onepage&q=abacus%20tessere%20samian&f=false

 Margaret - Here's an current article from an unexpected source telling the use for the abacus's pebbles being to account. Note the interesting Latin phrase "to take to the pebbles." I am sure that is traceable and more evidence for the accounting idea. But as we are thinking ersatz, why wouldn't the Roman be as versatile with his or her abacus as we would with a hand-held calculator? Did they buy tickets? Or did they count losses of man, animals, and material in betting on various other types of the games beside racing? In cases of the famed water naval battles, would they have calculated timing for the flow of water to fill the arena. How about the quantification of force used by the ancient machinery used to lift the elevator platforms for animals and gladiators. Any number of things in my view could have required an abacus-calculator.

Margaret - I have found something I believe will interest you. I requested the article through my library system at Walden University. They could not obtain the copy but sent me this information that I pass to you:

Thank you for contacting the library for assistance finding the following:

Kretzschmar, Fritz ; Heinsius, Elli: Über einige Darstellungen altrömischer Rechenbretter. - S. 96-108, Taf. 3-4

I am not able to locate this for either free or for purchase online. From what I can tell the only library that owns this item is Zentralinstitut fur Kunstgeschichte, Bibliothek, Munchen, 80333 Germany. Unfortunately this is not one of the libraries that we are able to borrow from. You could try to email them to see if they would be able to send you a photocopy. Whether they can or not will likely be based on their policies and possible copyright issues. If you want to email them to ask about getting the article the address is [email protected].

I hope this information helps. Please let us know if you would like further assistance with this or anything else.

Best,

Nykol Eystad

Reference Librarian

Walden University Library

[email protected]

1-855-764-4433 (toll free) 

I anticipate that you will be able to acquire your copy by e-mail and if it's not too much trouble and doesn't conflict with your University's policies, I would also like a copy for my records. Thank you so much.  

Thanks very much, John. Sorry, I am currently unable to access a university library [Cambridge being the obvious one], which is why I haven't found this article. My academic contacts are trying to obtain a copy through the European system. Will let you  know if they, or the excavation directors, succeed.

That sounds great. Thank you.(

Hi Margaret,

Depending on the markings, you may be looking at a board game as they have been attested regularly at Roman theaters. If you have some more detail about the incision, I could point you towards the relevant literature.

Cheers,

Alex

Thanks very much, Alex. As I said, I don't have instant access to an academic library, and am working to a deadline, trying to follow up references.

The remains are fragmentary and too much weight should not be [metaphorically] placed on them. I cannot give details over the internet [or comment on] the Oxford epigraphist's report before publication. But yes, if not an abacus, a board-game [but one with very simple parallel lines] could be a possibility. 

More to follow, Alex.

The chances are slim that it is a game after reading your description but you may wish to check. If you have access to the journal Antiquity, you will find some publications by Mulvin & Sidebotham and also by myself. If not, I can send you some articles by email. Just let me know.

Thanks, Alex. I have access to various journals, but Antiquity is not one of them. Please see private message for my email address. 

Will keep you updated, but until sizes are  checked, the epigraphist is inclining towards a fragment of a make-shift abacus rather than of a duodecim scripta board....

An update. The epigraphist notes that he didn't mention Latrunculi, for the reason that the incisions are parallel lines and for Latrunculi, one would have to suppose more cross-lines than there are here. It does look like a very small part of an abacus, but there is too little to be sure. Kretzchmer [1951] reproduces the Paris abacus, with a horizontal line below a series of parallel vertical lines. 

As for Duodecim Scripta, the epigraphist's  knowledge is second-hand, but he understands the board as rather like a backgammon board, not really a grid, but two sets of columns, one below the other, separated by a horizontal space. While it is inherently more likely as a find in an amphitheatre, and likewise consists of parallel columns, if understood aright, we must posit twelve double columns. Multiplying the width of the counters would be another approach: they would require at least 0.18 m width.

 The internal base of large examples of this samian dish form, Walters forms 79 or the heavier 79R from Lezoux may be c 200 and c 240 mm at the usable diameter. Since there is a space of 240 mm available, this would be ample for nine vertical pairs of lines 13 mm apart, each separated by a space from the next, the arrangement necessary for an 'abacus'. On the other hand, a grid of 13 lines (12 spaces) would also be quite feasible for Duodecim Scripta.

