Ok, finally worked things out for climbing without a stopper, and including single jumps. Can't guarantee its accuracy, but it seems solid.
Results vary based on the amount of risk you're willing to take. That is, if you're at floors 92-98, do you take a random jump when there's a risk of going past 100? This is measured by the jump gap -- how many floors away from your target you're willing to still use a random jump. It has the same range of values as the limits on the jump -- 2 to 9 floors.
As the target of most interest is floor 100, will examine that.
Code:
Gaps/Risk of overshooting
Jumps 9 Risk 8 Risk 7 Risk 6 Risk 5 Risk 4 Risk 3 Risk 2 Risk
13 0.01% 0.00% 0.01% 0.00% 0.01% 0.01% 0.01% 0.01% 0.01% 0.02% 0.01% 0.02% 0.01% 0.02% 0.01% 0.02%
14 0.07% 0.00% 0.11% 0.04% 0.15% 0.10% 0.17% 0.16% 0.18% 0.22% 0.20% 0.27% 0.20% 0.31% 0.21% 0.34%
15 0.40% 0.00% 0.64% 0.20% 0.83% 0.51% 0.98% 0.89% 1.09% 1.28% 1.18% 1.66% 1.24% 2.00% 1.29% 2.30%
16 1.45% 0.00% 2.25% 0.55% 2.92% 1.51% 3.47% 2.73% 3.93% 4.11% 4.30% 5.55% 4.60% 6.97% 4.79% 8.33%
17 3.85% 0.00% 5.72% 1.07% 7.36% 3.01% 8.78% 5.63% 10.02% 8.76% 11.08% 12.23% 11.93% 15.89% 12.46% 19.61%
18 8.21% 0.00% 11.65% 1.57% 14.77% 4.54% 17.60% 8.74% 20.13% 13.95% 22.32% 20.01% 24.05% 26.70% 25.07% 33.85%
19 14.97% 0.00% 20.34% 1.94% 25.34% 5.70% 29.97% 11.16% 34.15% 18.17% 37.73% 26.57% 40.45% 36.18% 41.97% 46.81%
20 24.34% 0.00% 31.85% 2.14% 38.94% 6.37% 45.52% 12.60% 51.40% 20.77% 56.29% 30.76% 57.54% 42.46% 44.27% 55.73%
21 36.40% 0.00% 46.10% 2.23% 55.24% 6.67% 63.62% 13.28% 70.90% 22.03% 67.14% 32.86% 54.27% 45.73% 39.46% 60.54%
22 50.74% 0.00% 62.50% 2.26% 73.43% 6.78% 83.18% 13.53% 77.48% 22.52% 66.29% 33.71% 52.91% 47.09% 37.38% 62.62%
23 65.92% 0.00% 79.40% 2.27% 91.62% 6.81% 86.39% 13.61% 77.33% 22.67% 66.01% 33.99% 52.44% 47.56% 36.65% 63.35%
24 79.53% 0.00% 94.22% 2.27% 93.18% 6.82% 86.37% 13.63% 77.28% 22.72% 65.93% 34.07% 52.31% 47.69% 36.43% 63.57%
25 89.53% 0.00% 97.73% 2.27% 93.18% 6.82% 86.36% 13.64% 77.27% 22.73% 65.91% 34.09% 52.28% 47.72% 36.38% 63.62%
Here we have a complex interaction between the number of jumps you make and the gap you've chosen as the limit. You need to be able to reach single-climb range earlier than your absolute max number of climbs, but the closer you try to get in that range, the higher the risk of overshooting.
Working down the list of the number of jumps you think you can clear, we can work out the highest chance for success based on the gap value.
Code:
Jumps Gap
25 8
24 8
23 7
22 6
21 5
20 3-4
19 2
18 2
17 2
16 2
15 2
14 2-4
13 any
So until you can hit 20 jumps, you pretty much want to restrict yourself to randoms unless you hit floor 99.
But then there's the flip side -- if you -could- have cleared an additional floor, but took the risk and failed. At what point does the risk of failure outweigh the benefits?
What we want to look at here is whether the increase in risk as you drop the gap value is higher than the increase in chance of success. In all cases with a gap of 5 or less, the increase in risk is higher than the increase in reward, or at best 0.
However a better way of looking at it would be as such:
How much additional risk is incurred by dropping the gap by 1 point (eg: with 18 jumps, a 5 gap is 13.95%, a 4 gap is 20.01%)
If that additional risk was instead applied to an additional floor at the current gap level, how much of an increase in success would you see?
(eg: 18 floors at gap 5 is 20.13%; 19 floors at gap 5 is 34.15%; 20.01% - 13.95% = 6.06%; 34.15% * 6.06% = 2.07%
If that potential reward was added to the existing reward, would it beat the reward of dropping the gap value?
(eg: 20.13% for 18 floor/5 gap + 2.07% = 22.20%; 18 floor/4 gap is 22.32%, which is higher than the gain of converting the risk to an additional floor)
So for this example, the additional risk of lowering the gap is worth more than the chance at an additional floor at the current gap.
After accounting for that, we have a new set of optimal gap selections.
Code:
Jumps Gap
25 8
24 7
23 7
22 6
21 5
20 3-4
19 3
18 3
17 3
16 2-3
15 2-3
14 2-4
13 any
For the common viable range of jumps -- 15 to 20 -- it looks like a gap of 3 is your best overall choice. That is, random jump on floors 97 or less, and only single climb from 98 or 99.
So, given that, we can give a quick summary of the chances of reaching floor 100 for a given number of jumps, using a 3 point gap (except for 21 floors, which gets a 5 point gap):
Code:
14 0.20%
15 1.24%
16 4.60%
17 11.93%
18 24.05%
19 40.45%
20 57.54%
21 70.90%
Obviously all this is moot once they introduce the stopper, but hopefully it can be useful for those using the current system.