The past few weeks we have been working on a problem called ‘Win At The Fair.’ For the first lesson we were given a game board to play. Once we got a prize we had to tally it on the board.
How to play:
Roll the dice and add the two numbers together. See where the number is on the key and move one space in that direction. Once you land on a prize the game resets.
Our class managed to play 149 games. After we discussed the data we found that we made $149 since each game is $1, and lost $187.40 and payed out $336.40 for all the prize money won. NO profit. So landing on the five was not good for the store owner. (us) Then we discussed some strategies if we were to create our own.
We all then decided that this was the ‘losing version’ so we went off to create our own game boards. This was known as a ‘creative board.’ We could include black holes, rivers etc. And the numbers can be placed anywhere as well as changing the arrow directions. We had to remember to make sure our game board was making us profit but also enticing. Here in my ‘creative board i made 4 and 3 go left. 2,5 and 7 to the right and 6,7,8,9,10,11 and 12 up. Since the numbers going up are the most likely to be rolled i put $1 at the top (if they won that the’d get their money back) and 20c either side. My twist was i put $10 to the right but blocked off the $100 to the left by a $3.
The next lesson we were to create another game board except using the software Maths300. This was known for our ‘Official Board.’ Using our game board we would run it through 1000 trials and see the out put. The only thing was we couldn’t include black holes, ladder etc and all the numbers were doubled up and placed around the edges. We were expected to play 1000 games (each $1) But of course they didn’t succeed the first time round. This is my first game board…
This clearly is not a good game board because i’m paying out $2,928.25. For this board i made the arrows directions , 2 and 4 go left, 3 and 5 go right and the rest go up. Because 2,3,4 and 5 are the least likely to be rolled (because there are 2 dice) That is why i put my $20 down the bottom. And since the most likely numbers to be rolled are facing upwards i put 75c there.
Afterwards my thinking was to see where the most hits were coming for and lower my price there and where the least hits are and raise my prise there. Coming from that strategy my game board then looked like…
Then i created my thought so ‘official board’ clearly i was making profit and i was only paying out $378. Then i thought to myself if it was enticing. I think that the prices were reasonable but then i had a look at the arrows. Obviously it’s some what impossible to land on 20. When i shared this with a friend they intelligent spoke “why would they play if they use $1 and only win 5c or something back?”
Since my jackpot ($20) was on the bottom right and left corners i knew it was highly unlikely to land on that. Because if there are two dice 2,3,4 and 5 are the least likely to win. So if 10c and 5c are up the top its pretty obvious which is going to get the most hits…
Then i made a decision to change
For my arrow directions i chose/changed (thanks Archer) and bam it worked!
This is my ‘official game board.’ I am very happy with it because it is making me profit, i’m not paying out more than $1000 and it is enticing! I collaborated with Chloe and together we achieved an amazing amount of work! I have also figured out some helpful strategies if i ever do this again in the future.