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.
(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
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Posted by Charlie
on 2011-01-25 15:40:17 |
re: Hmm. Good strategy.
