We all know that chess is considered the ultimate of strategy games. It's about the long term game not the short term. Yes of course tactics come into it but only to set up your battle plan for the long term strategy.
It's not the only game where this is true. A lot of board based games - the less random ones - are built this way. In fact, I'd go so far as to say all the best games are made this way. Games such as 'snakes and ladders' are fun to play with young ones, but only because of all the groans and taunting involved. The game itself has no skill element and the result is purely random - pretty boring for repeated play. There are a couple of variations you might like to try and introduce however which add some skill element to the play. Firstly you can add a rule to allow players to move any amount of spaces up to the maximum of that rolled by the die. This is an easy adaptation for youngsters, which simply means they now have to look out for ups and downs on the way and choose the best ones. Not a lot more interest, but slightly better. You can then shift towards a game where both players can move either counter and the player who moves the last counter home is the winner.Slightly more challenging and it has to be better for the brain.
Another of the world's most popular games designed for randomness, but thought by many who play it not to be, is the lottery. Of source designing a true random machine is a complex science in itself. One could argue it is fundamentally impossible to design something truly random. Problems even come with testing such a lottery draw machine to see if it is random. At what point do you declare it truly random? The answer is that you don't - you declare it sufficiently random to a certain tolerance of error. Which does leave open the potential for that game to have an element of bias or predictability. In reality it's unlikely to be of any use, but that's not the only strategy one can apply to such games. When you play, how you order you selections, and even which lottery game you choose all affect that overall strategy. Though to be honest most people just jump on the game with the biggest jackpot, typically Euromillions and play that. Of course stopping to compare the odds to decide if to play Euromillions or Lotto could make a marked difference to the ultimate result - but few bother to consider it.