Reputation
Top tag
Next privilege 250 Rep.
View close votes
Badges
9
Impact
~2k people reached

Aug
17
comment Expected travel of random walk in arbitrary game with multiple payouts
@Did: Can you expand the formula for clarity? I think by a 'mean increment', you're referring to the expected payout (which is $prob_1*pay_1 + prob_2*pay_2 + prob_3*pay_3$), but I'm not sure how to interpret o(N) from your comment...
Aug
17
comment Expected travel of random walk in arbitrary game with multiple payouts
@Did: Ah, in that case, can you give me the new revised formula which takes into account non-centered paytables?
Aug
17
comment Expected travel of random walk in arbitrary game with multiple payouts
@Did: Thanks for the feedback. Your formula works for the coin and dice rolls, but when I tried for three entries or more, it differs from the simulation. An example is: probabilities = [0.75, 0.1, 0.15] and payout = [-1, 0.5, 4.5]. That's a variance of 3.811875, but the average 'travel' according to your formula is 155.779 (to 3dp), whilst I get approx 268.8. Could you check your formula?
Aug
17
revised Expected travel of random walk in arbitrary game with multiple payouts
deleted 10 characters in body
Aug
17
revised Expected travel of random walk in arbitrary game with multiple payouts
added 64 characters in body
Aug
17
revised Expected travel of random walk in arbitrary game with multiple payouts
deleted 1 character in body
Aug
17
revised Expected travel of random walk in arbitrary game with multiple payouts
added 42 characters in body
Aug
17
asked Expected travel of random walk in arbitrary game with multiple payouts
Jul
4
comment Algorithm for tetration to work with floating point numbers
Looks interesting. Can you link to the precise page on the tetration forum? When I get more time, I might have a go at implementing the code you have, or maybe you or someone else could expand some of those high level functions to lower level ones at some stage.
May
14
comment Algorithm for tetration to work with floating point numbers
Sorry, no it didn't. 2^^3 should = 16, but it comes out as zero with your algorithm.
May
14
comment Algorithm for tetration to work with floating point numbers
Just to confirm - I certainly do not just want to "convert from float to int", so maybe you can remove that bit of the answer :)
May
14
comment Algorithm for tetration to work with floating point numbers
No joy. 2^^2 and 2^^3 both come out as zero. And 2^^2.5 comes out as about 1.5E-05.
May
13
comment Algorithm for tetration to work with floating point numbers
Your alg would calc 2^^2 and 2^^3, but not 2^^2.5 (which would only default to 2^^2). b gets converted to an integer (even in my original code if it was C#), so it's of no use. The algorithm would have to be a heck of a lot more complicated.
May
13
comment Algorithm for tetration to work with floating point numbers
I think you misunderstood what I wanted. I wanted the exponent to allow fractional numbers. This would completely rewrite the algorithm.
May
12
comment Algorithm for tetration to work with floating point numbers
@DanielGeisler: I don't see a particular piece of math I can immediately convert to a function (I at least looked for two-parameter functions). Then again, it would take me quite a while to digest the info in those links (especially the second) with my current level of knowledge.
May
10
comment Continuum between addition, multiplication and exponentiation?
@GottfriedHelms: Oh btw, I'm the guy who discovered the Mandelbulb formula. You mentioned that here - glad you like the pics! :)
May
10
comment Continuum between addition, multiplication and exponentiation?
You're right in saying my question is practically the same as the one asked in the link you've supplied. Sad in one way to see that it hasn't been solved yet. Happy in another way that it provides mystery and adventure for mathematicians like you, and also in regards to the kind of progress math might see if it was solved. A tick to any answer so far remains elusive for now, but let me know if a solution arises! (And have an upvote in the meantime!)
May
10
comment Continuum between addition, multiplication and exponentiation?
@MphLee: Funny you should mention that - I was just looking at commutative exponentiation yesterday. I'll be honest - I was hoping for the standard non-commutative flavour...
May
10
comment Continuum between addition, multiplication and exponentiation?
@MphLee: Perfect thanks! (so the latter of what I was thinking was correct). I just stumbled as the usual definition of the iterated logarithm is different, but he did use h-times which made me pause for thought.
May
10
comment Continuum between addition, multiplication and exponentiation?
I've had chance today to try and wrap my head around this. I'm making progress I think. When you say h-times iterated logarithm, do you mean not the usual mathematical definition of the iterated logarithm (which calculates how many times you need to log() before the number gets below 1), but instead, something more along the lines of "Define how many times you log() a number, and then log it those amount of times" ? If you can give the best/simplest version of the formula which includes the fractional iterated logarithm/exponentiation math too, then I'll be very tempted to tick this.