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When u are betting odd and even u have to bet in calculated steps.. Instead to bet on the total score odd or even,break into the 4 quarters using the backup betting system. With this u can earn up 45% of all your stake..

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If we say that the results of a basketball game are a couple of positive integers less than a fixed value (say, 1000) with the only constraint that they are different, consider the score $N$ of the winner. The loser may have scored with the same probability a value from 0 to $N-1$; if $N$ is even, the odds are even, but if $N$ is odd it is more probable that the sum is odd.

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Friend and i are betting on the ending total scores of basketball game, he says odds are greater it will end with an even sum, i say the odds are equal. Who is right?

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In theory @gev is correct, but I don't think it's a reasonable assumption that it's equally likely for either team to score odd vs even.

If I had to guess which is more probable I'd say odd. Suppose that team A scored X points. Then team B can score anything BUT X, meaning there's one less possibility to get an even sum.