Alex de Voogt's paper, 'Mancala players at Palmyra' in Antiquity vol 84, 1060, shows a game at bottom left, incised on the theatre steps which seems quite reminiscent. However, our fragment was on a relatively small dish/platter, of course.....Until a better preserved example turns up, I think, these can only be mentioned as possibilities.  

Incidentally, these Chester amphitheatre excavations also revealed more than 50 counters [mostly of diameter 13-15 mm]. Some dice, too, but they are currently considered post-Roman.

Any comments on measurements, etc, would be gratefully received!

Roman culture had spread widely in Europe by the Middle Ages and the Roman numeral system was commonly used for arithmetic. While addition and subtraction are relatively easy with the system, anything more advanced even multiplication or division is difficult; the lack of zero poses a particular problem.

https://www.google.co.in/url?sa=t&rct=j&q=&esrc=s&source=web&cd=99&cad=rja&uact=8&ved=0CEoQFjAIOFpqFQoTCP7t1sjBrcgCFUMSLAodnvkL-w&url=http%3A%2F%2Fsciencechica.com%2F2011%2F05%2F11%2F&usg=AFQjCNFLSfxnSyo1F0Dpf8kZgpY9a1cpiw&sig2=2ut6wvcEWUa80JOmO47OQQ

Thanks to all, including Krishnan, for your helpful responses.

I should add to my last comment - I do hope that the theatre at Palmyra will survive......

Thanks Krishnan. Sad news of more destruction of the heritage in the East. But we in the West need to remember also how much we owe to our friends far East - including ancient astronomers, mathematicians, scientists, philosophers, and all thinkers, both ancient and modern.

I'm still looking for written evidence concerning betting, or the playing of board-games, at Roman arenas - if anyone can help?

As Alex de Voogt indicated at Palmyra, the theatre had games incised on its steps. I wonder if the incisions have been allowed to remain in existence, in that they are not 'idolatrous' per se. [But then, what is idolatry, in logical terms??]

Dear Margaret,

there are several depictions of Liberalitas holding an abacus on roman coins. It is said that abaci were used for distribution of coins to the citizens:

"Geta augustus, 209 – 212

Aureus 210-212, AV 7.55 g. P SEPT GETA – PIVS AVG BRIT Laureate bust r., with drapery l. shoulder. Rev. LIB AVGG V ET V Caracalla and Geta seated l. on platform; in front, Liberalitas standing l., holding abacus and cornucopiae; on platform, citizen. C 70 var. (no drapery). BMC 64 var. (no drapery). RIC 87 var. (misdescribed). Calicó 2889 (this obverse die). Very rare. A very interesting reverse composition and a bold portrait struck on a very large flan, about extremely fine / extremely fine When this aureus was struck the fate of the empire was in the balance, for the brothers Caracalla and Geta were bitterly at odds. The congiarium (imperial bounty) celebrated on this coin took place upon the brothers’ return to Rome after concluding a war against the Caledonians with their father, who died of natural causes at York early in February, 211. The inscription names the distribution as the sixth of Caracalla and the fifth of Geta, thus demonstrating there was no concord between the emperors. By now their relationship had been reduced to a bitter contest in which the elder Caracalla would prove victorious by murdering Geta before the year 211 had closed. The brothers are accompanied on the platform by Liberalitas, who personifies the distribution. She holds a cornucopia – a symbol of bounty – and a board with a handle that is perpetually mis-described as an abacus (a counting device). In fact, it is a flat board with circular depressions, each designed to accommodate a single coin. This made the distribution of the correct number of coins more efficient. In practice, these distributions would have been tightly controlled affairs, with many soldiers and bureaucrats on hand to assure they were handled properly. For evidence we need only examine a large frieze on the north face of the Arch of Constantine, on which a line of citizens with outstretched hands await the distribution of coins. In two windows above there is a repeated scene of togate officials and their assistants removing coins from a strongbox for placement in the depressions in the tray, which represented each citizen’s allotment. Meanwhile, a secretary records each distribution on a scroll. Once filled, the trays are passed to a senior official at the emperor’s side, at which point the coins are distributed."

http://www.acsearch.info/search.html?id=1995991

For a more detailed depiction of Liberalitas with an abacus see:

"Balbinus, 22 April – 29 July 238

Sestertius April-July 238, Æ 18.90 g. IMP CAES D C AEL BALBINVS AVG Laureate, draped and cuirassed bust r. Rev. LIBERALITAS AVGVSTORVM Liberalitas, draped, standing facing, head l., holding abacus and cornnucopiae. C 11. BMC 2. RIC 15. A bold and finely detailed portrait well struck on a full flan, reddish tone and extremely fine Ex Vecchi sale 16, 1999, 528."

http://www.acsearch.info/search.html?id=1589145

May the distribution of coins have been taken place in the amphitheatres? However, the coins of the missilia were rather randomly scattered.

