I advocate the same (teaching kids) Poker for the same reasons you mentioned (certain self-control and tactical/strategy concepts) but this is often greeted with controversy anytime I voice it.
Learning to weigh the odds, exercising patience, taking calculated risks in the face of incomplete information, making allowance for the vagaries/emotions of your opponent all seem like great skills that would help one in life.
However, people often voice indignation at teaching kids the "vice" of gambling.
I agree that poker teaches many useful lessons about probability and weighing your decisions, but it's not just a moral panic to say that's it's maybe not the most appropriate game for kids. Poker is genuinely very harmful for a non-trivial number of it's players, and it can be a destructive force in a way that (say) chess is not. I've had more than one friend lose tremendous sums of money and had to go cold turkey on the game, lest it completely ruins their life.
Started looking at backgammon after reading your comment. I find it fascinating. I'm probably going to go ahead and invest some time learning it. Thanks.
I found this section on the Backgammon Wikipedia page relevant to this discussion:
Yeah, Backgammon is rad, I really enjoy playing it. It's also an incredible tool to teach both probability (given that you use two dice, and understanding the probabilities of dice events is crucial) and risk/reward judgment calls. It teaches many of the same lessons of poker, but without the gambling aspects.
As for the section on that page, you could make the same arguments about monopoly, or any game that uses dice. Backgammon can be played for money like any game, but it's not the usual way to play it, and it's not integral to how it functions. Indeed, the conclusion of the judge in that case was that it was NOT gambling, but a game of skill.
There's gambling on backgammon in the same way there's gambling on chess (or any game): sure, you can play for money, but that's not really the usual way to do it. Nothing in the game requires it. Backgammon clubs work essentially like chess clubs.
And no, the doubling cube does not make it similar to poker. The doubling cube is just a way to add another element of risk/reward to the game. In poker, you literally have (fake or real) money in front of you and the entire point of the game is moving that money into the pot and trying to win the pot to gain more money. There's nothing comparable in backgammon.
Poker is great. The other big thing it teaches is that luck is real. A hand can be played perfectly, and the player can still lose. Long term, the better player will win, but any player can get sucked out on any given hand. Losing in this way is tough, but a great lesson.
Winning 50NL poker player (US) here. That's basically as good as you're gonna get without spending a ton of time. I've probably played somewhere around 3k hours of poker, with about 1k hours live and 2k online.
You will be a top 20% poker player if you can do two things right. 1) Play the hands you should preflop. This is the poker equivalent of learning blackjack strategy. "Starting hand ranges poker" will start you down that rabbit hole. 2) Figure out pot odds. If you have a straight draw, how often will it hit and is that worth calling a bet? That takes a bit of math that seems hard at first, but gets a lot easier as you start to cache common scenarios. Google "Pot odds poker" to go down that rabbit hole. Review interesting hands and share them online. twoplustwo is the "main" poker forum. Good luck!
I had the good fortune of being introduced to it by someone who was steeped in Poker theory (a colleague at work).
Following that I picked up some more formalism from the book by David Sklansky that features prominently in the other comment in response to your question.
However, the person I mentioned before had already given me a head start on most of the practical aspects mentioned in the book. I also benefited from having him to practice against and learn from.
Learning to weigh the odds, exercising patience, taking calculated risks in the face of incomplete information, making allowance for the vagaries/emotions of your opponent all seem like great skills that would help one in life.
However, people often voice indignation at teaching kids the "vice" of gambling.