I'm typing all of this out here so I can link to it later when I need to show this to someone. It's a toy poker game that can be used to illustrate a large number of important ideas and concepts. I'm also going to change things up a little from how this is normally presented for the sake of clarity.

The Rules

We're heads-up with two players that we will call Hero and Villain, with Hero always in position. We use a deck that contains one each of three cards (an Ace, a King, and a Queen). Each player posts a $0.50 ante and is then dealt a card out of the 3-card deck.

After the cards are dealt, Villain checks in the dark. Hero then has to the choice to make a bet of size B or check to see a showdown. If Hero bets, then Villain has the options to either fold or call to see a showdown. At showdown the high card wins.

Hero's Strategy

If Hero is dealt an Ace, he always bets because there is a non-zero chance that Villain will call, making betting better than calling. (Similarly, you wouldn't check behind the nuts in poker on the river). If Hero is dealt a King, he always checks because he can't get his opponent to fold a better hand (Villain never folds an Ace for obvious reasons) or call with a worse hand (Villain never calls with a Queen for obvious reasons). If Hero is dealt a Queen, he will have the option to bet with it some percentage of the time since he can possibly get his opponent to fold a King.

Villain's Strategy

Villain only gets to make a decision if he's facing a bet. With an Ace he always calls. With a Queen he always folds. With a King, he has the option to call some percentage of the time since he can possibly pick off his opponent's bluff.

Looking at these two strategies show an example of looking at a player's entire range and deciding how to play the entire range, an important skill.

Essence of the Game

The real point of this game is that Hero and Villain only make 1 decision each. Hero decides how often to bet a Queen, and Villain decides how often to call with a King. Everything else is forced.


So talk about this a bit and see what you can figure out and I'll post more on this later.