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:
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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.

[/ 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:
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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.
------------------------------------------------------------------------
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?

[MeetUrTwin]

[ QUOTE ]
So why are we arguing?

[/ QUOTE ]
Considering only a single hand, you are correct, scooping is more than 2x as profitable as splitting. However, this is useless information in isolation, and by constructing a case where the EV of the scoop vs. the split are equal, Buzz has inadvertantly created an idea that is very easily misinterpreted (by himself even). The mistake he uses is that he will run the split case twice, allowing the player to win the same revenue while risking two bets, yet he only runs the scoop scenario ONCE. Apples to oranges.

Let me draw up another example. Suppose you have a 50% chance of splitting. However, instead of a 25% chance of scooping, let's say you have a 10% chance of scooping only. Now, the scoop is still "more than doubly profitable" than the split; however, we would never be so stupid as to believe that this is justification for thinking it is better to draw to this scoop than to the split. Even if we run the split case twice, we arrive at EXACTLY the same conclusion Buzz arrives at in his article. From Buzz:

"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."

BUT THIS IGNORES THE FACT THAT THE SCOOP ONLY COMES 10% OF THE TIME! You must take 10 trials here; 1 in 10 where the scoop wins, 5 in 10 where the split comes. ONLY then can you see how ridiculous it is to claim that the scoop is more valuable than the split.

Now, you might claim that everybody understands these concepts perfectly well (still, I'm not completely convinced that's the case). However, the spirit of Buzz's article and his usage of this confusing concept is entirely misleading to O8 players, and that is the real reason I'm arguing about it. Buzz is clearly trying to use this scenario study to promote the old adage in O8 that we should aim to scoop rather than split is correct in many senses. Unfortunately, his argument offers absolutely no justification for that adage, because in his scenario, a scoop is exactly identical to a split, in any intelligent interpretation of the scenario (which requires several trials to allow the true odds to be revealed). The "try to scoop not split" adage primarily is concerned with starting hands--it is the reason why we might prefer to play a hand like A234ds rather than A29Qr in a full ring game, since the A234ds will make many more nut high hands than the A29Qr against a field, DESPITE the fact that A29Q is statistically better head to head if both hands are always played to showdown:

Omaha Hi/Low 8-or-better: 500000 sampled boards
cards scoop HIwin HIlos HItie LOwin LOlos LOtie EV
4c 3c Ad 2d 122764 215220 263769 21011 129827 0 143051 0.485
2s Ac Qd 9h 167107 263769 215220 21011 0 39534 143051 0.515

However, to say that scoop outs are "worth more" than split outs, using exactly the case that Buzz uses, where the EV of the two scenarios is identical, is complete nonsense. When it comes to scenarios where you split 50% of the time vs. scenarios where you scoop 25% of the time, the two ARE IDENTICAL.

edit: holy sht. I just realized that in the example he is using, hero has exactly the same % chance of making a winning hand in both cases. Then obviously the scoop draw is better. Jesus, I thought this article was analogous to that old thread, which was actually interesting. Instead, it's just an obvious spot of playing to half the pot for the same odds as playing to the full pot. Duh, Buzz.

btw, the thread I'm referring to is here:

http://forumserver.twoplustwo.com/showfl...rt=all&amp;vc=1 (http://forumserver.twoplustwo.com/showflat.php?Cat=0&amp;Number=3967982&amp;page=0&amp;fpart=all &amp;vc=1)

[Brocktoon]

[ QUOTE ]
Considering only a single hand, you are correct, scooping is more than 2x as profitable as splitting.

[/ QUOTE ]

I agree. Honestly I believe this is all that Buzz was trying to say the whole time. If you agree with the above then again, I don't see why we're arguing.

[ QUOTE ]
Instead, it's just an obvious spot of playing to half the pot for the same odds as playing to the full pot. Duh, Buzz.


[/ QUOTE ]

He's saying that its more than twice as good to play for the whole pot than to play for half the pot with the same odds. Intuition would tell you that it is exactly double the profit of splitting.



FWIW, I found this from the original Super System:


David Sklansky wrote:

[ QUOTE ]
Your primary goal at High-Low is to win the WHOLE pot.



"Who didn't know that?" you might say. Well...a lot of people don't know it. Because if they did, they wouldn't be in the pot so often trying to escape with half of it. They don't know how much more profitable it is to win the whole pot. A simple example will show you what I mean. Let's say you're in a three-handed pot and each player has $600 in the pot when it's over. If all you do is split the pot, you wind up with a $300 profit (half of the $600 that one of the players lost). That's really not much when compared to the $1,200 you'd win if you won the whole pot. As you can see, its not twice as good... its four times as good. And when the action is only heads up, a split means mearly that you get your money back (with the exception of the very small profit you get from splitting the antes). But when you win the whole pot heads up, its the difference between winning practically nothing and winning everything.

