@Salil. The point that is incorrect is: 2. Now, by shooting in air C increases his probability by your argument, which is not good for A. Thus, P(A shooting at C) should NOT be 0 if A is intelligent.
If A shoots C, then B hits A with 50% probability, but if A shoots B, then C hits A with only 33% probability. Thus, A's probability of survival is higher if he shoots B rather than C. Hence, P(A survives) = .67 * P(A shoots B) + .5 * P(A shoots C). But since P(A shoots B) + P(A shoots C) = 1, it follows that P(A survives) = 0.67 * P(A shoots B) + 0.5 * [1 - P(A shoots B)] = 0.17 * P(A shoots B) + 0.5. Therefore, P(A survives) is maximized when P(A shoots B) = 1 and P(A shoots C) = 0. Dave On Jan 2, 11:07 pm, Salil Joshi <joshi.sali...@gmail.com> wrote: > @Dave, > Can you please point out which of the 3 points mentioned earlier sounds > incorrect? Because I think that this problem is much like the Three Body > problem, and we can not just maximize the likelihood for C, ignoring A & B. > They will also try to maximize their survival likelihood.... > > > > > > On Mon, Jan 3, 2011 at 1:34 AM, Dave <dave_and_da...@juno.com> wrote: > > @Salil: If C shoots at A instead of into the air, he increases the > > odds that he will be shot by B, because if C hits A then B will shoot > > at C instead of A. > > > On the other hand, if C shoots at B instead of into the air, he > > increases the odds that he will be shot by A. > > > Thus, shooting at either A or B decreases his odds of survival. > > > Dave > > > On Jan 2, 12:25 pm, Salil Joshi <joshi.sali...@gmail.com> wrote: > > > @Dave > > > 1. In the end only 1 will survive (after max of 2 rounds). > > > i.e. P(A survives in end) + P(B survives in end) + P(C survives in end) = > > 1 > > > > 2. Now, by shooting in air C increases his probability by your argument, > > > which is not good for A. > > > Thus, P(A shooting at C) should NOT be 0 if A is intelligent. > > > > 3. If it is not 0, P(C's survival) decreases (doesn't remain 0.49624). > > > > Please let me know if this is clear enough. > > > > On Sun, Jan 2, 2011 at 11:15 PM, Dave <dave_and_da...@juno.com> wrote: > > > > @Salil: Just to make sure we are on the same page, A hits with 100% > > > > probability, B hits with 50% probability, and C hits with 33% > > > > probability. C shoots first, then B, then A. Then the shooting > > > > continues among the survivors in that order until only one is > > > > standing. > > > > > If all three are alive and it is A's turn to shoot, he logically will > > > > choose to shoot at B rather than C since B has a greater probability > > > > of hitting him. Thus, your P(A shooting at C) = 0 if B is unhit when > > > > it is A's turn. > > > > > Similarly, if it is B's turn to choose between shooting at A or C, he > > > > rationally will choose A since A will shoot at and hit B if A gets a > > > > turn. So your P(B shooting at C) = 0 if A is unhit when it is B's > > > > turn. > > > > > If you dispute either of the above two paragraphs, please clealy state > > > > your objection. > > > > > Dave > > > > > On Jan 1, 11:19 pm, Salil Joshi <joshi.sali...@gmail.com> wrote: > > > > > @Dave, > > > > > Yeah, I had read those numbers on internet as this puzzle is well > > known. > > > > > However I am not convinced with the calculations because of following > > 2 > > > > > points: > > > > > > 1) If C shoots in air, the probability of survival is more for the > > > > > probabilities considered in the calculations with which A & B will > > shoot > > > > at > > > > > him. > > > > > Now, if A & B are intelligent, they will know that increasing > > survival > > > > > probability for C is bad for them (you can calculate survival > > probability > > > > > for A & B in each case), and therefore they will shoot at C with > > higher > > > > > probability than what they were planning earlier. > > > > > > 2) C's survival probability depends on P(A shooting at C) * 1 and P(B > > > > > shooting at C) * 1/2. > > > > > If C shoots at A, P(A shooting at C) is less by 33% and P(B shooting > > at > > > > C) > > > > > is more by 33%. So, if P(A shooting at C) dominates by logic in 1st > > > > point, > > > > > C's survival probability will be now more. > > > > > > On Sun, Jan 2, 2011 at 7:59 AM, Dave <dave_and_da...