1. if you get 3 card of a wheel (7,5,4,3,2), what is the chance you make a 8 low?


2. if you get 4 card of a wheel, what if the chance you make a 8 low?

I presume you mean that you are dealt 3 or 4 wheel cards and you want to know the prob of making an 8 low or better by the end of the three draws.

Of course, the 4-card case is easier. Excluding draws that would make a flush, straight, or pairs, I count that there are 66,087,672 deals out of a grand total of 124,531,200 deals that would make either a 7-low or 8-low if originally dealt four wheel cards. This is 53.07%.

The 3-card case is more difficult, especially if you don't have special software to handle triple draw. I will look into it tomorrow if I have some time.

Lacking specialized software applicable to triple-draw, I attempted to calculate the 3-card case in a spreadsheet. Since a spreadsheet is far from the ideal environment there is no guarantee that I got the correct result.

I find that the overall probability of making a 7-low or 8-low hand at the end of three draws when dealt three wheel cards is 39.27%.

The cases run from the highest probability of around 44% when you are dealt 752 rainbow to the lowest probability case of around 34% when you are dealt 543 single-suited.

Before using these results for anything of importance, I would seek confirmation (or rebuttal). Maybe someone handy with a poker simulator can look into this.

Since the 752 rainbow case is so straightforward, I was able to program a simple triple-draw simulation for it. I ran the simulation for 10,000 deals and a player starting with 752 rainbow (and two other bad cards) makes either a 7-low or an 8-low hand in 4,293 deals, which is, obviously, 42.93% of the time.

I am now more confident that the results posted earlier are probably correct.

Thanks!