That's why I am looking for one that is designed specifically in such a way as to deter computer algorithms/heuristics or render them less effective than human brains (and not just those at the elite level of the game ---although if arrived to point of exceeding over half of club+ -level players, then outperformance of top humans likely not far away) shy of self-learning AI, without sacrificing the underlying 'puzzle' theme, with potential even still for tactics.
What strategy-based board games will never be bested by computers?
Arimaa is a game that was designed to be easy for humans to learn and play, but difficult to program a computer to play. It can be played on a chess board with chess pieces, but as it became (relatively) popular, unique boards and pieces were created for it.
The link I posted is to the Wikipedia page for Arimaa - the page talks about the rules to Arimaa and also (in my opinion, more interestingly) Omar Syed, the game's creator.

I believe computers haven't conquered Go yet, so until now I guess Go still has not been 'solved' by a computer.
Neither chess nor go are close to being "solved" by computers, but both have computer players that are better than the best humans now.

I believe computers will dominate humans at every pure strategy game. The only way to avoid that is to go for games so obscure that nobody's created a top notch computer program for them yet.
I'm a big fan of the game Yinsh. It has surprising depth, world class players use a variety of different playing styles, it can be strategic or tactical. There's no appreciable advantage to going first or second, there's no opening theory to learn, draws are very rare, and the games are shorter and faster than chess. They're more competitive too: you never fall in such a big hole in the opening that you can't recover from it.
The one big downside is that nobody plays it.
https://boardgamegeek.com/boardgame/7854/yinsh

I believe computers will dominate humans at every pure strategy game.
The question here is: what is meant by bested?
Computers will be "better" than any (not-artificially enhanced) human being in the future I guess, Maybe there will be a computer with a database that will contain all possible games from move one to the last move, be it checkmate, win, loss or draw. When this happens it will be: "White begins and wins".
It will mean that whatever game you're playing, the computer has already played it and you can look it up and find the logical conclusion of the position. But the computer has to be complete in ALL possible games and this amount is staggering. It is close to infinite. The question remains: is it doable?
Until then I'll be happy continuing to play against not-perfect human beings.
Once I thought computers could never beat the world champiom at chess because the number of possible moves gets to big. Some thirty years ago this has been proved wrong depriving the game of its magic to non players. But go has to be impossible because the possiblities are astronomical? No, Hassabis program does not need bruce force. A neural network suffices apparently for machine learning to the level of top professionals. I agree with iProCheckmateKing that closes the discussion once and for all.
Another thing is when will a computer be able to explain these games so everyone can easily make progress. Once that is acchieved I think the fun of playing is ruined once and for all and I do think it will happen within another decade.
As for solving a game like chess or go I think its a pure academic discussion. Even if something like that would happen the "solution" would not mean a thing even to the world champion. Its like solving the R+B vs R ending where no one can learn the tablebase by hard.

Stratego, because there is luck involved.
The same can be said about Backgammon! A computer can easily figure out if they win the face off with 6-2 that going 13-11 and 13-7 opens up fewer combinations to put his chip on the bar (17 ways, the first 2 leading to both chips on the bar: 64 46 51 15 42 24 33 61 16 62 26 63 36 65 56 66 22) than going 13-11 and 24-18 (33 ways, two on the bar with 15 51 65, 56 16 61, or 66, though the first four send far back chips home at the risk of near bearing off chips having to go all the way around again, and 61 16 sends 2 chips on the bar for only 1 exposed, but it's on the 1-spot, would have to go all the way around again, 66 would of course suck - 13-7 (bar), 13-7, 7-1 (bar), 7-1): 11 12 13 14 15 16 21 31 41 51 61 26 36 46 56 66 65 64 63 62 52 53 54 55 45 35 25 24 42 23 32 33 22 - Everything except 43 34 44).
That said, I don't claim to be a master at Backgammon, but I've played my fair share of it, and I can tell you that I would easily do 24-18 and 13-11 long before I'd do 13-11 and 13-7. Sure there may be more ways to get captured in the former case, but many of those captures are extremely undesirable. Like if you roll 5-3, are you going to use the 5 to play 6-1, capture my guy in the back anyway, and risk having to go all the way around the board again if I throw a 1 on either die? (11 out of 36 chance)
So it's a much more complicated game than just the math of how many of the 36 possible rolls puts me on the bar! Doubt computers have it all figured out!
Stratego, because there is luck involved.
The same can be said about Backgammon! A computer can easily figure out if they win the face off with 6-2 that going 13-11 and 13-7 opens up fewer combinations to put his chip on the bar (17 ways, the first 2 leading to both chips on the bar: 64 46 51 15 42 24 33 61 16 62 26 63 36 65 56 66 22) than going 13-11 and 24-18 (33 ways, no way to put both on the bar: 11 12 13 14 15 16 21 31 41 51 61 26 36 46 56 66 65 64 63 62 52 53 54 55 45 35 25 24 42 23 32 33 22 - Everything except 43 34 44).
That said, I don't claim to be a master at Backgammon, but I've played my fair share of it, and I can tell you that I would easily do 24-18 and 13-11 long before I'd do 13-11 and 13-7. Sure there may be more ways to get captured in the former case, but many of those captures are extremely undesirable. Like if you roll 5-3, are you going to use the 5 to play 6-1, capture my guy in the back anyway, and risk having to go all the way around the board again if I throw a 1 on either die? (11 out of 36 chance)
So it's a much more complicated game than just the math of how many of the 36 possible rolls puts me on the bar! Doubt computers have it all figured out!
They likely will be in time. There are different ways to play games of gamble: risky or safer; short timeframe or long haul; how much to water. Depending on the programmed goal there is likely one or maybe two equally probable beneficial system to apply for maximizing returns.
Are there as yet any worthwhile spatial/logic-based boardgames that are sufficiently complex or rely heavily enough on human wholistic reasoning that take too much search depth to be supplanted/surpassed by computer-programming without inciting chance elements (e.g. dice, shuffling, drawing) in the foreseeable future?