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I have investigated the relation between chess and draughts in a number of European countries, see chapter 3. In some (all?) of these countries, draughts in the period c. 1500-c. 1850 was more popular than chess. But there is more: in this period chess players were influenced by draughts players on everything which had to do with the promotion.
In Holland, this influence is manifest in the language. A promoted pawn for instance was called dam, i.e. king, the promoted draughts singleton. See for details Stoep 2005:81-83. Owing to a lack of factual information, it is impossible to establish if there were consequences for the way chess was played.
This cannot be excluded, for it is certain there was influence from draughts on the chess strategy in France and Germany in the 18th c. We have to thank no less a person than the strongest chess player of his time, the Frenchman Philidor, for this information. The influence from draughts has been fundamental and lasts up to the present day. Click here for evidence.