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05122006  #1 
Join Date: Mar 2006
Posts: 12

Math Games  How to Win
I have been asked by WhiteJones, how I win at the maths games.
Well it is generally down to, two things. Either a) Developing an optimal stratergy. or b) Increasing the speed with which I can enter the answers. or BOTH Firstly let be give you an idea of an optimal strategy (Bit reluctant to do this, as people are going to start beating me, ah well.) Take the Wheel of Fortune games, Firstly I only play when I get a good phrase, after I have played a few times I can recognize the word patterns of the long phrase. A) OPTIMAL STRATERGY Say I am playing the Wheel of Fortune  Numbers and Computation Edition and I get the following pattern    This is most likely LEAST COMMON MULTIPLE, ok how good is this to play? Well what you want is a phrase that can get you a high score (You are not going to get a high score getting an answer like PI (in the other wheel of fortune game) Well what is the maximum score for LEAST COMMON MULTIPLE? Removing vowels we get LST CMMN MLTPL, max score per letter is 12 x 1000 = 12000. This will beat my current high score, so it is good. However what are the chances of actually doing this? HINT: A phrase which has a smaller number of different constants would be better, but I will look at bit more at this one. Well I would need to get 4 x M, 3 x L 1 each of C, N, P, S, T So 8 correct guesses, however I want to get correct guesses when the pointer is on 1000 or at the very least 400. So there are 10 segments the pointer could point to, but say I want a score of around 9000, not bad, the only one with a higher score than that at the moment is myself. So what do I need to do, well if I guess M and L when the pointer is on 1000, and C, N, P, S and T when the pointer is on 400. I will get a score of 9000. (7 x 1000) + (5 x 400) What are the changes of doing this, well if I am looking to spin the wheel seven times and get all 400’s and 1000’s (at least 2 being 1000). Not very high (not going to work the probability as I am not going to depend on being lucky) However in 20 spins of the wheel (assuming each number/bankrupt is equally likely 400 will come up twice and 1000 twice), which when thinking about it, if I spin the wheel 20 times in 4 games, in one of those games I will get 8 spins landing on 1000 or 400. (On average, not guaranteed) That’s more like it, but this also means that there is a chance I will be bankrupted during this game. Well the chance of not hitting bankrupt in 20 spins is 0.9^{20} = 0.12%. Bit low, but when you think about it not two bad because this is how I play. Spin the wheel, If I don’t get a 400 or 1000 guess wrong (that’s right, you are not playing against the clock, or someone else, this is not the TV game. So deliberately guess incorrectly if the pointer is one a low value.) That’s why I picked 20 spins (there are about 20 constants, well 21 but 20 is easier to work with) If I get 1000 then I guess in this case the letters M and L FIRST followed by the others. If I get a 400 guess the letters C, N, P, S and T first. Only guess M and L is all the others have already gone. This gives me potentially 21 spins (21 constants), but the longer I play then the more likely I will bankrupt. (This is one of the reasons why a phrase with a smaller number of DIFFERENT constants would be better) If I hit bankrupt BEFORE I have correctly guessed any letters it doesn’t matter and I will continue playing. If I have guessed some letters then I just start another games, no point in continuing this one. This means that 75% of my games in this example I will abort, 12% of the remaining games I will be bankrupted (approx). But the strategy with this phrase will give me a high score in 2% of my games. Since I am aborting 75% of games very early on, and a full games takes me less than 1.5 mins. I will actually get a high or close to high score about every half hour. Now there is a certain amount of luck involved sometimes this will mean my highest score is a little lower in that half hour, but sometimes it will mean more. Never going to win this game again So think about how you are going to play. B) SPEED Ok, I am not going to give you my technique away, as this is the single most significant advantage I have in playing the games. But here are some ideas. BTW The speed typing world record is actually based upon typing numbers rather than letters. I suppose if letter were used then some keyboard layouts would give some people advantages, and some languages with higher frequencies of a few letters could be typed quicker. Anyway, I wanted to speed up. My typing isn’t that fast, I just could practice but this could take a while and I have had nerve damage to my left hand, so I am not going to be able to out type someone with two good hands. Ok, I started using the numeric keypad, but others are doing the same, so that didn’t help much. So here are some big hints. Using an abacus is faster than a calculator, because a calculator