So this week was strange... I spent a lot of time working on my senior research project at ASU. I did a lot of cool things.
First, I wrote a couple of programs for finding win percentages of different variations of nim. The variation of nim that I considered first was similar to fibonacci nim. From the last post, we know that in nim, there is a set number of stones in the middle, with each player taking turns to remove a certain amount from the pile. The goal of each player is to take the last stone. However in fibonacci nim, after each turn, the other player is allowed to take up to a fixed multiple of the previous players move.
For example, consider a game with a 100 stones in the middle. If a player took 5 stones in his previous turn, fibonacci nim would allow the next player to take up to 2*5 = 10 stones from the middle on his turn. This would mean that the players would not only have to consider the number of stones in the middle, but also the number of stones removed in the previous turn.
As for handicapping this game, the method I considered was changing the "multiplying factor" of each player. In fibonacci nim, we can say that this factor is 2 for both players, since each player is allowed to take up to twice as many stones as the previous player. However, one method of handicapping would be to limit the multiplying factor of the better player. This would limit the possible moves he could make, reducing his chances of winning. This would mean that the skilled player, who plays perfectly, may not be able to always defeat the unskilled player, who plays randomly.
The second cool thing I did at ASU was attend a talk (there are weekly geometry seminars on Friday) about subriemannian geometry. Now I wish I could say I understood the talk, but I most definitely didn't. I understood the definition of a subriemannian manifold and that was pretty much it. The talk seemed cool though. There were a lot of pretty pictures and stuff. Other people seemed to like it.
The last thing I did was sign up for Math 494 at ASU. So over the next quarter, I'm going to be attending a differential geometry class, taking the tests and doing homework with the students there. The class actually started four weeks ago, so I've got a bit of studying to do. But the class seems fun, so I'm gonna try to learn the stuff.
Ok that's all. Thanks for reading~
First, I wrote a couple of programs for finding win percentages of different variations of nim. The variation of nim that I considered first was similar to fibonacci nim. From the last post, we know that in nim, there is a set number of stones in the middle, with each player taking turns to remove a certain amount from the pile. The goal of each player is to take the last stone. However in fibonacci nim, after each turn, the other player is allowed to take up to a fixed multiple of the previous players move.
For example, consider a game with a 100 stones in the middle. If a player took 5 stones in his previous turn, fibonacci nim would allow the next player to take up to 2*5 = 10 stones from the middle on his turn. This would mean that the players would not only have to consider the number of stones in the middle, but also the number of stones removed in the previous turn.
As for handicapping this game, the method I considered was changing the "multiplying factor" of each player. In fibonacci nim, we can say that this factor is 2 for both players, since each player is allowed to take up to twice as many stones as the previous player. However, one method of handicapping would be to limit the multiplying factor of the better player. This would limit the possible moves he could make, reducing his chances of winning. This would mean that the skilled player, who plays perfectly, may not be able to always defeat the unskilled player, who plays randomly.
The second cool thing I did at ASU was attend a talk (there are weekly geometry seminars on Friday) about subriemannian geometry. Now I wish I could say I understood the talk, but I most definitely didn't. I understood the definition of a subriemannian manifold and that was pretty much it. The talk seemed cool though. There were a lot of pretty pictures and stuff. Other people seemed to like it.
The last thing I did was sign up for Math 494 at ASU. So over the next quarter, I'm going to be attending a differential geometry class, taking the tests and doing homework with the students there. The class actually started four weeks ago, so I've got a bit of studying to do. But the class seems fun, so I'm gonna try to learn the stuff.
Ok that's all. Thanks for reading~
Very interesting! So, for fibonacci nim, the second player could take less than or more than 5 stones, up to 10? And if the first player took 4, would it be up to 8 instead of 10? Also, for the handicapping method, is the multiplying factor changing after each turn or is it still set for the entire game? Good luck catching up on the class!
ReplyDeleteSo the multiplying factor for each player would remain constant throughout the game, although that might spark another cool problem if the factor changed throughout. If the multiplying factor were 2, then you'd be able to move up to twice your opponents previous move. So if your opponent took 4, you'd be able to take up to 8 on your next turn.
DeleteNithin, it's only been two weeks and I'm already alarmed by the amount of stuff you have going on (in a good way). It must be nice being able to attend talks and classes at ASU, though I know so little that I misread the geometry seminar topic as Subramanian.
ReplyDeleteHow many variations of nim are you going to be looking at? Do you expect the handicaps to be very different for each variation or could you use the same method to even the playing field for multiple versions of the game?
Wow you sure have a lot of stuff going on already! I had a question about how you were trying to handicap the fibonacci him though. By limiting the multiplying factor, do you mean that the better player for example would only have a factor of 2 while the other player could have a factor of Maybe 4?
ReplyDeleteWow you sure have a lot of stuff going on already! I had a question about how you were trying to handicap the fibonacci him though. By limiting the multiplying factor, do you mean that the better player for example would only have a factor of 2 while the other player could have a factor of Maybe 4?
ReplyDeleteYou started differential geometry four weeks late! You are brave
ReplyDeleteYou started differential geometry four weeks late! You are brave
ReplyDelete