What are the odds of low in Stud 8 or Better

[Buzz]

Mack - Wait! I see it!

The following differences must represent the low draws.
437_____431_____394_____414_____382_____418_____40 2
_50______41______41______44______38______35______2 5

Thus the low draws must be as follows:
387_____390_____353_____370_____344_____383_____37 7
Total low draws from simulation data must be 2604.

69827 - 2604 = 67223.

Thus someone has a qualifying low in a seven handed game of stud-8 about 67% of the time.

As an aside, when you make a winning low hand in a seven handed stud-8 game, according to Mack’s simulation data, evidently you are quartered about 3.8% of the time. (Interesting. Getting quartered for low in stud-8 occurs much less often in stud-8 than in Omaha-8. In a loose seven handed game of Omaha-8, an A-2 nut low figures to be quartered 31% of the time and sixthed another 3% of the time).

Darned if I didn’t turn this into an Omaha-8 post.

Buzz

[therazz]

Buzz & Mack, thank you very much for efforts. It is greatly appreciated.

[Phat Mack]

Buzz, I don't get it. (My Chem Prof heard this a lot.) What are you subtracting from the draws?

[Buzz]

“Buzz, I don't get it. (My Chem Prof heard this a lot.) What are you subtracting from the draws?”

Mack - You provided data for seven “hands.” (Actually “hand,” as we’re using it here, might better be termed “position”). You listed wins, draws, and losses for High Card, Pair, Two Pair, Trips, Straight, Flush, Full House., Quads, and Straight Flush. These are obviously all listings for high (and not low). This data is very interesting data, and relates, I think, indirectly to lows.

I had my computer add together the total wins, draws, and losses for each hand. (I prefer using the word “ties” here instead of “draws,” because draw also means seeing another card, but I will continue to use the “draw” and “hand” terminology evidently provided by the simulator).

The totals are given below for each hand. This chart is one I developed from totaling data from charts you provided.

Chart I
Hand no....win.....draw.....lose.....
...1........14236.....50.....85714
...2........14099.....41.....85860
...3........14228.....41.....85731
...4........14318.....44.....85638
...5........14303.....38.....85659
...6........14392.....35.....85573
...7........14287.....25.....85688

You also provided another chart:

Chart II
Hand
|.....1....|.....2.....|....3.....|.....4....|.... .5.....|.....6....|.....7....|
|------+--------+--------+--------+--------+--------+--------+--------+
High
| 10189 | 10022 | 10119 | 10216 | 10053 | 10230 | 10173 |
Draw
|..437...|...431...|..394...|..414...|...382...|.. 418...|...402..|
Lose
| 75501 | 75486 | 75418 | 75380 | 75403 | 75236 | 75375 |
Scoop
| 4047...| 4077..| 4109...| 4102...| 4250...| 4162..| 4114.. |
Low
| 9879.. | 10040 | 10016 | 9938.. | 9963.. | 9998.. | 9993.. |

The total “draws” for each “hand” in one chart are listed vertically, and in the other horizontally, but you can easily see there is a huge discrepancy. The explanation must be that the draws in this last chart refer to both high and low.

Making that assumption, I subtracted the “draws” for high in Chart I
from the total “draws” for both high and low in Chart II to get the “draws” for low. (“Draws,” as I’m using the word here, means “ties”). Some of the ties for low could be due to sixthing, rather than quartering, but I suspect not many, since the frequency of ties for low is only 3.8%. That’s assuming I have correctly interpreted your data. Never a guarantee, but at least my interpretation makes sense to me, and I hope also makes sense now to you. If not, let me know and I’ll try to make my explanation clearer.

Buzz

[Phat Mack]

I see what you did. Ingenius! I never looked past the upermost chart. A minor quibble: I think you should have taken the number of ties for low, 2604, halved it to 1302 and then added it to the other lows for a total of 71129. JMO, let me think about it some more. I also note that the figures in what you call chart 2 above seem to have 50-something too many hands in them and this troubles me a little.

[Buzz]

A minor quibble: I think you should have taken the number of ties for low, 2604, halved it to 1302 and then added it to the other lows for a total of 71129.

Mack - Yes. I agree. Thanks.

(It would depend on how the simulation results were recorded. I had already concluded that each hand must have been given credit for a win for low in the low column of the chart, even when it only tied for low, and that therefore the total times low was possible was even lower than the number reported. Then when I stumbled upon a way to make sense out of the discrepancy between “draws” reported for high hands and “draws,” my thinking was still that the draws had already been double reported).

But, yes, your way makes more sense to me now. The lows as reported in “Chart II” are probably un-quartered lows and the difference between the “draws” in the two charts probably represents the number of quartered (and sixthed) lows.

Getting sixthed for low happens often enough in Omaha-8 that it needs to be taken into consideration, but I think it is much rarer in stud-8. (I’ve never seen it). At any rate, if we ignore getting sixthed for low in stud-8, then
69827 + 2604/2 = 71129.

<font color="red">About 71% of the time in a seven handed stud-8 simulation, low is possible. </font color>

And in that case, you evidently should expect to get quartered for low when you have a winning low hand in a loose game of stud-8 as much as 3.7% of the time.

I also note that the figures in what you call chart 2 above seem to have 50-something too many hands in them and this troubles me a little.

I merely left the win % off the bottom of data you provided and called the collection of numbers chart II to try to explain my reasoning to you. (There was no reason to leave off the win %, but there also was no reason to include it). But except for leaving off that win % line and then trying to get the columns to align by putting in some dots as spacers, the numbers in Chart II are copied and pasted exactly as you reported them. But, yes, I noticed the same discrepancy and wondered why the numbers in the columns for each hand added up to about 50 more than 100000. (Janne Raevaara, who sometimes posts on r.g.p., might know). Seems like they should add up to 100000. but I don’t think the extra 50 out of 100000 is significant. We’re rounding off by dropping the last three digits anyway.

Looks like you get the reported win per cent by
(1) dividing the draws by 4,
(2) dividing the highs by 2,
(3) dividing the lows by 2,
(4) dividing the scoops by 1,
then adding the results of (1), (2), (3), and (4) together and dividing by 100000.

If you do that, the win % numbers correspond.

But I don’t know why there seem to be 50-something too many hands reported for each position. If anyone else knows, an explanation would be appreciated. At this point I’m guessing it has something to do with the way the simulations are run and tabulated. This computer stuff is mostly a mystery to me.

Buzz

[Phat Mack]

</font><blockquote><font class="small">In reply to:</font><hr />
But I don’t know why there seem to be 50-something too many hands reported for each position. If anyone else knows, an explanation would be appreciated. At this point I’m guessing it has something to do with the way the simulations are run and tabulated.

[/ QUOTE ]

This morning, as I stood looking at my truck's dead battery, it occurred to me that ties for high might get double counted, and three-way ties might get triple counted. This for no other reason than similarity in numbers. I might send Janne an email, although something tells me that he has grown sick of hearing from me over the last month...