tag:blogger.com,1999:blog-4115025577315673827.post2192596049648037986..comments2019-10-08T12:02:40.465+05:30Comments on CSE Blog - quant, math, computer science puzzles: World Series PuzzleUnknownnoreply@blogger.comBlogger16125tag:blogger.com,1999:blog-4115025577315673827.post-12687720300558849522014-10-21T01:19:34.281+05:302014-10-21T01:19:34.281+05:30@ Pratik : Does this solution assumes equal probab...@ Pratik : Does this solution assumes equal probability of winning for both teams or is the answer same with any prior probs ??rajesh iitmhttps://www.blogger.com/profile/04472744824090370564noreply@blogger.comtag:blogger.com,1999:blog-4115025577315673827.post-1057801584025811692014-06-22T23:28:49.405+05:302014-06-22T23:28:49.405+05:30Thanks for the images, btw :)Thanks for the images, btw :)Pratik Poddarhttps://www.blogger.com/profile/11577606981573330954noreply@blogger.comtag:blogger.com,1999:blog-4115025577315673827.post-63518049692491369202014-06-22T23:26:23.861+05:302014-06-22T23:26:23.861+05:30Wrong solution. What square are you referring to?Wrong solution. What square are you referring to?Pratik Poddarhttps://www.blogger.com/profile/11577606981573330954noreply@blogger.comtag:blogger.com,1999:blog-4115025577315673827.post-62510491413250134042014-06-22T23:25:00.345+05:302014-06-22T23:25:00.345+05:30It is a delightful puzzle indeed. ThanksIt is a delightful puzzle indeed. ThanksPratik Poddarhttps://www.blogger.com/profile/11577606981573330954noreply@blogger.comtag:blogger.com,1999:blog-4115025577315673827.post-12406883258823909642014-06-22T23:24:40.429+05:302014-06-22T23:24:40.429+05:30Awesome. ThanksAwesome. ThanksPratik Poddarhttps://www.blogger.com/profile/11577606981573330954noreply@blogger.comtag:blogger.com,1999:blog-4115025577315673827.post-21092688618417453712014-06-22T23:24:04.245+05:302014-06-22T23:24:04.245+05:30Kiran, Let the bet be y after (3,2,x) . So, win le...Kiran, Let the bet be y after (3,2,x) . So, win leads to (4,2,x+y) and loss leads to (3,3,x-y)<br />But the valid states are (4,2,100) and (3,3,0) , x is 50 and y is 50.Pratik Poddarhttps://www.blogger.com/profile/11577606981573330954noreply@blogger.comtag:blogger.com,1999:blog-4115025577315673827.post-15279904723072250602013-10-06T17:16:38.626+05:302013-10-06T17:16:38.626+05:30The point of this puzzle is to understand the conc...The point of this puzzle is to understand the concept of backward induction in simple, intuitive terms.Ashwin Raohttps://www.blogger.com/profile/01414549370613459334noreply@blogger.comtag:blogger.com,1999:blog-4115025577315673827.post-11071425094988354612013-09-29T23:38:05.095+05:302013-09-29T23:38:05.095+05:30How did you come up with numbers +50/-50 for (3,2)...How did you come up with numbers +50/-50 for (3,2)/(2,3) state? Is it some random numbers which eventually gets us to the correct answer ?kiranhttps://www.blogger.com/profile/02469643883317281166noreply@blogger.comtag:blogger.com,1999:blog-4115025577315673827.post-86770146842234832442013-06-08T00:35:05.327+05:302013-06-08T00:35:05.327+05:30It should be $37.5, since one should have $100 at ...It should be $37.5, since one should have $100 at the end if Team A wins in 4, 5, 6 or 7 matches. Similarly, one should have -$100 if Team B wins. Going backward through the square, we get the betting amount to be $37.5NGhttps://www.blogger.com/profile/10534772173717464065noreply@blogger.comtag:blogger.com,1999:blog-4115025577315673827.post-88391302698898578542013-04-20T21:38:56.372+05:302013-04-20T21:38:56.372+05:30There is a problem with this strategy. Suppose you...There is a problem with this strategy. Suppose you support team A and team A wins the first game. Then you are ahead by $100. Now suppose that B wins the next 4 rounds. So A loses but you have made $100. sidhttps://www.blogger.com/profile/04179126136399818676noreply@blogger.comtag:blogger.com,1999:blog-4115025577315673827.post-3936501488804899632013-04-08T12:51:12.579+05:302013-04-08T12:51:12.579+05:30Suppose the person bets for Team A.
