20150502, 14:16  #1 
Aug 2002
3·43·67 Posts 
May 2015

20150502, 21:44  #2 
May 2013
East. Always East.
11×157 Posts 
My work on this was going so well until I hit a big hiccup: Even though players can't START with more than 255 dollars, they can go higher than 255.
I created a list of all possible starting configurations (keeping in mind that the order does not matter so I had [1,4,6] but didn't keep [6,4,1] and [1,6,4] etc). For any that contained duplicates, I tagged them as possibly ending on the first tun. For any that did not, I generated the three possible configurations that they could lead to and I was going to start working on the logic that if any of those three possibilities ended on turn 1, then the initial config ended on turn 2, and so on. Unfortunately, for example, [32,254,255] can lead to [1,32,508] which is not in my list of possible configurations. I will need to think of something to deal with this. It is good to know that 508 is the largest amount any player can reach, but that still makes a shit load more configurations to deal with. And yes, I AM trying to go for the full enchilada. EDIT: I am going to need 64bit excel to do this... Last fiddled with by TheMawn on 20150502 at 21:48 
20150503, 01:19  #3 
May 2013
East. Always East.
6BF_{16} Posts 
As far as I can tell, it is not possible for two players to both be above 255 if they start at or below 255. I would like a counterexample if someone is only marginally interested in this problem.
I can't use words to make a proper sounding proof but I feel like I've tried everything. 
20150503, 01:38  #4  
"Forget I exist"
Jul 2009
Dartmouth NS
2×5^{2}×13^{2} Posts 
Quote:
[253,254,255]>[253,508,1]>[506,255,1]>[505,255,2]>[503,255,4]>[499,255,8]>[491,255,16]>[475,255,32]>[443,255,64]>[379,255,128]>[251,255,256] (sped ahead originally from[506,255,1], not saying how right now)>[502,4,256] I believe is the path you mean ? Last fiddled with by science_man_88 on 20150503 at 01:49 

20150503, 02:58  #5  
May 2013
East. Always East.
11×157 Posts 
Quote:
I guess I have a bit of code to rewrite. I suppose this also raises the question of whether two numbers > 256 is possible. It looks like your nonbruteforce insights into this problem are a bit better than mine, especially if you saw how to get from [506,255,1] to [502,4,256] in one big movement. 

20150503, 10:20  #6  
"Forget I exist"
Jul 2009
Dartmouth NS
10000100000010_{2} Posts 
Quote:
Last fiddled with by science_man_88 on 20150503 at 10:21 

20150503, 12:21  #7  
"Forget I exist"
Jul 2009
Dartmouth NS
10000100000010_{2} Posts 
Quote:
[506,255,1]>>[506,0,256]>>[250,0,512]>>[500,0,262] if you allow 0 in the mix. >> is my way of saying fast forward to I guess. Last fiddled with by science_man_88 on 20150503 at 13:09 Reason: deleted an earlier edit 

20150503, 13:58  #8 
"Forget I exist"
Jul 2009
Dartmouth NS
2102_{16} Posts 
I think I have an answer without my code. Well that seems like a waste.
0 makes at least 127 trivial answers if it's allowed at the start. Last fiddled with by science_man_88 on 20150503 at 14:30 
20150503, 15:15  #9 
May 2013
East. Always East.
11·157 Posts 
Zero is impossible by the rules of the game. You would have to lose to someone who has the same amount of money as you, which is a game end.

20150503, 15:28  #10 
"Forget I exist"
Jul 2009
Dartmouth NS
2×5^{2}×13^{2} Posts 
I mean't at the start for those trivial answers. but yeah I forgot but I can tell you why this one would hit a 0 if left indefinitely have you figured out what I figured out about how to show each branch quickly ? I just don't seem to be able to code it for some reason.

20150503, 16:40  #11 
May 2013
East. Always East.
11·157 Posts 
[506,255,1]>>[506,0,256]
This cannot legally happen. And this is clearly not a case where a player starts with zero. You end up at [506,128,128] and you cannot get to [506,0,256] because the rules of the game state that if two players with equal amounts of money are matched up, then the game ends. A player CANNOT end up with 0 dollars because they would have lost to someone with the same amount of money as them which ends the game. I don't know how else to say this. 
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