Some "higher" STEPs math.

[buddybudrow]

Not if you're talking about the average player. Each of those has a 10% chance of moving the player back up a level from where they went down to. Very small compared to the stuff I accounted for. I would challenge you to prove otherwise mathmatically

[Nottom]

When you are talking about calculating the odds a player will go all the way up though the steps starting at lvl 1, discounting the free re-tries they get is a significant error. I don't feel like doing the math, but this seems obvious

[buddybudrow]

Let's make an estimate of the effect of these terms and see what the numbers show.

1) Take the effect of the step 1 re-rolls you get from step 2. Because of the large number of hands, this will be the largest of the "unaccounted" terms. Take the needed 458 step 2s from my equations. Of those 458 step 2s, 458* 30%(places 5 thru 7) = 137.4 step 1 re-rolls. From those 137, 1/6.67 (from the calculations will advance to step 2) = 137/6.67 = 20.5 extra step 2s. Continue the division for each step -

step 3s = 20.5/7.7 = 2.66 extra step 3s
step 4s = 2/66/8.33 = 0.32 extra step 4s
step 5 = 0.32/7.14 = 0.05 extra step 5s

2) Take the effect of the step 3 re-rolls you get from step 4. Same calculation as above. The 7.14 needed step 4s * 20% (places 6 and 7) = 1.42 extra step 3s

step 4s = 1.42 /8.33 = 0.17 extra step 4s
step 5 = 0.17/7.14 = 0.03 (rounding up) extra step 5s

Since the two examples are roughly the same, lets just say that for each instance of a lower level re-roll you get it adds an extra 0.05 (I'll use the higher of the two) step 5 plays. There are 7 places within the structure that you get lower level re-rolls. 7*0.05 = 0.35 extra step 5s. This is actually higher than I thought it would be, so you are partially right.

So for the 3056 step 1s started you actually get closer to 1.35 step 5 plays. The number of step 1s starts need to get 1 step 5 entry is then 3056/1.35 = 2264 step 1s.

As a result a better estimate of the cost to reach a step 5 is 2264 * $33 = $74,700. So, I stand corrected. The lower level re-rolls have a bigger effect than I thought, but I think this shows the cost is still much higher than the $23K number. I think the $74K is a pretty close estimate. However its still just an estimate, which by the way I spent way too much time on. I am now brain-dead from all the math. Time for a beer!

[Nottom]

Ok but what about the step 1s you get from moving down from step 3 or from moving up from a freerolled step 2 and winnign another step 1. Unless I'm missing somethign, these still aren't accounted for, and these add up very quickly.

[buddybudrow]

I counted it. Its one of the 7 step down opportunities I accounted for. In actuality there are only 5 loop back spots in the structure. Not sure where I got the 7 from. (beer deprivation) I'll calculate it to see if its close to my 0.05 each estimate.

59.5 step 3s * 10% (9th place) = 5.95 extra step 1s
5.95 step 1s/6.67 = 0.89 step 2s
0.89 step 2s/7.7 = 0.116 step 3s
0.116 step 3s/8.33 = 0.014 step 4s
0.014 step 4s/7.14 = 0.002 step 5s

In my updated estimate I accounted this term for an extra 0.05 step 5s, not the 0.002 calculated here. I'll stick with the 0.05 number though and redo it for the actual 5 looping spots instead of my imaginary 7.

3056 step 1s gets 1 + 0.05*5 = 1.25 step 5 entries
3056/1.25 = 2444 step 1s entries required

2444 * $33 = $80.6K

Probably more becuase I've proven that at least two of the 5 looping spots account for less than the 0.05 I used in this rev 3 estimate.

[Apathy]

[ QUOTE ]
Not if you're talking about the average player. Each of those has a 10% chance of moving the player back up a level from where they went down to. Very small compared to the stuff I accounted for. I would challenge you to prove otherwise mathmatically

[/ QUOTE ]

Work through the algebra solution given, you will see your error.

[buddybudrow]

I stand corrected. I worked through the S1 equation numerically and see how you get the 1/5 number. I have to assume the coefficients to all your other equations are correct as well. Did you use some sort of series expansion to account for all the looping correctly? I would be interested to see how you got the coefficients for all the terms in your equations. I'm a little rusty on my math I haven't used since college.