Suited bonuses

[Aisthesis]

Another aspect of comparing wrappy hands is attempting to quantify just how the suits figure in. On wraps not including a suited A, we're really just talking about redraws when you already have the made nuts. But the bonuses can be significant, I think.

I think it's pretty clear that ds is the best suited bonus. Since about 55% of all boards are 2-suited, you're going to hit nearly half of these. So, you get a strong redraw in roughly 25% of all situations where you have your straight.

Second place here is ss, which I'm restricting to exactly 2 of a single suit (hence taking away none of your own outs). Here, you'll get your redraw almost exactly half that much, so let's call it 13% of the time.

3-suited is pretty similar, although 2 things go down. You get your redraw slightly less often because you've taken away one of your outs, and your redraw is slightly weaker for the same reason. So, something like 12% of the time you get a slightly weaker redraw.

Same on 4-suited: Slightly weaker draw and slightly less frequent.

Rainbow is certainly the weakest of all, since you are guaranteed to have no flush redraw.

I'll thus propose the conclusion that 4678ds is about as strong as 5678r (?)--maybe even a little stronger.

[Kuso]

[Aisthesis]