@juno.com> > > wrote: > > > > > > @Salil: Working out the probabilities, we find that: > > > > > > > 1. If C initially shoots at A, C's probability of survival is ~ > > > > > > 0.35867. > > > > > > 2. If C initially shoots at B, C's probability of survival is ~ > > > > > > 0.27679. > > > > > > 3. If C initially shoots in the air, C's probability of survival is > > ~ > > > > > > 0.49624. > > > > > > > Dave > > > > > > > On Jan 1, 11:30 am, Salil Joshi <joshi.sali...@gmail.com> wrote: > > > > > > > @Rahul, > > > > > > > As per my understanding, > > > > > > > In any round P(C is dead) = P(A is alive * A shoots C * A's shot > > is > > > > > > > accurate) + P(B is alive * B shoots C * B's shot is accurate) > > > > > > > this is to be minimized. > > > > > > > by not shooting at either A or B in 1st chance, how is this > > > > probability > > > > > > less > > > > > > > for C? > > > > > > > > On Sat, Jan 1, 2011 at 10:43 PM, Salil Joshi < > > > > joshi.sali...@gmail.com > > > > > > >wrote: > > > > > > > > > @Rahul, > > > > > > > > What purpose is served by wasting the shot? If C shoots at A or > > B, > > > > at > > > > > > least > > > > > > > > some probability that C is dead in future will be reduced. > > > > > > > > > On Sat, Jan 1, 2011 at 10:14 PM, RAHUL KUJUR < > > > > > > kujurismonu2...@gmail.com>wrote: > > > > > > > > >> @snehal: > > > > > > > >> will the shooting take place in increasing order of accuracy > > of > > > > > > hitting > > > > > > > >> the target and is that at a time only one person can take a > > > > shot??? > > > > > > > >> if yes then > > > > > > > >> @Salil: > > > > > > > >> my answer would be the same as above. what C will do is that > > it > > > > will > > > > > > first > > > > > > > >> let A and B kill each other first. > > > > > > > >> After C wastes his shot it will be B's turn. B can kill C, but > > in > > > > that > > > > > > > >> case the turn would go to A and he would surely kill B. If B > > goes > > > > > > after A, > > > > > > > >> then B may hit it or miss it(as its probability of hitting is > > 50%) > > > > > > > >> If B misses it > > > > > > > >> then > > > > > > > >> it depends on A whom to kill. A may kill B or C. A will try to > > > > kill > > > > > > one > > > > > > > >> who is better shooter i.e. B as C is less likely to hit A. > > > > > > > >> If B hits A then we are done. Round 1 is complete(as required > > in > > > > the > > > > > > > >> question) and C survives the first round. > > > > > > > >> Look the problem is not that who gets killed at last but > > rather > > > > what C > > > > > > > >> should fire in the first round obviously to survive(as I > > > > understood > > > > > > the > > > > > > > >> problem). It may happen that eventually C gets killed. But > > what > > > > should > > > > > > C > > > > > > > >> shoot in first round to survive. > > > > > > > > >> -- > > > > > > > >> You received this message because you are subscribed to the > > Google > > > > > > Groups > > > > > > > >> "Algorithm Geeks" group. > > > > > > > >> To post to this group, send email to > > algoge...@googlegroups.com. > > > > > > > >> To unsubscribe from this group, send email to > > > > > > > >> algogeeks+unsubscr...@googlegroups.com<algogeeks%2bunsubscr...@googlegroups.com> > > <algogeeks%2bunsubscr...