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interesting game - Don Shepherd - 07-01-2017 01:35 PM
Here is an interesting game. What would be a good strategy for winning? RE: interesting game - Bill (Smithville NJ) - 07-01-2017 06:53 PM
(07-01-2017 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 RE: interesting game - Dave Britten - 07-01-2017 07:09 PM
The simple approach: look at the totals you can make with your roll, and choose the "rarest" one. [attachment=4992] RE: interesting game - Don Shepherd - 07-01-2017 11:56 PM
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 1-3 and 3-1 are the same. I considered these possible rolls: 1-1 1-2 1-3 1-4 1-5 1-6 2-2 2-3 2-4 2-5 2-6 3-3 3-4 3-5 3-6 4-4 4-5 4-6 5-5 5-6 6-6 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 3-2 roll could only yield 5, 1, or 6. Don RE: interesting game - Dave Britten - 07-02-2017 12:21 AM
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 1-2-3 (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. RE: interesting game - Paul Dale - 07-02-2017 12:25 AM
(07-01-2017 11:56 PM)Don Shepherd Wrote: I don't consider 36 possible rolls, because 1-3 and 3-1 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 1-2 as it is 1-1. You'll have to weight unequal rolls twice that of pairs. Pauli RE: interesting game - Don Shepherd - 07-02-2017 03:51 AM
OK, considering 36 possible rolls, I get these frequencies: 1-17 2-17 3-14 4-12 5-10 6-11 7-6 8-7 9-5 10-5 This was from paper-and-pencil 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. RE: interesting game - Bill (Smithville NJ) - 07-02-2017 11:28 AM
(07-02-2017 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 RE: interesting game - Don Shepherd - 07-02-2017 01:01 PM
(07-02-2017 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 3-month-old granddaughter is probably too young, however! |