Not only pirates, but British sailors also had their allowance of rum. The Royal Navy gave sailors a rum ration, called a tot, of 1 pint per day. The rum, known as grog, was diluted with 2x water and, after 1756, some lemon or lime juice to prevent scurvy. The rum ration was continued until 1970. Alternatives to rum were Beer(1 gallon/day) and wine/arracks or other spirits.

For $1000 a bottle you can get some Black Tot "Last Consignment" British Royal Naval Rum. It is the leftover RN rum from 1970, pour a pint add 2x water and some lime juice and you should have something close.