[M.B.E.]

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Let’s say your opponents will contribute a total of $80 to the pot and it will cost you $24 to play a hand all the way to the showdown.
• When you scoop, you will be awarded all $104 in the pot of which $24 is your own investment.
• When you split the pot, you will be awarded $52, of which $24 is your own investment.

Each time you split such a pot, you only actually win $28. When you win half such a pot twice, what you actually win is $56 (and you get your own investment back). If you go home after splitting two such pots and losing none, you’ll be $56 richer.

On the other hand, when you scoop once, you actually win all $80 your opponents have contributed to the pot (and you get your own investment back). If you go home after scooping one such pot and losing none, you’ll be $80 richer.

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All you've proved in this example is that it's better to have a 1/2 probability of scooping than a 2/3 probability of splitting.