I computed those numbers via exhaustive search through all possible combinations. Doorcards are assumed to be neutral/unknown. Maybe I'll do some computations with known doorcards if someone comes up with an interesting example. Feel free to verify the numbers by comparing with charts from the net or via manual calculation.

3rd Street:

We start with a quality hand, 3 wheel cards, such as



Probability of improving to 8-or-better-low: 48%
Probability of improving to 7-or-better-low: 33%
Probability of improving to 6-or-better-low: 19%
Probability of improving to wheel: 7%

4th Street:

We catch a nice card:



Probability of improving to 8-or-better-low: 71%
Probability of improving to 7-or-better-low: 59%
Probability of improving to 6-or-better-low: 43%
Probability of improving to wheel: 23%

We catch a brick:



Probability of improving to 8-or-better-low: 32%
Probability of improving to 7-or-better-low: 21%
Probability of improving to 6-or-better-low: 11%
Probability of improving to wheel: 0.04%

We don't have to give up yet. Look at the opponent cards, unless someone shows 2 wheel cards, we can still continue with the hand.

5th Street:

Continuing with the brick on 4th and catching on 5th:



Probability of improving to 8-or-better-low: 57%
Probability of improving to 7-or-better-low: 45%
Probability of improving to 6-or-better-low: 31%
Probability of improving to wheel: 16%

6th Street:

Continuing with the last hand, not catching on 6th:



Probability of improving to 8-or-better-low: 35%
Probability of improving to 7-or-better-low: 26%
Probability of improving to 6-or-better-low: 17%
Probability of improving to wheel: 9%

This is interesting. We can still call a bet here I suppose, unless the 5s are dead and there's a risk of being up against a made wheel already.

Final note: The above percentages for improving to a wheel apply to all wheel cards, so if we have 542A on 4th for instance the numbers are the same of course. It also doesn't matter if we catch a king or queen on 4th. The cards shown above are just examples. You can use those numbers whenever you have a scenario with wheel cards / bricks showing as in the hands above. The order also doesn't matter, if you have K23 in the hole and catch an ace, you're in the same spot as having A23 and then catching a king.

Nice post, rep +1