The usual is the combination is chess / checkers / backgammon. Some many even have a deck of cards and dominoes included. This is the first I've seen with a roulette wheel.
Combination game sets

The older ones of any size almost always had roulette (and cribbage). There were also a lot made that were much smaller (and therefore didn't have as much in them).
I have a couple of these (this one isn't mine but it is pretty much identical to mine). There is a scrabble game included here.
This one isn't mine but I have several of these. The chips, dice and backgammon pieces (which are aout 3/4" in diameter) would sit in the shelf/compartments. Usually there would be the wood divider , two decks of cards and a cribbage board. (Occasionally the divider and cribbage board would be bakelite). I have two that came with a small wood chess set and only one deck of cards.
One of the many things I collect besides chess sets are combination game sets (generally housed in briefcases) that were popular in the twenties and on up until even today - their heyday was in the post WWII period through the fifties. This is a pretty good example that I recently picked up:
Most of the stuff in here is made of bakelite - the backgammon/checkers, the roulette wheel, the dominoes and the dice that are original (not all the dice here are original). The dice cup may not be original since most of those were bakelite. It is missing a few things - some of the dice,a cribbage board and two decks of playing cards.
The chess set is a gallant knight (probably a 2 3/4" or a 2 1/2" set - it doesn't have the "x" on the rooks that gallant knight usually has - the companies likely had gallant knight produce them and since they weren't marketed as such the "x" was omitted either by the company or by gallant knight. (The pieces are made of tenite and are weighted and felted.) There are several companies that might have made this game set - my guess is that is was made by either Pattberg or Rottgames. When it gets to me I will likely be able to figure it out.
The boards used in these were generally nice heavy duty ones that folded and stored in the lid. The covering material is black and the white squares were painted on. (The back side is a backgammon board and is also painted on.)
Some of these sets were huge - big enough to be a small suitcase. (Some were much smaller.) They could contain all sorts of games - for example I have some that have horse race sets (some with cast iron horses) and some that have chuck a luck cages.
The case is really rough on this one - so I am going to use the various pieces to fill out other sets that are missing components.