Omaha 8 article -- The Flaws

[Ergodicity]

[ QUOTE ]
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.

[/ QUOTE ]

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

[ QUOTE ]
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.

[/ QUOTE ]

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."


[ QUOTE ]
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.

[/ QUOTE ]

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.

[Ergodicity]

The other piece that is misleading in the article is that it says "1 scoop out = approx. 3 low outs", and implies that this somehow has to do with the fact that this is a split pot game (since it says it literally 1 sentence below where it says "two outs for half the pot are not equal to one out for the whole pot")

The reality is that outs for half the pot are exactly equal to half of the value of scoop outs. It's just that given the nature of the game, its fairly common for someone to have your identical hand (ie. you both have A2).

But the fact that someone else has your identical hand is not specific to a split pot game -- you will very often have someone else have your same straight (and less commonly your same fullhouse) in pot-limit omaha (high only), and it happens in holdem also.

You could just as easily change the example to say, "If you run a ten handed simulation 100000 times, giving Hero A2TT, making the board 45JQK rainbow, then Hero is scooping unless someone has his same straight, so his scoop here is not really scooping all the time and thus "1 scoop out = approx. .8 scoop outs."

So adjusting the approximate value for outs for low is something you need to do because of your opponents likely holdings and your hand reading -- NOT because of anything inherent in a split pot game. In fact in Stud8, you will tie much less frequently for low and thus don't discount your outs.

[Buzz]

[ QUOTE ]
Quote:
------------------------------------------------------------------------
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.
------------------------------------------------------------------------
Yes, it is. Equity calculators like twodimes are entirely correct.

[/ QUOTE ]Ergoicity - There is a typo in what you have quoted. I didn’t mean two “cards” (which doesn’t make any sense). I meant two “hands.” Here’s the correction:

<font color="red">Thus it may seem as though two hands that win half the pot for Hero are equivalent to one hand that would scoop the pot for Hero. However, that is not true.</font>

And, with that correction, I think that which I wrote is true. I am not saying twodimes is not correct. (I find twodimes very useful). Instead I am saying it’s misleading to think of winning two halves of a pot as equivalent to winning one whole pot (assuming the pots are of equal sizes).

They are only equivalent in a simulation where you simulate being dealt a given hand a certain specified number of times and where you lose when you don’t win.

Otherwise, assuming pots of equal sizes, being awarded two half pots does not equal being awarded one whole pot, in terms of what you net as winnings.

Instead, two half pots equal one whole pot plus one entirely losing venture.

Perhaps it is a subtle difference, but I think the reader should see it.

[ QUOTE ]
Quote:
------------------------------------------------------------------------
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.
------------------------------------------------------------------------
The bolded statement is where you go astray with your logic, because you are comparing apples to oranges.

[/ QUOTE ]No. I am comparing <font color="blue">your net</font> in winning half of a pot twice to <font color="blue">your net</font> in winning all of a pot once.

[ QUOTE ]
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.

[/ QUOTE ]No. A hand that has a good chance of scooping is more than twice as good as a hand that has an equal chance of winning half the pot.

I do not have to play every hand I am dealt. I do not have to play hands that have a very poor chance of scooping.

You very well may be able to play circles around me. But I can protect myself at least somewhat by sticking to starting hands that have a decent chance of scooping.

[ QUOTE ]
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.

[/ QUOTE ]Exactly!

[ QUOTE ]
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.

[/ QUOTE ]Are you more likely to see a split pot in Texas hold ‘em or Omaha-8? (rhetorical)

[ QUOTE ]
paying the cost of playing a hand to showdown is irrespective of the game being played.

[/ QUOTE ]Agreed. However, what you don’t have to do is always pay the cost of playing every hand to the showdown.

[ QUOTE ]
Just as your equity is irrespective of o8 being a split pot game.

[/ QUOTE ]This statement does not logically follow as a consequence of those preceeding it. And perhaps ”equity” does not have the same meaning to me as to you. (I don't think it does).

Buzz

[Ergodicity]

[ QUOTE ]
Thus it may seem as though two hands that win half the pot for Hero are equivalent to one hand that would scoop the pot for Hero. However, that is not true.

[/ QUOTE ]

The above statement is now technically true using your strange assumption that one player plays more hands than another one. But its still completely irrelevant for determining how you should play a given hand.

And it has nothing whatsoever to do with O8 or split pot games, and nothing to do with your equity in a split pot game. Change the above statement to "Two hands that win a $500 pot are not equivalent to one hand that wins a $1000 pot, when you have to put $250 of your own money in on each hand" and it applies equally well to all poker games, split pot or not.

Let's take two examples that come up pretty often in O8. in both cases you call 1 bet on to see the river and your opponent is all in.

Hand 1: You have AAKK, and your opponent has A2QJ, and the board is KT98. So your opponent has the straight and you have a set and need to hit your full-house on the river to win, and there is no low draw. 10 of 40 unseen cards make your boat, and 30 of 40 cards get you nothing. So your equity as calculated by twodimes is 25%. You have 10 scoop outs.

Hand 2: You have A23K, your opponent has KKJ8, and the board is 679K. So your opponent has top set (KKK) and thus will always win high. You are drawing for low, and have 20 outs to win the low half (any A,2,3,4,5,8 that are not already in someone's hand). So 20 of 40 cards win you the low half of the pot, and the other 20 of 40 cards give you nothing. So your equity in twodimes is 25%. You have 20 half-pot outs.

Here's the important part: Your equity in both cases is the same. Your profit in both cases is the same your bank account after running this situation millions of times will be identical. A half pot out is equal to exactly one-half of a scooping out in terms of the money you win or lose.

So when you are playing the hand, you should not be discounting any outs "just because its only half the pot". You can only discount outs if someone else will have your hand and split.

