The basic code in South Dakota is such that simpler is better and it makes any form of gambling not specifically authorized by the state a Class II Misdemeanor.
While bookmaking is separate and carries with it stiffer penalties, it seems that the basic law in South Dakota would be applied equally to both players as well as operators.
The text is below:
22-25-1. Gambling defined--Keeping gambling establishment--Letting building for gambling--Misdemeanor. Any person who engages in gambling in any form with cards, dice, or other implements or devices of any kind wherein anything valuable is wagered upon the outcome, or who keeps any establishment, place, equipment, or apparatus for such gambling or any agents or employees for such purpose, or any person who knowingly lets any establishment, structure, place, equipment, or apparatus for such gambling is guilty of a Class 2 misdemeanor.
It would seem that the first part of that could be applied to players and the general term, “Implements or devices,” could be argued as covering computers in the event that an individual is gambling on the Internet.

This is another one of those oddball states...
...that seem to make it illegal for people acting as mere players to gamble, but then also gives them the ability to recover any losses (within six months) via lawsuit. Again, it seems counterintuitive because the player would be trying to recover losses that were incurred during the commission of what is technically a crime.
Further codes in South Dakota address Internet Gambling, but only have separately listed penalties for operators. It doesn’t explicitly say so, but it is quite possible that the first part of the code would generally only be applied to operators.
In any event...
...there is little information pertaining to any gambling-related arrests in the state, perhaps because it is so sparsely populated. Therefore, we definitely have not found any instances of anyone arrested for gambling online as a mere player, but in our searches, I believe we have only ever found one instance in any state in the entire country.
For that reason, almost all online casinos who make their services to players in the United States do the same in South Dakota, and they can be found below: