This is the value of the Brand...
The problem is that there are 200,000 games on the app store, and no one has ever heard of 199,000 of them.
But tens or hundreds of millions have heard of "Risk" or "Stratego", "mousetrap" etc.
So if were to for example, make a Stratego game, the value of the brand would be 90% of the value of the game and your implementation would be 10% of the value.
If it's a popular game, they probably have had multiple offers to make their game for mobile.
I presume you've checked to see if this game is already available?
If not, then I'd definitely contact them. They may be a small enough game that they'd like to see their property ported to mobile. A somewhat riskier plan would be to go ahead and make the game, but not use any of their artwork, names, logos, etc. Then contact them and say that you have a finished "zero sum" game, ready for market, but that you'd like to talk to them about branding your game with their property. That can be more attractive for a small/medium sized brand, since they don't have to take your word that you'll make the game--you've already done it. Yep, that's riskier (because if they say no then you may be stuck), but, hey, business is about taking risks.