Math Problems
- Thread starter AnonymousDeac
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AnonymousDeac
Well-known member
Wow, okay nice. And putting that formula into excel, you get the following options based off your success ratio, with the perfect score being that 292.5.
1 292.5
0.9 250.425
0.8 211.2
0.7 174.825
0.6 141.3
0.5 110.625
0.4 82.8
0.3 57.825
0.2 35.7
0.1 16.425
smallbigtall
jon gruden's haircut
I played around with it for a little bit. It's extremely complicated and conditional on a more than just a few things.
For example, if you miss two shots the entire time, there are three possible outcomes: (calculations are for total score)
1a) miss your first two shots: (2*0)+(1*7.5)+(17*15)=262.5
1b) miss your last two shots: (2*0)+(1*7.5)+(17*15)=262.5
1c) miss your first and last shots: (2*0)+(1*7.5)+(17*15)=262.5
2a) two consecutive misses, but not on first two or last two shots: (2*0)+(2*7.5)+(16*15)=255
2b) two non-consecutive misses, one on first shot, the other not your last shot: (2*0)+(2*7.5)+(16*15)=255
2c) two non-consecutive misses, one on last shot, the other not your first shot: (2*0)+(2*7.5)+(16*15)=255
3) two non-consecutive misses, neither on first or last shot: (2*0)+(3*7.5)+(15*15)=247.5
I may have left some scenarios out, but this gets even more complicated as the number of misses increases, since there are more possible combinations of consecutive misses, non-consecutive misses, consecutive misses on first/last shots, non-consecutive misses on first/last shots, etc.
For example, if you miss two shots the entire time, there are three possible outcomes: (calculations are for total score)
1a) miss your first two shots: (2*0)+(1*7.5)+(17*15)=262.5
1b) miss your last two shots: (2*0)+(1*7.5)+(17*15)=262.5
1c) miss your first and last shots: (2*0)+(1*7.5)+(17*15)=262.5
2a) two consecutive misses, but not on first two or last two shots: (2*0)+(2*7.5)+(16*15)=255
2b) two non-consecutive misses, one on first shot, the other not your last shot: (2*0)+(2*7.5)+(16*15)=255
2c) two non-consecutive misses, one on last shot, the other not your first shot: (2*0)+(2*7.5)+(16*15)=255
3) two non-consecutive misses, neither on first or last shot: (2*0)+(3*7.5)+(15*15)=247.5
I may have left some scenarios out, but this gets even more complicated as the number of misses increases, since there are more possible combinations of consecutive misses, non-consecutive misses, consecutive misses on first/last shots, non-consecutive misses on first/last shots, etc.
UMTerp
New member
LOL @ your complicated formulas.
Attempt 1: 0.6 * 7.5
Attempts 2 thru 20: 0.24 * 7.5 + 0.36 * 15
ANSWER = (0.6*7.5) + 19 * (0.24*7.5 + 0.36*15) = 141.3
Hello, new Wake board.
Attempt 1: 0.6 * 7.5
Attempts 2 thru 20: 0.24 * 7.5 + 0.36 * 15
ANSWER = (0.6*7.5) + 19 * (0.24*7.5 + 0.36*15) = 141.3
Hello, new Wake board.
AnonymousDeac
Well-known member
Now, unless someone can figure out that we did something incorrect, let me explain part 2.
Let's call Part 1 as always attempting to score in the white zone. For Part 2, we mix it up a bit. If you score in the white, you then attempt to score in the blue. Since you scored in white, all future scores in blue count as double points.
When you aim for the blue, you have three possible outcomes: 40% of the time you score 8 points (times 2 for double = 16), 40% of the time you score 6 points (times 2 for double = 12), and 20% of the time you score 0 points. However, you have to score the 8 points one for your next shot to count double, meaning the only time you will go for blue back-to-back is if you make your blue shot in that 8 points zone. However, in the 40% of times you score in the 6 point zone or the 20% of times you score no points, you then go back to white with your next shot.
The end goal is to figure out which strategy is the higher EV scenario. My brain is starting to hurt and I have a 4 hour meeting at noon so hopefully if it's not figured out by then, I'll be able to get it then.
Let's call Part 1 as always attempting to score in the white zone. For Part 2, we mix it up a bit. If you score in the white, you then attempt to score in the blue. Since you scored in white, all future scores in blue count as double points.
When you aim for the blue, you have three possible outcomes: 40% of the time you score 8 points (times 2 for double = 16), 40% of the time you score 6 points (times 2 for double = 12), and 20% of the time you score 0 points. However, you have to score the 8 points one for your next shot to count double, meaning the only time you will go for blue back-to-back is if you make your blue shot in that 8 points zone. However, in the 40% of times you score in the 6 point zone or the 20% of times you score no points, you then go back to white with your next shot.
The end goal is to figure out which strategy is the higher EV scenario. My brain is starting to hurt and I have a 4 hour meeting at noon so hopefully if it's not figured out by then, I'll be able to get it then.
AnonymousDeac
Well-known member
That's the exact same formula as here:
(((p^2)*15)+(((1-p)*p)*7.5))*19+(p*7.5)
I just have p equaling chance of success so if you want to fidget with the chance of success later, you can.
UMTerp
New member
By shooting for the blue every time you can, you have an EV of 154.208333... points in the game.
AnonymousDeac
Well-known member
Okay, but do you have any idea of how to figure out the white then blue method?
The thing is, I made up those percentages. The real goal is to find a formula solving for the two missing variables (of percent chance of the blue 6 pointer and percent chance of the blue 8 pointer) at which their rates make it better to use that method.
For example, while we started off part 1 using 60%, we were able to successfully find a formula that gives us our EV at any success rate. What about with two variables for the blue?
Last edited:
UMTerp
New member
UMTerp
New member
Who needs math when you have Excel? Just mess with the numbers in the third row if you want to change any of the parameters.
smallbigtall
jon gruden's haircut
This. I was playing around on paper and a TI-83 and mirrored his numbers through line four. Interesting how the expectations oscillate as the attempts elapse.
smallbigtall
jon gruden's haircut
Actually, I think this is the correct answer. The Terp's table didn't include the possibility of 15 points if your prior attempt resulted in 12 points in blue. It bumps the EV up by a pretty good amount.
UMTerp
New member
He said your next shot doesn't count double in that case.
