Omaha 8 article -- The Flaws

[Ergodicity]

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In simulations, winning half the pot two times in ten and losing the other eight times is exactly the same as scooping the pot one time in ten and losing the other nine times. Thus it may seem as though two cards that win half the pot for Hero are equivalent to one card that would scoop the pot for Hero. However, that is not true.

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Yes, it is. Equity calculators like twodimes are entirely correct.

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Case I. There is no possibility of low so that if you make your draw, (i.e. if the board pairs) you will scoop and win $500 (You get your own white chip back and win the five blue chips).

Case II. Low is possible, so that if you make your draw, you will probably have to split the pot with low. If so, you will win $200. (You get three chips (half) back from the six chip pot – make them your own white chip and two blue chips).

Winning half such a pot twice nets you $400. Winning all such a pot once nets you $500.

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The bolded statement is where you go astray with your logic, because you are comparing apples to oranges. If you look at a situation where winning all of the pot once is correct, then to win half the pot twice means you are twice as likely to win some portion of the pot. Which means the guy scooping is twice as likely to LOSE a portion of the pot.

If your equity was equivalent in each case, then the bolded statement would read, "Winning half a pot twice nets you $400 (because we ran this twice and both times you put in your $100 and both times you won half of the $600 pot). Winning all such a pot once also nets you $400 (because we ran this twice and both times you put in your $100, but once you lost and got back nothing and once you won the $600 pot). And obviously you had to have won half the pot twice for every once you won the entire pot (which is where the running twice piece comes in), otherwise you wouldn't have had the same equity."


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It’s true that if you scoop once and lose once, you end up with the same amount as when you win half the pot twice (assuming pot sizes are the same). However, you will end up with more chips if you only put your chips at risk once and if you scoop that one time, than if you put your chips at risk twice and win half the pot both times.

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Here is the mistake you are making: You are saying, "If I just play this hand out once, put in my $100 and win a $600 pot, that nets me a profit of $500. And its better than playing two hands, putting in $100 on each of those, and winning a pot that is half as big on each of those hands".

Of course it is. But that has nothing to do with O8 being a split pot game. Take the above sentence and simply translate it to holdem to see why.
"I played my AA, and had to call $100 at the river to win a $600 pot, which i won for a profit of $500, so I sat out. My buddy played his KK and QQ on successive hands and called $100 on each hand and won a $300 pot on each hand, so he netted $400".

On other words, paying the cost of playing a hand to showdown is irrespective of the game being played. Just as your equity is irrespective of o8 being a split pot game.