interesting game

07012017, 01:35 PM
Post: #1




interesting game  
07012017, 06:53 PM
Post: #2




RE: interesting game
(07012017 01:35 PM)Don Shepherd Wrote: Here is an interesting game. Hi Don, I love these simple games and whether there could be a strategy to winning them. Unless I have made a mistake (which would be very likely), the following are the possible combinations of dice rolls: There are 36 possible dice rolls. Here's the possible results for each number: 1 would be 18 out of the 36 2 would be 19 out of 36 3 would be 14 out of 36 4 would be 13 out of 36 5 would be 10 out of 36 6 would be 10 out of 36 7 would be 6 out of 36 8 would be 7 out of 36 9 would be 5 out of 36 10 would be 5 out of 36 So if possible, I would try to do 9 and 10 first, then 7 & 8, then 5 & 6, then 3 & 4, and save 1 & 2 towards the end. I had never heard of this game. These is also a variation on this using Letters on the Dice that you would then try to create words from. bill Smithville, NJ 

07012017, 07:09 PM
Post: #3




RE: interesting game  
07012017, 11:56 PM
Post: #4




RE: interesting game
Thanks Bill and Dave.
I must be doing something wrong, my figures don't seem to jive with either of yours, although the general approach seems right (go for the biggest numbers [9, 10] first since they are the rarest, I think). I don't consider 36 possible rolls, because 13 and 31 are the same. I considered these possible rolls: 11 12 13 14 15 16 22 23 24 25 26 33 34 35 36 44 45 46 55 56 66 Considering the add, subtract, multiply, and divide for these combinations, I get the following possibilities: 1  12 2  9 3  7 4  7 5  5 6  6 7  3 8  4 9  3 10  3 And I assume division must leave no remainder, so for example a 32 roll could only yield 5, 1, or 6. Don 

07022017, 12:21 AM
Post: #5




RE: interesting game
You have to remember that 3, 1 and 1, 3 are considered different outcomes for computing probability.
I just made a table of all possible outcomes in 123 (6x6x4), extracted all the integer results between 1 and 10, while removing duplicates (I think 1+1=1 and 1/1=1 is the only one), counted the frequencies, and slapped a graph on the results. 

07022017, 12:25 AM
Post: #6




RE: interesting game
(07012017 11:56 PM)Don Shepherd Wrote: I don't consider 36 possible rolls, because 13 and 31 are the same. I considered these possible rolls: If you do this, you will have outcomes with unequal probabilities. E.g. it is twice as likely to roll 12 as it is 11. You'll have to weight unequal rolls twice that of pairs. Pauli 

07022017, 03:51 AM
Post: #7




RE: interesting game
OK, considering 36 possible rolls, I get these frequencies:
117 217 314 412 510 611 76 87 95 105 This was from paperandpencil tallies and me eyeballing and summarizing the results, so I wouldn't swear to it but I think it is correct. The winning strategy is the same, go for the bigger numbers first. It would be interesting to write a simulation of, say, 1000 game iterations with 4 players, one of which follows this strategy and the other three just choose a random solution each time, and see the results. 

07022017, 11:28 AM
Post: #8




RE: interesting game
(07022017 03:51 AM)Don Shepherd Wrote: The winning strategy is the same, go for the bigger numbers first. A more fun test would be to play the game with a young person. Too bad my grandchildren are too old to want to play. But it would be interesting to see how long it would take for a young person to figure out what the better strategy is and see if they adjust their play over time. Of course, it also would be a great opportunity to discuss probabilities with them and how it can affect their game play. Bill Smithville, NJ 

07022017, 01:01 PM
Post: #9




RE: interesting game
(07022017 11:28 AM)Bill (Smithville NJ) Wrote: A more fun test would be to play the game with a young person. Too bad my grandchildren are too old to want to play. But it would be interesting to see how long it would take for a young person to figure out what the better strategy is and see if they adjust their play over time. Of course, it also would be a great opportunity to discuss probabilities with them and how it can affect their game play. That's a good idea. My 3monthold granddaughter is probably too young, however! 

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