Best wishes,

Stefan

Dear Stefan,

Thank you so much! That is extremely interesting. Whether it's an abacus or not, I'll consult the project's Roman numismatist immediately about the putative abacus on coinage. Amazing!

Kind regards,

Margaret 

I see that the coin distribution-board  in the hand of Liberalitas, mentioned above by Stefan as occurring on coinage, is said to have been mis-described as an abacus.

I should add that 'our' dish has no depressions for coin placements. The grid is flat and appears to have had discs/counters/'pebbles'/calculi pushed along and/or across it.

Meanwhile, the research nears completion - with thanks to classical sources including Ovid and Juvenal.

I'm sincerely sorry that I can't thank all of you 'modern sources' in the acknowledgments, but perhaps you would accept my thanks here, instead? Again, sincerely!

The massive report on the amphitheatre excavation is still 'in progress'.

Amazingly, Marcel Lambrechts has posted a relevant link in his totally unrelated question at: 

https://www.researchgate.net/post/Do_you_think_that_animals_think_and_if_so_why_or_how#view=57c59f3c217e20c71b3f1ed2

There is a photo of a counting board incised on marble, from Salamis c 300 BCE - the wrong area and the wrong era, but it says:

'The gaming boards used by cultures like the Babylonians and Romans are seen as the "prototypes" of the Abacus. As most counting boards during this period of time, this Salamis board may most likely have been used for other activities than accounting, e.g. gaming. The board is ~150 x ~75 x ~4.5 cm (1 inch = 2.54 cm) and made of marble. Parallel grooves and Greek symbols are carved into it; with just four grooves it is possible to add and subtract to 10,000. The counting method used here is bi-quinary.'

See the link below - but it's in the unusually elongated 'pre-historic' section, for some strange reason.

http://www.thocp.net/timeline/0000.htm

Abacus is mother of calculator

It is basically a tool for counting and performing basic arithmetic. Most often constructed of a wood frame with beads sliding on wire or wooden pegs, the abacus is still used today in many cultures.

http://humansarefree.com/2014/11/22-chinese-inventions-that-changed-world.html

Thanks, Krishnan. I remember a wooden abacus with beads that I had when I was little...

I've been wondering why the Salamis counting-table is said to be Babylonian if it's 300 BCE...? See the link which Marcel kindly posted:

https://www.researchgate.net/deref/http%3A%2F%2Fwww.thocp.net%2Ftimeline%2F0000.htm

https://www.bing.com/search?q=picture+of+abacus&form=EDGHPC&qs=PF&cvid=6ce0b23a19f545238ad3c0e499b1e71b&pq=picture+of+abacus

I cannot the Roman ones were built from stone

In other words, the discussion is already guided/directed when you name the object you are investigating?

Thanks, Cecilia - there is, of course, a lot of evidence for gambling, including at the circus [races], but less so for the amphitheatre [gladiatorial games]. We generally presume they gambled on fights because they gambled on everything.

As Marcel infers, much in archaeology is based on presumption.

Marcel, yes we presume too much [but personally, I always point out the hypothetical]. However, the Romans were good at 'ersatz' and loved making one thing into another - and would use, for instance, a samian dish as a gaming board - or a calculating table. It was perhaps the former, but the latter is equally feasible. So, we should mention both options.

The alternative is to revert to the pre-1970s' practices in British archaeology - and not publish it at all.

Merely for general interest, here is a recent survey of spectacula in the amphitheatre at Pompeii:

https://www.academia.edu/2074177/Spectacula_in_First_Century_A.D._Pompeii

Why should the spectacles in Rome/Pompeii have been the same as in Britain?

What can be used to know what happened in an amphitheatre in Britain?

What is historical evidence in general?

Good questions, Marcel. It's mainly guesswork, and many strands of evidence suggest differences from Italian arenas, as one would expect [eg lions in Rome, but none -so far, if ever? - evident at British instances].

