Timeline for Does War have infinite expected length?
Current License: CC BY-SA 2.5
9 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Oct 5, 2010 at 4:22 | comment | added | Mike Spivey | I suspect the rule "P1's card is always added before P2's card to the bottom of the winner's stack" makes cycles more likely than, say, "the winning player's card is always added before the losing player's card to the bottom of the winner's stack." The reason: In the first case, the winning card ends up in a different parity position depending on whether P1 or P2 was the winner. So in this case high cards will tend to battle low cards, which means wars are less likely, which means the aces are less likely to switch hands... and if the aces never switch hands the game will cycle. | |
| Sep 3, 2010 at 23:54 | comment | added | Michael Lugo | Matthew: this seems like something best addressed by Monte Carlo methods, although being a less-than-great programmer I leave that to someone else. | |
| Jul 9, 2010 at 13:51 | comment | added | Matthew Kahle | This is a great example. A more subtle question, and something a friend asked me several years ago: what is the probability that a games goes on forever? | |
| Jan 12, 2010 at 14:52 | comment | added | Joel David Hamkins | @Kevin: I recommend the Math War variant. Each person plays two cards, and then use the product (or sum) for batttle. It's great arithmetic practice, and it seems that the kids can go forever with it. | |
| Jan 12, 2010 at 14:00 | comment | added | Joel David Hamkins | @Ben: Thanks. I was hoping for a succinct understanding of how it repeats, but I suppose a simulation at least proves the point that the expected value is infinite. (Also, the fellow's page is unfortunately broken for me---somehow I only get the first few paragraphs, without the relevant part.) | |
| Jan 12, 2010 at 9:59 | comment | added | Kevin O'Bryant | I know I've played games of War with my 7-year-old that felt endless. | |
| Jan 12, 2010 at 5:52 | comment | added | user1073 | The proof that this deal leads to a periodic game of War is by simulation. It's the example given in the 'Simulations of War using MATLAB' page cited on the Wikipedia page you linked to. | |
| Jan 12, 2010 at 5:17 | comment | added | Joel David Hamkins | That's great! But could you explain why? Also, your re-loading rules are slightly different from the ones I had mentioned. Can your shuffle be modified to accomodate that? | |
| Jan 12, 2010 at 5:11 | history | answered | user1073 | CC BY-SA 2.5 |