@googlegroups.com> > > > > <algogeeks%2bunsubscr...@googlegroups.com> > > > > > > <algogeeks%2bunsubscr...@googlegroups.com> > > > > > > > >> . > > > > > > > >> For more options, visit this group at > > > > > > > >>http://groups.google.com/group/algogeeks?hl=en. > > > > > > > > > -- > > > > > > > > > -------- > > > > > > > > Thanks & Regards > > > > > > > > Salil Joshi. > > > > > > > > CSE MTech II, IITB > > > > > > > > A-414, Hostel 12 > > > > > > > > +91.9819.442.865 > > > > > > > > > This is a confidential E-Mail. If it has reached you by mistake > > or > > > > if > > > > > > you > > > > > > > > are not the intended receiver, please send it back to me. > > > > > > > > -- > > > > > > > > -------- > > > > > > > Thanks & Regards > > > > > > > Salil Joshi. > > > > > > > CSE MTech II, IITB > > > > > > > A-414, Hostel 12 > > > > > > > +91.9819.442.865 > > > > > > > > This is a confidential E-Mail. If it has reached you by mistake > > or if > > > > you > > > > > > > are not the intended receiver, please send it back to me.- Hide > > > > quoted > > > > > > text - > > > > > > > > - Show quoted text - > > > > > > > -- > > > > > > You received this message because you are subscribed to the Google > > > > Groups > > > > > > "Algorithm Geeks" group. > > > > > > To post to this group, send email to algoge...@googlegroups.com. > > > > > > To unsubscribe from this group, send email to > > > > > > algogeeks+unsubscr...@googlegroups.com<algogeeks%2bunsubscr...@googlegroups.com> > > <algogeeks%2bunsubscr...@googlegroups.com> > > > > <algogeeks%2bunsubscr...@googlegroups.com> > > > > > > . > > > > > > For more options, visit this group at > > > > > >http://groups.google.com/group/algogeeks?hl=en. > > > > > > -- > > > > > > -------- > > > > > Thanks & Regards > > > > > Salil Joshi. > > > > > CSE MTech II, IITB > > > > > A-414, Hostel 12 > > > > > +91.9819.442.865 > > > > > > This is a confidential E-Mail. If it has reached you by mistake or if > > you > > > > > are not the intended receiver, please send it back to me.- Hide > > quoted > > > > text - > > > > > > - Show quoted text - > > > > > -- > > > > You received this message because you are subscribed to the Google > > Groups > > > > "Algorithm Geeks" group. > > > > To post to this group, send email to algoge...@googlegroups.com. > > > > To unsubscribe from this group, send email to > > > > algogeeks+unsubscr...@googlegroups.com<algogeeks%2bunsubscr...@googlegroups.com> > > <algogeeks%2bunsubscr...@googlegroups.com> > > > > . > > > > For more options, visit this group at > > > >http://groups.google.com/group/algogeeks?hl=en. > > > > -- > > > > -------- > > > Thanks & Regards > > > Salil Joshi. > > > CSE MTech II, IITB > > > A-414, Hostel 12 > > > +91.9819.442.865 > > > > This is a confidential E-Mail. If it has reached you by mistake or if you > > > are not the intended receiver, please send it back to me.- Hide quoted > > text - > > > > - Show quoted text - > > > -- > > You received this message because you are subscribed to the Google Groups > > "Algorithm Geeks" group. > > To post to this group, send email to algoge...@googlegroups.com. > > To unsubscribe from this group, send email to > > algogeeks+unsubscr...@googlegroups.com<algogeeks%2bunsubscr...@googlegroups.com> > > . > > For more options, visit this group at > >http://groups.google.com/group/algogeeks?hl=en. > > -- > > -------- > Thanks & Regards > Salil Joshi. > CSE MTech II, IITB > A-414, Hostel 12 > +91.9819.442.865 > > This is a confidential E-Mail. If it has reached you by mistake or if you > are not the intended receiver, please > > read more »- Hide quoted text - > > - Show quoted text - -- You received this message because you are subscribed to the Google Groups "Algorithm Geeks" group. 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