tag:blogger.com,1999:blog-235276292454918436.post6368274486875073513..comments2024-03-23T17:12:29.672-04:00Comments on Math Hombre: Decimal RaceJohn Goldenhttp://www.blogger.com/profile/18212162438307044259noreply@blogger.comBlogger5125tag:blogger.com,1999:blog-235276292454918436.post-25314357770590604982011-02-10T12:36:20.795-05:002011-02-10T12:36:20.795-05:00$1.70! None of the kids caught that. Just my mist...$1.70! None of the kids caught that. Just my mistake.<br /><br />Excellent work on the probability, Hao! <br /><br />And I'm glad to know there's an MtG reader of the blog. Did you see http://mathhombre.blogspot.com/2010/05/this-and-that.html? It's the only other time I've tried to connect magic and teaching.John Goldenhttps://www.blogger.com/profile/18212162438307044259noreply@blogger.comtag:blogger.com,1999:blog-235276292454918436.post-44870205147535710852011-02-10T01:21:41.014-05:002011-02-10T01:21:41.014-05:00"I was surprised no one chose the 10 times th..."I was surprised no one chose the 10 times the .2 spinner." In addition, you win in 9 moves due to the bonus on 0.2.<br /><br />Expectation is a weird measurement here, because presumably the game ends when one player wins, so what we really care about is how often one strategy (aka a spinner) wins in comparison to another one.<br /><br />In this case, I played around with a couple variations before settling on [0.85, 0.85, 0.1, 0.1, 0.1, 0, 0, 0, 0, 0] because it gives fairly good chances of hitting either of the bonuses on 0.2 or 0.85, while making it very hard to hit the penalties on 1.5 and 1.75. This strategy wins in 9 turns or less with probability ~ 0.509, which means you expect to win or tie the "all 0.2" strategy more than half the time. Expected number of turns is at least 10.7, but if we only care about how often we lose (as opposed to by how much we lose), it's ok.<br /><br />Alternatively, a spinner that is [2 0 0 0 0 0 0 0 0 0] will finish in the first 9 turns with probability ~0.613, so it's even better (esp. if you like high variance).<br /><br />The MTG references were great, as I did a double-take when I first saw Vorthos.<br /><br />Also, what happened to 1.7 on the board?Haohttps://www.blogger.com/profile/02348974241652264510noreply@blogger.comtag:blogger.com,1999:blog-235276292454918436.post-74966032494556478292011-02-10T01:09:16.686-05:002011-02-10T01:09:16.686-05:00This comment has been removed by the author.Haohttps://www.blogger.com/profile/02348974241652264510noreply@blogger.comtag:blogger.com,1999:blog-235276292454918436.post-47342997529120233372011-02-04T10:51:43.171-05:002011-02-04T10:51:43.171-05:00Thanks, Mr. H! I think you're exactly right. ...Thanks, Mr. H! I think you're exactly right. One of the groups decorated their spinner, and after they played with another pair, the new pair almost always decorated their spinner afterwards. Alternating colors were key in their designs. <br /><br />I like the idea of alternating values... guess I was being mathematician-like by organizing them.John Goldenhttps://www.blogger.com/profile/18212162438307044259noreply@blogger.comtag:blogger.com,1999:blog-235276292454918436.post-24240027312630157612011-02-04T01:56:07.101-05:002011-02-04T01:56:07.101-05:00Thanks for sharing the activity.
I was surprised ...Thanks for sharing the activity.<br /><br />I was surprised no one chose the 10 times the .2 spinner. It requires the least amount of work, and pieces can be moved without waiting for the spinner to stop.<br /><br />Possible way to add to the excitement is alternate between high and low values. You can win big or lose big, and you won't know until the spinner stops completely.<br /><br />One thing that might help is adding color. While spinner is going around, it'll be difficult to see the numbers well. Colors will make them stand out. Adding color to the high and low values, at least, could do the trick.Mr. Hhttp://mrho.net/blog/noreply@blogger.com