will only work the answer out at the speed of pushing the buttons. RPN (Reverse Polish Notation) calculators are faster than normal ones, because you need to push less buttons. Ok, you say, but that is not helping. If I need to type in 0.18 I am going to have to type 0.l8 (four key presses). Maybe the game will let me leave out the zero (always worth checking) but I am still going to have to press three keys you say, I cannot reduce that. You would be correct. However Dvorak keyboards are faster that normal keyboards because the most common letters are all home keys, the next most common and pressed with the index finger etc. Speed is increased because finger movement is reduced, by cutting down on how far your fingers move. How is this going to help me, you ask? The numbers are equally likely you say, well that is not actually true. BTW: In life the number 1 tends to be the first digit of a number 30% of the time, 9 is the first digit only 4% of the time. This due to several things, the use of base 10, rules of rounding etc. If you would like to know more there is a BBC radio programme on it at http://www.bbc.co.uk/radio4/science/further5.shtml (You can listen via RealPlayer online if you want.) Well how does this apply to the games, well this rule won’t help me because it only works with measurements, not random numbers. But although the numbers in the problems are random, the spread of numbers in the answers is not. Lets look at Integers Multiplication: 9 to +9 If each number is equally likely then we are going to get positive of negative versions of the times tables 0 to 9 So out comes my copy of Excel and I set up a times table grid and count the occurrences of each number and here are my results. 0 16 1 21 2 23 3 11 4 20 5 12 6 14 7 7 8 12 9 4 Converting these into percentages 0 11.43 1 15.00 2 16.43 3 7.86 4 14.29 5 8.57 6 10.00 7 5.00 8 8.57 9 2.8 2 will need to be pressed 16.43% of the time. (I am excluding the minus sign and the enter key) The reason some numbers will be more popular can be discovered with a little thought. For instance, 1 in ten answers will be zero, because zero need only appear as one of the numbers for the answer to be zero. 5 numbers are odd and 4 are even, but if one numbers is even then the answer will be even. Odd number answers only occur when BOTH numbers are odd, so, there will be more even answers. How does this help me you ask well if my fingers were resting on the 2 and the 1 as “home keys” your fingers would have less distance to travel in answering problems. HINT: You could even remap your number key to other keys on your keyboard to decrease time. BIG HINT: You could set up your own “DVORAK” keyboard for numbers by remapping your keyboard. Is it wise to hover over the minus sign? Well you will only get a negative answer if only one of the numbers is negative, so if you ignore the 10% zero answers, only 25% of the remaining answers will be negative. (22.5%) Is it worth it, you decide. If you are playing a game with more than one box to fill in then, you are probably using the tab key rather than the mouse to move between boxes. But that is over the other side of the keyboard from the numeric keypad. So remapping a closer key, might be another idea. (Or changing the key used to move between fields in the windows preferences  HINT) You could try another method of entering data altogether, of one of those keyboards with keys you can place anywhere. Such as the DX1 Input System, seen here, http://www.thinkgeek.com/computing/input/77ba/ (No I don’t have one) What about that enter key, do you need to press it with a finger? I started out tying up a whole hand just pressing the enter key. How about using a mouse, how about not using a hand to click the button (HINT, HINT) Have you got a teacher with a presentation remote? With one of these resting on the table you can use your forearm to work the “enter button”. BIG HINT: How about using two numeric keypads? (You can use a PS2 and USB Keyboard at the same time under Windows, not to mention my wireless keyboard for my Mac works with a Belkin receiver on my windows machine) What about those USB keypads? (Haven’t got one of those either) There are lots of ideas for improving you input times. Think up your own. Do you even have to use a keyboard at all? So although you will still need to get the answers right you can use your brain to play smarter, come on, I want some competition. All the best  Shura
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"Mathematics is the gate and key to the sciences."  Roger Bacon 
05122006  #2 
Join Date: Mar 2005
Posts: 10,653

Amazing analysis of the games. This motivates me to start creating more games again.
The tournaments are coming soon. I can't wait.
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Do Math and you can do Anything! 
05122006  #3 
Guest
Posts: n/a

omg
omg shura ur 2 smart and whitejones is my friend and hes not that bright so thats y im telling u
u no u arn't mat 
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