Re: Drawing for Dinner
ummmmmmmmm ..... I think ......
In your specific example, where F waited to see the 5 [img]/images/graemlins/club.gif[/img], F is better off with a 6 way draw.
Under all cases, in the original draw, she'd have a 1 in 6 chance of driving.
With the new draw, she has a 12/52 of losing outright (>1/6) PLUS either a 1/13 or 1/52 chance of a tie (in which she has a 50/50 shot of driving), in any case greater than 1/6.
Now, if we generalize, with 5 people drawing, you would expect, on average, that 1 card will be in each 5th of the deck. If suit rankings are used
Bottom fifth (11th card) -- 4 [img]/images/graemlins/heart.gif[/img] or lower
Fourth fifth (21st card) -- 7 [img]/images/graemlins/club.gif[/img] to 4 [img]/images/graemlins/spade.gif[/img]
Third fifth (32nd card) -- 9 [img]/images/graemlins/spade.gif[/img] to 5 [img]/images/graemlins/club.gif[/img]
Fourth fifth (42nd card) -- Q [img]/images/graemlins/heart.gif[/img] to 10 [img]/images/graemlins/club.gif[/img]
Top fifth (52nd card) -- A [img]/images/graemlins/spade.gif[/img] to Q [img]/images/graemlins/spade.gif[/img]
In this case, taking the midpoint of the band, for the bottom fifth, F expects to see the low person with the 6th card (i.e., 3 [img]/images/graemlins/diamond.gif[/img]), in which case, the expectation is that there is slightly greater than a 10% chance that she will drive, vs 16.7% in the original draw.
It's very late at night, so this whole analysis may not fly, but this is my impression.
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