Scoops worth more than twice as much as 1/2 pots...

[Brocktoon]

[ QUOTE ]
Case I. You're getting 5 to 1 money odds for the whole pot.

Case II. You're getting 2 to 1 money odds for half of the pot. (We’re assuming in addition to the spade flush or straight, your opponent also has low).


[/ QUOTE ]

I just read the article and while I agree that scooping is more than twice as good as taking 1/2 the pot, because of the investment of the last bet, it cannot be shown to be 2.5 times better because it happens to net you 2.5 times more than splitting in the given example. The 5:1 vs 2:1 ratios arrived at are purely a function of the pot size in relation to the final (all-in) bet. Different pot sizes would yelid completely different results.

Lets say the pot has 1000 chips in it and everything else is exactly the same as the example in the article including the opponent going all in for 100 chips on the end.

Now it looks like this:

Case I. You scoop the $1200 pot, getting your own $100 last bet investment back plus winning the $1100 that was in the pot.

Case II. You win half the $1200 pot, getting your own $100 last bet investment back plus another $500 of the $1100 that was in the pot.

Case I you are getting 11:1 money odds for the whole pot.

Case II you are getting 5:1 money odds for for half of the pot. (We’re assuming in addition to the spade flush or straight, your opponent also has low).


Now while scooping is still better than 2X as profitable as splitting, its not by the same 2.5:1 ratio because the pot is bigger.

Similarly, if the pot had 100 chips in it and the opponnent went all in for 100 chips scooping is WAY more than twice as profitable as splitting. It looks like this:

Case I. You scoop the $300 pot, getting your own $100 last bet investment back plus winning the $200 that was in the pot.

Case II. You win half the $300 pot, getting your own $100 last bet investment back plus another $50 of the $200 that was in the pot.

Case I. You're getting 2 to 1 money odds for the whole pot.

Case II. You're getting .5 to 1 money odds for half of the pot. (We’re assuming in addition to the spade flush or straight, your opponent also has low).

Here scooping is 4X better than splitting! However, clearly this cannot be used to say that scoop outs are ALWAYS worth 4 times as much as split outs.

Its all relative. As pot size increases splitting becomes closer to truly being worth 1/2 as much as scooping, while never quite getting there. As the pot size decreases as a proportion of the final bet, scooping becomes increasingly more profitable to splitting.

In the most extreme example, no chips on the pot on the turn and facing a bet, scooping is worth infinitely more than splitting.

[Buzz]

[ QUOTE ]
scooping is more than twice as good as taking 1/2 the pot, because of the investment of the last bet, it cannot be shown to be 2.5 times better because it happens to net you 2.5 times more than splitting in the given example.

[/ QUOTE ]Brocktoon - Agreed. Scooping is not always (or even usually) exactly 2.5 times better. I was not trying to imply that scooping is always 2.5 times better than winning half the pot. I was trying to use a simple example to show scooping is clearly more than twice as good as winning half the pot.

[ QUOTE ]
The 5:1 vs 2:1 ratios arrived at are purely a function of the pot size in relation to the final (all-in) bet. Different pot sizes would yelid completely different results.

[/ QUOTE ]Yes. Good point. I was trying to use a simple clear example to make my point. I didn't mean the ratios would always be 5:1 and 2:1 (and it seems obvious they would not be).

And yet it turns out to be very handy to give approximate relative values to outs, some of which typically are for the whole pot and others which are for part of the pot. In a typical full loose game, an out that would win the high half the pot often is worth about 0.4 as much as a scoop out (rather than being worth exactly 0.500 as much as a scoop out). And that’s where the ~2.5 comes from. I think the reader has to appreciate that since the relative value of an out for half the pot varies, the value given is an approximation for a typical situation at a typical full casino table.

1 scoop out = ~2.5 high outs = ~3 low outs is useful as an approximation at a typical full table, and certainly truer than
1 scoop out = 2 high outs = 2 low outs.

Funny. I used to prepare lectures and I'd try to anticipate questions. Sometimes I'd spend hours figuring out how to answer questions that never got asked. Other times it wouldn't occur to me that someone would misunderstand what I meant at some particular point. It's much the same writing a short article. You want to keep it brief and concise and yet cover the topic thoroughly enough for the reader to grasp the principles involved.

Anyhow I hope this clears up any misunderstanding. And thank you for taking the time to share your thoughts about the topic.

Buzz

[MeetUrTwin]

Brockton, this scoop-vs-1/2-pot thing has been beaten to death before, in this thread. (http://forumserver.twoplustwo.com/showflat.php?Cat=0&Number=3967982&page=0&fpart=all &vc=1) As you can see, the message did not sink in to all parties.