Revised: Conditional probability sports league involving sums of numbers

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Suppose we have a sports league where 45 games will be played and the results listed. A gambler chooses 8 games from the 45 that will be played. Her hope is to choose games that will end in a tie. For each tied game, the gambler gets 3 points; if the visiting team wins, the gambler gets 2 points; and if the home team wins, the gambler gets 1.5 points. In each game, the home team's probability of winning is 0.5; the probability of the visiting team's winning is 0.4; and the probability of a tie is 0.1. So, what is our gambler's probability of getting a total of 22 points or more?