[Phat Mack]

[ QUOTE ]
[ QUOTE ]
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.

[/ QUOTE ]

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.


[/ QUOTE ]

The examples Buzz gives for scooping and splitting both have ten outs, therefore their winning frequency is identical, so I don't think he is comparing apples and oranges. For every pot the splitter drags, the scooper drags one. Yet the scooper nets $500 for a $100 investment, while the splitter nets $200 for the same buck.

I don't think Buzz is criticizing 2dimes or any other software, nor is he discounting the possibility of being quartered for high or low, nor is he implying there is anything magical about hi-lo games. He's merely suggesting that it is more than doubly better to scoop a pot than to split it.

[Phat Mack]

[ QUOTE ]
Hand 1: You have AAKK, and your opponent has A2QJ, and the board is KT98. So your opponent has the straight and you have a set and need to hit your full-house on the river to win, and there is no low draw. 10 of 40 unseen cards make your boat, and 30 of 40 cards get you nothing. So your equity as calculated by twodimes is 25%. You have 10 scoop outs.

Hand 2: You have A23K, your opponent has KKJ8, and the board is 679K. So your opponent has top set (KKK) and thus will always win high. You are drawing for low, and have 20 outs to win the low half (any A,2,3,4,5,8 that are not already in someone's hand). So 20 of 40 cards win you the low half of the pot, and the other 20 of 40 cards give you nothing. So your equity in twodimes is 25%. You have 20 half-pot outs.

Here's the important part: Your equity in both cases is the same. Your profit in both cases is the same your bank account after running this situation millions of times will be identical. A half pot out is equal to exactly one-half of a scooping out in terms of the money you win or lose.


[/ QUOTE ]

Here's another example: No suits; you have KKQQ; opponent has A256; pot $800; opponent bets $100; 4th street.

Hand one: Board is K34 7. You have 10 outs to split. You call $100. Run four times, you will invest $400 and win one $500 pot for a $100 profit, or $25 per hand.

Hand two: Board is K78 9. You have 10 outs to scoop. You call $100. Run four times, you will invest $400 and win one $1000 pot for a $600 profit, or $150 per hand.

No getting quartered, no duplicated hands, yet the 10 scoop outs are worth six times as much as the 10 split outs.

You may occasionally have to worry about splitting in high-only games, but not nearly to the same extent. Omaha 8, Stud 8, Binglaha, Studugi, River-down hi-lo hold 'em, Anaconda--all the hi-lo games share this fundamental concept.

jmo

Mack

[Buzz]

[ QUOTE ]
Let's take two examples that come up pretty often in O8. in both cases you call 1 bet on to see the river and your opponent is all in.

Hand 1: You have AAKK, and your opponent has A2QJ, and the board is KT98. So your opponent has the straight and you have a set and need to hit your full-house on the river to win, and there is no low draw. 10 of 40 unseen cards make your boat, and 30 of 40 cards get you nothing. So your equity as calculated by twodimes is 25%. You have 10 scoop outs.

Hand 2: You have A23K, your opponent has KKJ8, and the board is 679K. So your opponent has top set (KKK) and thus will always win high. You are drawing for low, and have 20 outs to win the low half (any A,2,3,4,5,8 that are not already in someone's hand). So 20 of 40 cards win you the low half of the pot, and the other 20 of 40 cards give you nothing. So your equity in twodimes is 25%. You have 20 half-pot outs.

[/ QUOTE ]Ergodicity - I follow what you are saying. And it makes complete sense for simulations.

However, when you’re involved with a hand and facing a bet, you’re not going to be playing the hand 40 times (or whatever). You’re only going to be playing it that one time. And if you actually will win $750 if you scoop the pot but only $250 if you win half the pot, and if the bet is $250 to you, then before you throw your bucks into the pot, an out that scoops the pot is clearly worth more than twice as much as an out that only wins half the pot. (You’re getting 3 to 1 odds for scooping and 1 to 1 odds for winning half the pot).

I realize you get your own $250 back in both cases. But you don’t have to make the investment. Do you want to invest your money for 3 to 1 or 1 to 1?

I have some other issues with what you wrote, but they're not to the point of the article.

Buzz

[Buzz]

Mack - Exactly.

Thank you.

Buzz

[MeetUrTwin]

[ QUOTE ]
He's merely suggesting that it is more than doubly better to scoop a pot than to split it.

[/ QUOTE ]

This is just a smoother way of saying the same mistake. It is NOT doubly better to scoop than to split when you take into account enough trials that the true odds of achieving a scoop or a split are "fairly" represented. When that happens, it is precisely "doubly good" to scoop.

[Brocktoon]

Scooping is quite obviously more than twice as profitable as splitting.

This can easily be shown with a hypothetical example where a player bets $X on the river into an empty pot. If the pot is heads up then the player who is calling the $X bet clearly makes ZERO profit if he wins half of the pot yet makes $X in profit when he wins. Here scooping is infinitely more profitable than splitting.

It is true that in the above example you recieve $X from the pot when you split and receive $2X for a scoop, which would seem to suggest that the split is indeed worth half of a scoop. However, when we subtract our investment (call) of $X from what we get from the pot we are only left with more than we started when we scoop. The split is worth $0 to us meaning that calling and folding when we have a definite split are equal in value.

The bigger the pot is in relation to the last bet called the closer splitting is to being exactly half as profitable as scooping, though it never totally gets there. If your lone opponent goes all-in for $1000 dollars into a $1 pot then splitting gets you a pack of gum while scooping might pay your rent for the month. If the same guy goes all in for $1 into a $1000 pot then splitting is just about exactly half as good as scooping and you need to call with any shot of getting 1/2 the pot.

This is all intuitive and we all understand this. So why are we arguing?