Marginal holdings

[Buzz]

[ QUOTE ]
the best 234x hands for scooping are almost twice as likely to scoop as the worst hands. So while you win only 33% more pots with the best hands, the fact that so many more are scoopers should show a much greater profit for the better 234x hands.

[/ QUOTE ]

Hi Chaos - I agree.

If there are four chips in a pot and one of them is yours, then when you scoop, you win three chips.

If there are four chips in a pot and one of them is yours, then when you get half, you win one chip. If you win two pots, then you win a total of two chips.

The simulator counts winning the half the pot twice the same as scooping once.

But you clearly win more by scooping once than by winning half twice.

In the example I used above, if 1/4 of the chips in the pot are yours, then you win 1.5 times as much by scooping once than by winning half twice.

But for a slightly different scenario, if 1/6 of the chips in the pot were yours, then you would win 1.25 times as much by scooping once than by winning half twice. (If anyone reading this finds it hard to follow, stack up different colored chips, one color for yours and another color for all your opponents, and it should be obvious).

Thus the factor by which scooping once is better than winning half twice is variable, depending on how many of your opponents see the flop and how long they stay in the hand.

And the variability of winning less of a fraction than one half complicates matters even more.

There's probably a better way to come up with the measure of a hand than just adding Wilson's three columns
(high only pots)
(low only pots)
(scooped pots)
together, as I did.

Wilson wisely does not add these three columns together, but I did in coming up with my totals.

However, I think there's probably a better way for me to come up with a comparative number for each hand.

For example, in the 234Kd hand, if I counted each scoop as 1.5 times more profitable than two half wins (or three third wins, or four quarter wins, etc.), then instead of
234Kd.....254......978.....538.....1770, I'd have
234Kd.....254......978.....538*1.5..2039.

And for 2348n, instead of
2348n.....151......972.....222.....1345, I'd have
2348n.....151......972.....222*1.5..1456.

Probably 2039/1456 is closer to the relative value of 234Kd/2348n than 1770/1345.

Makes it more complicated for anyone to follow, but probably better, although simple is nice.

At any rate, thanks for pointing the matter to my attention. I'll think about it some more and maybe revise my existing relative hand values. If anybody has any ideas, I'm all ears.

Buzz

[chaos]

I have been thinking about this some more. Decided to check the effect of having opponents who fold.

10,000 run simulation results from Bill Boston’s book

hand......high.....low....scoop.....total
2234d.....438.....815.....1206.....2459
2334d.....440.....811.....1219.....2470
2344d.....470.....784.....1258.....2512
234Kd.....477.....816.....1248.....2541

2346n.....439.....835.....899.....2173
2347n.....321.....714.....649.....1684
2348n.....310.....709.....624.....1634
2349n.....267.....749.....648.....1664
234Tn.....280.....754.....665.....1699
234Jn......287.....754.....704.....1745


His total column is the sum of the other three and is thus when you win some or all of the pot.

Very similar to your no-folding results. The good hands win more and they scoop a lot more. The main difference is 2346 not suited improves when simulated against players who fold.

[XxPenguinxX]

Thanks for all the advice - there's some fantastically helpful stuff here. And sorry it took me so long to offer those thanks!

[Buzz]

Chaos. Thanks.

If you play a hand 10 times and scoop 2 times, you end up with the same number of chips as if you play a hand 10 times and win half the pot 4 times or play a hand 10 times and win a quarter of the pot 8 times. So in a sense it’s correct to add the scoops and partial pot wins together. (That's what Bill Boston did, and that's what I did too). But that’s misleading, because if you bet $100 into a heads-up pot and break even, you don’t <font color="white">_</font>win anything. You put your chips at risk and although you didn’t <font color="white">_</font>lose anything, neither did you earn anything for taking the risk.

I’m not sure I’m explaining it very well, but I do think scooping once is better than winning half twice. You’re only taking the risk once instead of twice.

But I don’t know how to give a number to how much more scoops are worth.

At any rate, I’ve been thinking about it too.

Buzz