[Buzz]

TGoldman - That's beautiful!

What a well chosen set of cards and money! Did Greg do that, or did you? In any event, very clever!

Hero has either 20/40 outs to take half the pot or 10/40 outs to scoop.

And when the amount in the pot is three times the investment, the odds seem exactly the same. Well done!

But let's make the amount in the pot seven times the investment, as it would be if both players started with $100 each, each had already invested $75 in the pot, and Villain bet $25.

Now when Hero scoops he wins seven times what it costs him to call. But when he wins half the pot, he only wins three times what it costs him to call. He's getting 7 to 1 scoop odds but only 3 to 1 half-pot odds.

Or we could go back to the original example, I suppose. With $150 in the pot, Hero is getting 3 to 1 whole pot odds and only 1 to 1 half pot odds. It's made confusing because of the clever choice of cards and monies involved.

It reminds me of the old bell boy tip puzzle. (Where did the extra dollar go?)

The plain truth is you get better than twice the odds for scooping once than you get for winning half of the pot twice.

The way the simulators tally the results is slighlty misleading. They count two half pot wins the same as one whole pot win. And of course that makes sense.

It's in terms of the odds you're getting when you call the bet that there's the discrepancy. You have to put your chips at risk twice as often to get the same amount back!

Think of it this way: Suppose you were at the race track. Would you rather bet ten dollars once and win seventy dollars, or would you rather bet ten dollars twice and win thirty dollars each time? Either way, when you go to the window to collect, you are awarded a total of eighty dollars.

See it?

Even though you get your own money back, you don't want to be thinking you won eighty dollars. (You either won seventy dollars or sixty dollars).

If you bet ten dollars twice and only win seventy dollars once, that's the same as betting ten dollars twice and winning thirty dollars each time. Looks the same, but it's not.

I think the key to understanding is realizing you have to take twice the risk to get the same money back when you compare half pots to scoops.

And that makes scoops worth more than winning twice as many half pots. But when twodimes.net tallies the results, there's no way to account for that double risk factor.

I've got the much the same problem when I run simulations using Wilson. The low total displayed is the total number of half pots for low times two plus the total number of quarter pots for low times four plus the total number of sixth pots for low times six plus the total number of eighth pots for low times eight. In short,
H*2+Q*4+S*6+E*8 = the total given under "low only pots" in the totals frame of the statistical data to review.

Here are the results of two hands compared (both 10000 runs against eight random hands with random board cards)

hand......high...low....scoop
9JQQs.....471.....0.....815
A333n......77...1071....138

Wilson wisely doesn't total the highs+lows+scoops to get a total. (Twodimes.net does, and records it as "E.V.").

When I total them myself, I get:
hand......high...low....scoop...total
9JQQs.....471.....0.....815.....1286
A333n......77...1071....138.....1286

Neither starting hand is great, but I think
9[img]/images/graemlins/heart.gif[/img], J[img]/images/graemlins/club.gif[/img], Q[img]/images/graemlins/diamond.gif[/img], Q[img]/images/graemlins/heart.gif[/img] is a better starting hand than
A[img]/images/graemlins/heart.gif[/img], 3[img]/images/graemlins/club.gif[/img], 3[img]/images/graemlins/diamond.gif[/img], 3[img]/images/graemlins/spade.gif[/img].
I think that mainly because, although they both have the same winning total, 9JQQs scoops more than A333n.

But how do I quantify that difference?

Anyhow, I don't mean to steal your post with my own problems, and I hope I have made clear to you that scooping is worth more than winning half the pot twice, although the simulator has to show them as the same if the simulator tallies the results (as twodimes.net does).

Buzz