The Monty Hall Problem of Hearthstone Read: http://tl.gd/n_1sr04bf
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I feel like I'm missing something here, surely there are two types of cards in your deck, those that you keep in Mulligan and those you throw away, and every Mulligan slot gives you two chances to draw a 'keep card'. Playing quest makes one of your slots half as likely to do this
Yes playing the quest lowers your chance to find a particular card from your deck by 1/30. Think of it this way: you rate the cards in your deck from most 30 (most powerful/useful) to 1 (least powerful). Then replace the card you rate a 1 by the quest. Then by always mulliganing
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the card you rated 1 you increase the average value you have post-mulligan. Increases average powerlevel of hand, but reduces chance of finding particular cards.
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taking away the chance to have the worst card in your deck in that quest slot is still outweighed by you having no option to just keep a good card pre mulligan, so average power level of the hand(which should be based on how many good cards you have) would be lower imo.
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