[/ QUOTE ]

*all bold and italics are Sklansky's, not mine.

[MeetUrTwin]

[ QUOTE ]
He's saying that its more than twice as good to play for the whole pot than to play for half the pot with the same odds. Intuition would tell you that it is exactly double the profit of splitting.

[/ QUOTE ]

yes, my point of confusion is that Buzz has (in the past) claimed that scooping is more than equally profitable to splitting and winning half, when the chances of achieving the split are exactly twice the chances of scooping. That is, 50% chance to split in the split scenario, 25% chance to scoop in the scoop scenario. It is that claim that I thought he was repeating, and it is that claim which is incorrect.

The difference is subtle, because in his current analysis, you only have to run the outcome once since the odds are the same.

[Phat Mack]

I've noticed that one source of confusion is that there is no established algebra of outs. If you can say that having a hand with 10 scoop outs is more that twice as valuable as having a hand with 10 split outs, you can't derive from this statement a futher statement that having a hand with 10 scoop outs is greater in value to a hand with 20 split outs. The math won't support it.

OP starts with two quotes. The first quote talks about (hands) that win 1 scoop pot vs. hands that win 2 split pots. It is not clear to me that Buzz is discussing a split draw with twice as many outs as the scoop draw, but that is what OP assumes.

OP then projects this concept of twice as many outs on the second quote. But the second quote is about the same hand with the same number of outs drawing a scoop and then drawing for a split. It does not compare a hand with 10 scoop outs with a hand having 20 split outs.

While it is possible to say that 10 scoop outs equals 20 split outs, it is not possible--unless, as Brocktoon notes, the existing pot goes to infinity--to state that 10 scoop outs has exactly twice the value as 10 split outs.

The introduction to Buzz's article starts out by saying that a scoop out is more valuable than a split out, which is true when comparing hands with equivalent outs. It then goes on to say that 1 scoop out = ~2.5 split outs, which is fine if is discussing earning potential, but is confusing if it leads readers to believe that a hand with 10 scoop outs = a hand with ~25 split outs.

JMO

Mack

[jai]

The main point of Buzz's article—that a scoop out is better than 2 times a split out in terms of net winnings is irrefutable. But that is patently obvious to anyone who has spent more than 2 minutes thinking about split pot games and, to be frank, not very useful information. Furthermore, trying to quantify the relative value of a split out to a scoop out is absurd—it will be too heavily dependent on final pot size relative to bet size (as an aside, as pot size approaches infinity, the net winnings on scooping once approaches exactly twice the net winnings on splitting once). What *is* useful is being able to figure out EV knowing whether you have split outs or scoop outs. And when you think about outs in this way, then split outs are exactly equal to 1/2 of scoop outs.

To illustrate, let's look at the example that PhatMack provided where you have top set and are either drawing to scoop or split.

In case 1, we have 10 outs to split. What is our EV? Let's count our split outs as 1/2 outs, so we have 5 "outs" in this case. We are calling 100 into a pot that will be 1000 and our equity is 5/40, or 12.5%. 12.5% of 1000 is 125, so our EV=125-100, or 25.

In case 2, we have 10 outs to the whole shebang, so let's call that 10 outs. Equity is 25% into a pot size of 1000, which is 250. EV=250-100=150.

So split out equity is exactly 1/2 of scoop out equity. And in terms of actual dollar amounts, the split pot EV gets closer and clozer to 1/2 the scoop EV the larger the pot gets (to see this, increase pot size by 1000 increments and calculate EV).

[7n7]

[ QUOTE ]
But that is patently obvious to anyone who has spent more than 2 minutes thinking about split pot games and

[/ QUOTE ]

Well, not exactly true... /images/graemlins/blush.gif

[jai]

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

[/ QUOTE ]

If you are trying to compare the EV of scoop outs to split outs directly then you are not thinking about the problem in the right way.

[jai]

[ 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 ]

You are only partially correct. In the case where your split outs are exactly twice your scoop outs they have identical equity, hence the EV will be the same. When the ratio is different, you can not derive a general rule for how much scoop outs are worth, EV-wise, compared to split outs. PhatMack illustrates in his post an example where scoop outs are worth 6x as much as split outs.