We know nothing from historic documents of what went on in amphitheatres in Britain. All we can use is the evidence of finds [the structure, but also pottery, metalwork, faunal and/or human remains] and make some 'educated' guesses...

See London's previously published amphitheatre: http://www.mola.org.uk/publications/london%E2%80%99s-roman-amphitheatre-guildhall-yard-city-london

or the shorter version:

https://books.google.co.uk/books/about/Roman_London_s_Amphitheatre.html?id=ghUV_gAACAAJ&source=kp_cover&redir_esc=y

Here's the 'official' guide to Chester amphitheatre, but don't believe every word as being incontrovertible. New ideas will be published next year.

http://www.english-heritage.org.uk/visit/places/chester-roman-amphitheatre/history/

http://www.english-heritage.org.uk/visit/places/chester-roman-amphitheatre/

Imagine

In Roman/Pompeii the local population with local culture-based tastes was probably sufficiently large so that the amphitheatres might have attracted many 'Roman' visitors with local culture-based tastes every day/week/month (?), even if a single individual X would be willing to go to the amphitheatre only once a year

In Britain, the Roman population was obviously significantly smaller than in the Mediterranean, so that an attractive amphitheatre should also have been accessible to Brits to fill up the amphitheatre? Is it quite likely that the Brits had other culture-based tastes than the Romans, and that the Brits public imposed other kinds of spectacles in Britain compared to the Mediterranean? 

Perhaps the open-air Roman amphitheatres in Britain were less frequently used than those in the Mediterranean, also because of the geographic variation in local climate?  

It's unclear how far these structures were for the military [Chester was a legionary fortress] and how far the locals participated. Hence one reason for the importance of studying the finds.

Marcel, seeing where your more professional interest may lie, two papers strike me as being perhaps interesting to you, though not specifically about Britain:

https://www.academia.edu/11487599/The_Trade_in_Wild_Beasts_for_Roman_Spectacles_A_Green_Perspective

https://www.academia.edu/4309219/Roman_Amphitheatres_and_Spectacula_a_21st_-Century_PerspectiveArchaeopress_Publishers_of_British_Archaeological_Reports15._The_Magerius_Mosaic_Revisited

Archeology: the study of extended phenotypes (e.g. à la R. Dawkins) in the absence of those that constructed the extended phenotypes. It's like an ornithologist that wishes to study bird nests without having access to the nest builders, right? 

Wonderful. And I notice, Marcel, that you prefer [like Socrates] to ask questions in order to elucidate the truth. Right?

And why do I notice that, do you think?

I've uploaded a chapter from the Roman Piercebridge volume, which includes a section on re-worked samian ware.

Chapter Samian ware, Chapter 9 in 'Roman Piercebridge, excavations, 1969-1981'

The abacus “the first automatic computer” is the earliest known tool of computing. It was thought to have been invented in Babylon, circa 2400 BCE. The abacus generally features a table or tablet with beaded strings. The abacus is still in use today in China and Japan. It was only very recently (the 1990’s) that the availability and sophistication of the hand-held calculator supplanted the abacus. In 1115 BCE the Chinese invented the South Pointing Chariot, a device which was the first to use the differential gear, which is believed to have given rise to the first analog computers.

https://www.cs.duke.edu/courses/summer07/cps001/Lectures/History_CS.pdf

 In childhood, I had an abacus consisting of beads on bars across a wooden frame, Krishnan. The mention of the Antikythera object reminded me how fascinating that putative 'computing device' is. Thanks!

I've now uploaded my chapter from the Roman Piercebridge volume, which includes a section on the repaired and re-worked samian ware. There were one or two strangely reused items (see pages 192-193), but nothing like an improvised abacus or gaming board. 

Chapter Samian ware, Chapter 9 in 'Roman Piercebridge, excavations, 1969-1981'

Dear

I wish I can help you but it is out my region

regards 

I think our community working in rome; s northeastern provinces should be more conscient of oriental and hellenistic wisdo and knowledge. so thank your margaret.

Thank you, dear Professor Saeed Al Rashid! I wonder how far the use of the abacus spread across the Roman world. We certainly know that makeshift versions of the gaming board were being incised on the steps at the theatre in Palmyra.

