[ A Hitt at Backgammon - Thomas Rowlandson (1756-1827) ]

When I found this print in a book, the caption read, 'Danish King Christian IV & Swedish Lord Chansellor Oxenstierna playing bg for tax money'. -- But 'Stricken' at DailyGammon.com suggested that they are merely using the board as an abacus (calculator). 

'I cannot be absolutely sure without scrutinizing the original up close - but its a fact that many "game-boards" (i.e boards which looked like games in design - like backgammon, chess, checkers etc) had multiple uses since the Ancient times - resources were scarce so it made sense to have objects that could be put to multiple use.

The chinese abacus is the most commonly known design today - wood verticle rack with beads on wire poles - but long before this the flat abacus was used for the same calculating purposes since the oldest days in the Mid-East and this spread to Europe around the Crusades. The flat-bed abacus could be made simply by drawing the design in the dirt or engraved and made portable on stone or wood slabs.

In the Middle Ages of Europe (and up to the 19th century) most people were illeterate and calculations were not done with pen and paper but by using simple designs of old like the stone or wood flat abacus. Sometimes the pictures look like the characters are playing a game as the pieces may be clearly visible on the board set out in 'positions' of primes and points etc - but this is how the board would also look when used for accounting because each board-point represents place notation - i.e in decimal 1, 10, 100, 1000 etc. In fact because 5 objects in a row are the maximum that people can instantly recognize (i.e groups of 6,7,8 etc are hard to recognize without actually using the effort of counting one by one) the board-points probably went in the value 5, 10, 50, 100 etc. And this one of argument why the starting position of backgammon has a max of 5 checkers on the mid-point and 6-point etc).
Also it would be common for checkers to be placed on opposite sides of the board for calculations involving commerce and trade - balance of payments etc.

Chequered (chess and checkers) boards were also used for some calculations and were often used as a visual sign outside pubs and businesses etc to indicate that money changing and credit services were available etc. The word checker lingers on in modern economic and accounting terms such as "Chancellor or the Exchequer" - the official name of the Minister responsible for drawing up the governments budget in the UK. 

But then again - with reference to your comment that "it would make more sense than gambling with government revenue" - there is a story - probably legend - about some ancient kings around your part of the world gambling for territory.

I don't have the specific reference handy with the exact names dates and countries etc - but from what I recall - it was 3 kings of the Scandanavian regions who had a dispute over some land which bordered their respective territories and instead of committing troops to bloodshed, they came to a gentleman's agreement to play dice for it - who ever threw the highest number would win. The legend bit really kicks into gear with the rest of the story because apparently one king threw 6-6 and claimed it wouldn't be beaten. Then the next king throws 6-6 then the third king throws the dice and one of them splits into two pieces which results in two sixes and a one, landing face up! He claimed a total throw of 13 and won :-)

.... I know which book its in - "Chess in Iceland" by Willard Fiske.'