A ridiculously easy TD question (or is it?)

[MarkGritter]

Normally when I get a piece of crap hand like 753xx I just dump it unless defending my big blind or stealing on the button (and even then it's pretty bad--- the temptation to keep drawing after catching a 4 or a 6 can be just too much.)

What if it's double-paired so it's 75533? Would this change how you played the hand?

Can we give a numerical answer to how much stronger this hand is than 753xx?

[timprov]

I'd really like a good answer to this.

Of course, I hardly ever fold it anyway. The perils of rarely playing a full game. Kind of like how your post in the tourney thread about people who draw to 87s on the first draw confused me for a while.

[bobman0330]

Here's a start:
75533 vs. 742AA
http://twodimes.net/h/?z=1134803
pokenum -mc 500000 -l27 7d 4h 2c / ad as - 7c 5d 3h / 5s 3s
5-card Draw 2-7 Lowball: 500000 sampled outcomes
cards win %win lose %lose tie %tie EV
2c 7d 4h 241774 48.35 258184 51.64 42 0.01 0.484
7c 5d 3h 258184 51.64 241774 48.35 42 0.01 0.516

753AA vs. 742AA
http://twodimes.net/h/?z=1134802
pokenum -mc 500000 -l27 7d 4h 2c / ad as - 7c 5d 3h / ah ac
5-card Draw 2-7 Lowball: 500000 sampled outcomes
cards win %win lose %lose tie %tie EV
2c 7d 4h 265869 53.17 234064 46.81 67 0.01 0.532
7c 5d 3h 234064 46.81 265869 53.17 67 0.01 0.468

Also, while we're on the subject of 2-card draws, what was that 2-card draw you iso-3-bet me with Monday night?

[fnord_too]

Good question. I think one approach is to consider the likelihood of anyone having a one card draw to an 8 or a two ard draw with a 2 and a 7 or 8 (or maybe an 8(654)3 XX) given that you have killed 5 wheel cards.

If I had time I would start writing some code to answer this sort of question, because now I am thinking thinkgs like "With N players behind, what is the probability of one of them having X given my cards?" and "If I know the N people who folded would open wity X1..Xn, what is the liklihood of anyone behind me having a defendable hand?"

I go on vacation for a week the third week of december. I don't think I will have an internet connection, so I may do some coding then on this sort of thing, (or I may work on any of the billion other projects I have lingering, or I may actaully try to, ummm, what's that word? Relax? Nah, screw that, I have too much crap to do...)

[MarkGritter]

[ QUOTE ]

Also, while we're on the subject of 2-card draws, what was that 2-card draw you iso-3-bet me with Monday night?

[/ QUOTE ]

I will try to isolate with any 2-card draw to a 7 and sometimes with a 2-card draw to an 8 that includes a 2. Much better to be HU with position than to smooth-call and invite loose players in.

Some players only raise or reraise 1-card draws; I haven't really adjusted my play to this read yet, though.

[Quicksilvre]

A hand like 75533 is much stronger than 753KK for two reasons: cards that could pair you up later on are out of the deck, and cards that could hit your opponents' hands are dead. Danny N went over this is SS2. I couldn't give an exact numerical answer, but in his example, a hand went from 46% to win to 52% to win because of three dead low cards.

[MarkGritter]

[ QUOTE ]
Good question. I think one approach is to consider the likelihood of anyone having a one card draw to an 8 or a two ard draw with a 2 and a 7 or 8 (or maybe an 8(654)3 XX) given that you have killed 5 wheel cards.

[/ QUOTE ]

I did some fooling around on a spreadsheet just now. Suppose you have 753AK and your opponent is pat with an 8 or better. Then your opponent's hands are pretty evently distributed, all about 4-7% likely, with 20% probability he has a 7.

But, if you have 75353 and your opponent is pat, he is 4x more likely to have an 87642 (12%) than a 75432 (3%). The other 3% hands are 87653, 87543, 87532, and 76532. There is only an 18% chance he has a 7.

Of course, he is only .7% (735AK) or .4% (73535) to be pat anyway, but I thought it was interesting how the distribution changed. It should also be the case that there some relationship between the probability of a pat starting hand and the probability of drawing to that hand. (Do you see why? /images/graemlins/grin.gif )