Rather, you can derive that equity of 1 scoop out is equal to equity of 2 split outs. From there you can calculate EV.

[Phat Mack]

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

[/ QUOTE ]

If you are trying to compare the EV of scoop outs to split outs directly then you are not thinking about the problem in the right way.

[/ QUOTE ]

Agreed, I only meant it as an illustrative example. (I was toying with the idea of trying to find an algebraic structure for outs, but doing so would be both trivial and futile, and, as you say, not the correct way to think about the game.)

It would be nice to nail down some terms, however: Equity; EV; profit; revenue; worth, etc. I think confusion about what people were talking about drove a lot of this thread.

The summation in your first post tied things together nicely, I thought. (I'm not sure equity and EV are the same thing, but don't let's even go there /images/graemlins/smile.gif )

Congrats to Buzz for providing such an interesting and provocative article.

[jai]

[ QUOTE ]
The summation in your first post tied things together nicely, I thought. (I'm not sure equity and EV are the same thing, but don't let's even go there /images/graemlins/smile.gif )

[/ QUOTE ]

No equity and EV are not the same thing, but I think we should go there because it's important. The equity calculators like twodimes, as the name implies, tell you equity. Some people think that means they give you EV. That is not the case. Once you have figured your equity, you can use this number to calculate EV using the general formula: EV=pot equity*amount in pot after all bets are made-amount to call.


[ 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 ]

This is from Buzz's article. And the following point is even more important. Buzz is saying that winning a split pot twice nets you less than scooping the pot once. That's true. Any retard can see that winning 1/2 the dead money in the pot twice is not as good as winning all of the dead money in the pot plus what your opponent bet once. Buzz you're 100% right about that. But that is completely and utterly irrelevant to how you should play the hand. . Your net gain on average is exactly the same for both cases in the above example. It seems as though everyone on 2+2 has tried telling you this, but you still don't believe it. In the example you cited above, your EV is exactly the same with 2 split outs as 1 scoop out, so you should play them exactly the same way. All this nonsense about what fraction of a scoop out a low out is worth is just wrong, misleading, and bad advice.

[MeetUrTwin]

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Any retard can see that winning 1/2 the dead money in the pot twice is not as good as winning all of the dead money in the pot plus what your opponent bet once. Buzz you're 100% right about that. But that is completely and utterly irrelevant to how you should play the hand. . Your net gain on average is exactly the same for both cases in the above example. It seems as though everyone on 2+2 has tried telling you this, but you still don't believe it. In the example you cited above, your EV is exactly the same with 2 split outs as 1 scoop out, so you should play them exactly the same way. All this nonsense about what fraction of a scoop out a low out is worth is just wrong, misleading, and bad advice.

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Bingo.

Jai, well done in this thread.

[Phat Mack]

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All this nonsense about what fraction of a scoop out a low out is worth is just wrong, misleading, and bad advice.


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I disagree. Comparing relative worths is the correct way to approach the game. Trying to find a precise ratio between scoop outs and split outs might be futile, but understanding the difference between scoop and split EVs is a better approach to the game than by comparing equities. We can all think of examples where hero faces a bet on fourth street against a single opponent in a forked universe where is equities from scooping and splitting converge with his EV, but being able to do this doesn't help much in other situations.

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But that is patently obvious to anyone who has spent more than 2 minutes thinking about split pot games and, to be frank, not very useful information.

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This is grand to read, and I would love to believe it, but nothing in my experience leads me to believe it's true. In fact, I think the confused thinking about this issue by otherwise rational players is one of the reasons that hi-lo games can be so good.

[iH8poker]

I hate to bring this back up but want to state it one time simply.

Let's say your chance of scooping on the river is 25% in hand A and in you have a 50% chance of spliting in hand B.

Let's say you must call $100 to see the river in each scenario, creating a total pot size of $1000.
Let's assume no implied odds (if you make your scooping hand, he will fold any river bet, and if you split the pot, then you will get only 1 caller whom takes the other half).

Here the formula is:
Hand A = .25 X 1000 - 100 = $150 EV to scoop or
Hand B = .50 x 500 - 100 = $150 EV to split.

Ah that just solved it for me!
Now let's say the implied odds of a $200 bet being called on the river after your hand is made in the scoop and a $200 bet being called by one whom takes neither half of the pot in the split, then...

Hand A = .25 X 1000 - 100 + 200 x .25 = $200 EV to scoop or
Hand B = .50 x 500 - 100 + 100 x .50 = $200 EV to split.

I think I did that right. Presense of rake does not change the outcome.

iH8poker /images/graemlins/club.gif