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 Don't lose too fast (Posted on 2011-01-25)
A game is played starting with 6 fair coins laid out with heads face up.

Each round consists of flipping all of the coins showing heads.

If fewer than half of the flipped coins come up heads the player loses.

Rounds continue until the player either loses or has one heads remaining.

The player wins by getting to one heads without losing.

What is the probability of winning this game?

Examples: 6→4→1 would be a loss. (1 is less than half of 4.) 6→5→3→2→2→2→1 would be a win.

 No Solution Yet Submitted by Jer Rating: 4.0000 (1 votes)

Comments: ( Back to comment list | You must be logged in to post comments.)
 re: Hmm. Good strategy. | Comment 4 of 5 |
(In reply to Hmm. Good strategy. by Steve Herman)

Indeed, putting the various phases of play into the program I used:

5   point 10
9   for Pts=6 to 2 step -1
10    print pts,1-fnPLose(Pts),(1-fnPLose(Pts))/1
11   next
20    end

At various numbers of tossed coins:

n       prob of win     prob as decimal
6       52/279   0.186379928315412186379928315412186379928315412185
5       32/217   0.147465437788018433179723502304147465437788018433
4       12/35    0.342857142857142857142857142857142857142857142856
3       2/7    0.285714285714285714285714285714285714285714285713
2       2/3    0.666666666666666666666666666666666666666666666666

Edited on January 25, 2011, 3:40 pm
 Posted by Charlie on 2011-01-25 15:40:17

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