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{\bf Grzegorz Gutowski}
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{\bf Mr. Paint and Mrs. Correct go Fractional}
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We study a fractional counterpart of the on-line list colouring game
``Mr.\,Paint and Mrs.\,Correct'' introduced recently by Schauz.  We
answer positively a question of Zhu by proving that for any given
graph the on-line choice ratio and the (off-line) choice ratio
coincide.  On the other hand it is known from the paper of
Alon~et~al.~that the choice ratio equals the fractional chromatic
number.  It was also shown that the limits used in the definitions of
these last two notions can be realised.  We show that this is not the
case for the on-line choice ratio.  Both our results are obtained by
exploring the strong links between the on-line choice ratio, and a new
on-line game with probabilistic flavour which we introduce.



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