I wish Syria well, in every respect – and Iraq, too!

what i would like t say that rome did not begun with the construction of the limes in gemany or whne claudius realized his footprint on the beaches and landingfield of britan. we should more consider the mediterranean area.

Most certainly agreed, Joachim!

On Roman abaci the books by Alain Schärlig might be useful.

On betting in Roman times we know practically nothing.Ovidius at least mentions that he bet in the arena, but we don't know anything about the system, odds, bookmakers or so. The little knowledge we have about this has been summarized by Michael Maass, "Wie haben die Griechen und Römer gewettet? -- Zur antiken Sportwette, in the exhib. cat. of the Badisches Landesmuseum Karlsruhe "Volles Risiko! Glücksspiel von der Antike bis heute" (2008), p. 148-152-

Thanks very much, Ulrich - Alain Schärlig's work looks interesting...

Do you happen to have those catalogue pages, please? I have the amphitheatre publication proofs only for a short time now, and after that, it will be too late to alter anything. 

I have recently found a couple of classical references to betting at the arena, including Ovid's.

I have seen your references in your latrunculi research concerning incised latrunculi boards in Britain, but do you know of any for duodecim scripta?

Thanks again!

 We are still unsure whether this fragment represents an ersatz gaming board [for duodecim scripta] or a makeshift abacus - or what else...

No, I do not know of xii scripta boards incised in floors in Britain. There's only the board from the Roman military camp in Holt, as far as I know. And of course the proportions of the board from Stanway look rather like a xii scripta type board.

And here's Maass's text, the other pages are illustrations of objects, but nothing with a direct link to betting.

I cannot see your improvised abacus. Where is it?

Many thanks. What is the Stanway reference, please?

Sorry, I can't upload illustrations before publication - please see personal message, Ulrich.

There is a special museum dedicated to the mathematician Adam Ries at Bad Staffelstein, Franconia, his birth-place. My parents visited it some years ago. They sa that the abacus and its history is well explained. I will send a message to the museum.

Stanway: U. Schädler, "The doctor’s game – new light on the history of ancient board games", in: Philip Crummy et.al., Stanway: An Elite burial site at Camulodunum, Britannia Monograph Series No. 24, London 2007, 359-375

Ulrich, thanks -  have you seen my personal message to you?

As Ulrich agrees, it's impossible to be sure of the identity of this fragment. But its incredibly finely ruled lines required considerable technical skill - and merely on the internal base of a dish. Perhaps an abacus seems more likely, as the epigraphist first suggested, but it is a very small fragment.

Remember, the owner of the dish had incised his mark [less precisely] on the exterior. 

Dear Margaret,

the database http://artefacts.mom.fr/

has a nice page with abaci:

http://artefacts.mom.fr/fr/result.php?id=ABA-4001&find=ABA&pagenum=1&affmode=vign

Best wishes,

Stefan

PS: See also: https://www.researchgate.net/project/Artefacts

Thanks so much, Stefan. Great photos in the first link. I presume that the first and third items have been reconstituted with white filler, but are the beads not bronze, I wonder? I'll plough through the 1877 French text.....

Hard to imagine a version inside a pot base, but the epigraphist's estimate of size seems feasible.

Thanks to all, and very best wishes for 2017 to you - and to our world!

I am looking forward to Bad Staffelstein Museums' answer. Perhaps there are graffiti at Pompeji referring to betting at the ludi. I will have a look. It is possible, that Martial or other Roman comedy writer could bea source to investigate.

I wish you a happy new year.

Joachim

An author, Karl-Wilhelm Weeber (Alltag im alten Rom - Das leben in der Stadt, 200§ points outh, that betting was common in the places of public spectacles-the circus and the arena. Betting is sponsio in Latin.

 Thanks, Joachim- time [like 2016] will soon be running out for this project.

Again, I thank all of you for another fascinating discussion. You may wish to know that the first volume of the report on the excavations at Chester's amphitheatre has appeared in print, given a publication date of 2017.

Its price, for a book of 496 pages, is very low. I'm told that one third of the original print run was sold within the first two or three weeks.

See full details from the publisher:

https://www.oxbowbooks.com/oxbow/the-roman-amphitheatre-of-chester-volume-1.html

it is currently cheaper from the publisher than it is on Amazon. Here is the Amazon UK entry:

https://www.amazon.co.uk/gp/product/1785707442/ref=pe_2443691_229795891_em_1p_0_ti