I have been playing quite a bit of game lately as well as HORSE. I decided to have a look at the maths in some of these and started with 2-7 Triple draw, mostly because i didnt actually know the rules of the game.

Anyway here are my ideas.

1. The single card needed situation. You have something like 2,3,6,7,X where X is no good a pair or A,K.

On the first draw you need a 4 or a 5 which will arrive 17% of the time, which is not good. However if you continue for all three draws you will make your hand 43% of the time, this is very good in a multiway pot. You will always have the odds if 3 are playing and you go all the way. Importantly if you allow the 8 to be an out also your % of making an 8 high low hand goes to 58%. Making you a favourite even in Heads up as long as the other person isnt standing pat.

2. The double card draw. This time you have something like 2,3,7,XX where both the X cards need to be changed.

This time your odds of getting both cards on the first draw is less than 6%. It is also only 16% if you go through all 3 draws.

This has interesting implications. If you are heads up and the villain draws 2 cards or more he will miss 84% of the time. Bluffing opportunities here are large, also if you only need to draw one card you are a an 81% favoutite to win the hand, probably as good a set of odds as you will get anywhere in poker.

any comments much appreciated.