Let the states...Suppose the person bets for Team A.<br />Let the states be defined as (# wins for A,# wins for B,Money at hand)<br />We need to work backwards from Match 7 considering only the valid states.<br />For Match 7, valid states are (4,3,+100) and (3,4,-100)<br />For Match 6, the only valid state which can lead to Match 7 is (3,3,_). It is simple to see that this state comes to (3,3,0) and the amount to bet is 100.<br /><br />For Match 6, valid states are (4,2,+100), (3,3,0) and (2,4,-100). From Match 5, the valid states which can lead to Match 6 are (3,2,_) and (2,3,_). They work out to be (3,2,+50) and (2,3,-50) and amount bet is 25 for each state.<br /><br />Carrying this on, we get the betting amount for Match 1 to be 31.25Arnabhttps://www.blogger.com/profile/13734216328461677608noreply@blogger.comtag:blogger.com,1999:blog-4115025577315673827.post-69943948135678846102013-03-28T20:30:53.181+05:302013-03-28T20:30:53.181+05:30I went straight to the n=1 case looking for clues....I went straight to the n=1 case looking for clues. It was trivial and gave me a good feeling about this problem because I am an optimist (!!). I moved onto n=2 and AHA! realised that whatever the bets are here, they have to reduce to the n=1 case if the first two games go one each way. That insight expands and generalises to build the tree backwards from known bets, with the values easy to calculate as I drew it. While I was doing that, I thought "I couldn't work these out in my head so easily if there weren't the right number of equations and unknowns - I bet it can be done with a matrix" - hahaha!JDGMhttps://www.blogger.com/profile/11829357060109505064noreply@blogger.comtag:blogger.com,1999:blog-4115025577315673827.post-66370872662502676292013-03-28T07:59:58.631+05:302013-03-28T07:59:58.631+05:30The answer is $31.25.
What a delightful puzzle!
...The answer is $31.25.<br /><br />What a delightful puzzle!<br /><br />Spoilers: <a href="http://i48.tinypic.com/b6dndf.jpg" rel="nofollow">first shot</a>, <a href="http://i48.tinypic.com/11i1do1.png" rel="nofollow">neatened up</a>.JDGMhttps://www.blogger.com/profile/11829357060109505064noreply@blogger.comtag:blogger.com,1999:blog-4115025577315673827.post-18445898208575385942013-03-28T04:00:40.334+05:302013-03-28T04:00:40.334+05:30I get $31.25. You should bet that amount on the s...I get $31.25. You should bet that amount on the second game as well. (Then it gets more complicated.)<br /><br />I'm interested in hearing other people's methods, but I just turned it into a matrix equation and solved.Alexhttps://www.blogger.com/profile/11022494336441129718noreply@blogger.comtag:blogger.com,1999:blog-4115025577315673827.post-69460260976276691432013-03-27T23:25:58.607+05:302013-03-27T23:25:58.607+05:30Are the bets decided before the contest starts or ...Are the bets decided before the contest starts or they can be modifies as it goes on ?Rishabh Nigamhttps://www.blogger.com/profile/08924575717412089430noreply@blogger.comtag:blogger.com,1999:blog-4115025577315673827.post-85319476746517497632013-03-27T11:19:31.563+05:302013-03-27T11:19:31.563+05:30Can you bet $0 ? I think not, but if so, then the ...Can you bet $0 ? I think not, but if so, then the answer is to bet $100 on the first game and $0 in the remaining.Anonymousnoreply@blogger.com