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-   -   odds for starters in 2-7TD (http://archives1.twoplustwo.com/showthread.php?t=507213)

 spike420211 09-23-2007 12:24 AM

odds for starters in 2-7TD

no, didn't go in the wcoop event- but i got 3rd in the 10.00 mtt @ stars this afternoon...
anyways, a couple of weeks ago i glommed onto Tim Cooper's beginner's guide over @ lowballguru's.net...great stuff, helps me a lot...
but what i'm dying to know is the odds to get various starting hands (2 with 2 wheel cards, 2-wheel-7, 2-4-6-8, etc.) i've figured out on my calculator that there's a 40%+
chance of having a 2 in your starting 5, and interpolating from my old draw poker tables, about 260:1 to get any pat 7.
the in-between stuff, the 1-,2-, and 3-card draws, leave me hopelessly lost...i know how to calc nPr and nCr, but it gets hella involved for 3 or 4 out of 5 cards.
Any help would be appreciated
thx
spike
p.s. the 3-card draw scenario was a what-if kinda thing, in case i'm inclined 2 play 2-3-rag-rag-rag on the button
[just once in a while, to mix things up, i KNOW i ain't 'sposed to]

 MarkGritter 09-23-2007 01:25 AM

Re: odds for starters in 2-7TD

I worked these out a long time ago but I can't find anywhere I've already posted them. Maybe that 2-7 thread in the Sklansky forum?

For a pat 5-card hand there are 1020 ways it can be made from the four suits. This gives them each probability 1020/52C5 = 0.000392465. So over the 18 or so (pat 8 or better) that's a total of 0.7%.

There are 7680 ways to make a 1-card draw (like 7432x but you need to count x = one of 2347 as well.) So, 0.002955 each, and I count about 26 of them (including hands like 8763 but not bad starters like 7543) which makes 7.7% total.

There are 25200 ways to make a 2-card draw (432xx, counting all pair/trips combinations.) That makes them 0.0096962 each. How many you want to add up is a matter of some dispute. If you keep rough starters like 256 but not any 8 worse than 258 it works out to 12.6%.

 spike420211 09-23-2007 04:05 PM

Re: odds for starters in 2-7TD

tyvm mark. this helps lots from a reference perspective. I'll go check the sklansky forum for that

 BBQbowser 10-03-2007 11:58 PM

Re: odds for starters in 2-7TD

Mark, do you know the probability of being dealt 23, 24, 25, or 27 ?

 MarkGritter 10-04-2007 02:19 AM

Re: odds for starters in 2-7TD

I don't have that already calculated; let's see if I can come up with a quick estimate for 27xxx.

There are 4 deuces and 4 sevens, so if you don't care about drawing to 72s that gives 16 combinations. Now, how many cards can we fit into xxx?

If we say 9+ that gives us 24 choices, so there are 16 * 2024 possible combinations of 27HHH. That's 32,384 out of 52C5 = 0.0125.

Then we'd have to count 227HH, 277HH, 2277H, 2227H, 2777H, 22227, 27777, 22777, and 22277.

227HH = 4C2 * 4C1 * 24C2 = 6624
277HH= same
2277H = 4C2 * 4C2 * 24C1 = 864

The rest are gonna be even smaller, so let's say somwhere around 47,000 combinations, or 1.8%

Counting all of 23, 24, 25, 27 gives us a total of 7.2%.

 runninice 10-06-2007 11:51 AM

Re: odds for starters in 2-7TD

ty mark

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