Howdy!

I'm very interested in knowing the mathematics behind a NLHE starting hand chart! There must be a general "approach" when making these charts, right?

I realize that a complete derivation of a hand chart is a great deal of work and probably very hard to find.

Books, studies, videos- anything on this subject is greatly appreciated!!

Thanks, - TheInterested

There are two common ways to create a hand chart.

First is well-defined mathematically, but not always relevant to play. You can ask what the probability that each given hand will win a pot dealt to showdown versus some number of other random hands. This can be simulated or computed. The number of other hands matters somewhat.

Other rankings are based on playing assumptions. If a small pair wins the pot, for example, it is often because it formed a set on the board. But if the card that forms a set is on the turn or the river, the small pair is not likely to see it. So 40% of its set wins are irrelevant.

Similarly, straights and flushes will generally be folded if they require both turn and river to complete. That's 10 / 21 = 48% of them.

Hand tables based on playing assumptions are created by a combination of math and judgment.