Size and complexity of the search space (i.e., the game tree). The tree is several orders of magnitude larger for poker than for chess.
I've spent a non-trivial percentage of my life both playing and researching AI for poker. See http://poker.cs.ualberta.ca/publications/billings.phd.pdf for an initial discussion on the differences between the 2 games' search trees. He notes that for 2-player, limit hold-em, the game tree consists of 1,179,000,604,565,715,751 nodes. The tree expands exponentially as you add players and different betting sizes. For no-limit and other real-valued variants like pot-limit, the game has an effectively infinite search space.
If I recall, there are more possible chess games than atoms in the universe. So even if you were to quantify toughness as number of possible decisions, it would still be completely off. However, in both those games, a lot of the plays would be ridiculous.
It's easier to try and measure toughness by the time/effort it takes to be competent or the best. In this case I would say chess is hands down much tougher.
Sure, the number of possible moves is huge in both games. However, it's more about the number of relevant moves at a given game state. Alpha-beta algorithms for chess can do a much more thorough search than their poker-specific extensions and related methods like MCMC.
I suppose if you're measuring difficulty of a game as how difficult it is for a human player to beat the current masters, then that seems a little unfair. Poker has been around for less than 200 years and the current variants are less than 100 years old. Chess has been around since the late 1400s according to the Wikipedia article. There has been a lot more research and time spent on chess, and the community is consequently much more mature and skilled.
To clarify, before you were comparing a tree of every possible move in a chess game against the decisions in a poker game?
That has to be a joke to compare the games that way. Even here you mention number of relevant moves at a given game state. I have to be misunderstanding that. Bet/check/fold vs say half dozen candidate moves?
I've been assuming difficulty for a human the whole time, to attain any level of skill. Since the chess community/theory is more established, it's going to be a more difficult game.
A game tree search is not defined by the available options for the very next move. It's about the total possible paths to the end. In this case, poker is a much larger tree. Read the intro section of Darse's PhD dissertation that I linked to above and you'll understand.
Right, that would be what I meant by the poker-specific extensions. Most chess algorithms use minimax to search the game tree. The UoA team has extended the basic minimax algorithm to other variants like miximax which can handle partial information and stochastic outcomes.
I've spent a non-trivial percentage of my life both playing and researching AI for poker. See http://poker.cs.ualberta.ca/publications/billings.phd.pdf for an initial discussion on the differences between the 2 games' search trees. He notes that for 2-player, limit hold-em, the game tree consists of 1,179,000,604,565,715,751 nodes. The tree expands exponentially as you add players and different betting sizes. For no-limit and other real-valued variants like pot-limit, the game has an effectively infinite search space.