After some success he ventured north and played John McKerrow for £100 in 1858, a draw resulting. The following year he defeated James Wyllie in a match, establishing his claim to the World Championship. Altogether Martins faced Wyllie seven times. Martins was a gentleman of kind and genial disposition, well read, a thinker of some depth, and in his prime a considerable violinist.
By 1889 however his powers in long matches were on the wane. That year he played his last big match with Charles F Berker of Boston. During the course of this match, which was played in Glasgow, it became painfully evident to Martins' supporters that his match playing days were over: both memory and power of concentration being much impaired. Martins' principal backer, James Moir (originally from Tillicoultry and an excellent player) found that Martins had "dizzy fits and was unable to see the position or think clearly."
Nevertheless during the 1890's Robert continued to tour the draughts clubs giving excellent and succesful exhibitions. For example, in 1893 we find him at the "Old Black Bull Inn" in Cambuslang, or an item from the Glasgow Weekly Echo 1894 states "Mr R Martins, ex-champion of the World, will play all comers from the 31st inst. for a week, at 34 Ingram Street. He is perhaps the neatest player who ever moved a draughts piece."
In his later years the invalidity of his wife caused him to devote much of his time and effort for many years to caring for her, a duty which, though considered by him as a privilege, brought him on straitened times. Indeed the last meeting between himself and Wyllie, the so-called last battle, was a subscription match to raise money for the unfortunate Martins. He got about £36.
Martins lived in Douglas from 1864 until his death in 1904. he is buried in the Old St Brides Cemetery and has a fine tombstone which says "In memory of Robert Martins, noted draughts player, died 27th July 1904 aged 84" (is the birth date wrong?). Buried with him are his wife Lucie and five children.