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Topic Title: Let's talk 2-7 triple draw lowball
Created On 7/23/08 7:29 AM

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7/23/08 7:29 AM

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First an observation from playing last night with doggy:
Position is hugely important in this game. Perhaps moreso than any other "standard" Poker game (let's qualify that as games offered by PokerStars). But it is different important than most other games because the majority of the importance isn't because of betting. It is because of drawing. Knowing how many (or none) your opponent drew, particularly on the last draw is a huge advantage...

And now the question:
Based on above statement, you are last to act against an average opponent that will call almost any river bet. On the last draw he takes 1 card. You have 2347x. How bad does x have to be before you redraw it? I.e. If you have 23457T, would your redraw or hold the T? what if it were a 9? a J? a Q? What is the generally accepted correct play?

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7/23/08 7:47 AM

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Good question of which I have no clue of the answer. Twice last night I discarded the winning hand
on the third draw. Once I threw away a ten, the other time a jack and ended up pairing both times
@$#%@$@#.

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7/23/08 10:20 AM

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Okay I'll take a shot at this one. I found a 2-7 lowball calculator on Twodimes.net there might be a better one out there, but will work for now.

I'm going to make the assumption that our opponent is drawing to the nuts so I'll give him this hand

7h 5s 3c 2d / As

now well calculate it against 4 cases the 9, T, J, Q with 2347.

Your win percentages are below if you stand pat:

cards win %win lose %lose tie %tie EV
5s 3c 2d 7h 11 26.19 31 73.81 0 0.00 0.262
7s 2s 4c 9d 3h 31 73.81 11 26.19 0 0.00 0.738

cards win %win lose %lose tie %tie EV
5s 3c 2d 7h 15 35.71 27 64.29 0 0.00 0.357
7s 2s 4c Td 3h 27 64.29 15 35.71 0 0.00 0.643

cards win %win lose %lose tie %tie EV
5s 3c 2d 7h 19 45.24 23 54.76 0 0.00 0.452
7s 2s 4c Jd 3h 23 54.76 19 45.24 0 0.00 0.548

cards win %win lose %lose tie %tie EV
5s 3c 2d 7h 23 54.76 19 45.24 0 0.00 0.548
7s 2s 4c Qd 3h 19 45.24 23 54.76 0 0.00 0.452

lets also try standing pat on a K and A

cards win %win lose %lose tie %tie EV
5s 3c 2d 7h 27 64.29 15 35.71 0 0.00 0.643
7s 2s 4c Kd 3h 15 35.71 27 64.29 0 0.00 0.357

cards win %win lose %lose tie %tie EV
5s 3c 2d 7h 31 73.81 11 26.19 0 0.00 0.738
7s 2s 4c Ad 3h 11 26.19 31 73.81 0 0.00 0.262

Seems like The Queen is the boardline card you should keep or break otherwise you can stand pat and have an advantage. This also assumes that our opponent knows how to play the game and tends to draw to a big hand(sevens, eights, or nines).

A less sophisticated opponent such as myself may draw and showdown 76543 and think it's the nuts.

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Edited: 7/23/08 at 10:28 AM by sp1ke36

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7/23/08 1:17 PM

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Quote
Originally posted by: sp1ke36

A less sophisticated opponent such as myself may draw and showdown 76543 and think it's the nuts.

Or raise with an ace after the third draw such as I did on the first hand of the sng

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7/23/08 3:34 PM

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I think i'm standing pat.. there are just as many cards that hurt me as help me and he obviously hadn't made a hand yet.

In this spot I'd probably play even a K based on the fact he's drawing so at worst I'm in a flip and more likely ahead.

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7/24/08 1:16 PM

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Quote
Originally posted by: sp1ke36
Okay I'll take a shot at this one. I found a 2-7 lowball calculator on Twodimes.net there might be a better one out there, but will work for now.

I'm going to make the assumption that our opponent is drawing to the nuts so I'll give him this hand

7h 5s 3c 2d / As

I'm not sure how big of a flaw this turns out ot be in your calculations, but by putting him on a specific hand, you are eliminating cards from the deck that are bad for him. For instance, if we have 2347 as stated and we put him on the hand you listed above, that means the bad pairing cards are reduced to 2 twos, 2 threes, 3 fives, and 2 sevens or 9 total.

If however, in turn we give him 2568, then the bad pairing cards are: 2 twos, 3 fives, 3 sixes, and 3 8's or 11 total cards out of 42 or about a 5% difference.

Also, if we work on the premise that holding the J wins 55% of the time. Is it not possible based on the strength (I would qualify the 4 cards I gave us as the best 4 card hand you can have when drawing) or weakness of our hand that folding the J might win an even better % of the time? It seems to me we should be able to figure this out, but for whatever reason I can't get my head completely around it yet.

Still, this is a good start sp1ke. Thanks!

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7/24/08 1:42 PM

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Dont forget the cards that are bad for him that DON'T pair his hand.

Also, I could have picked any hand. The thing is we have a pat hand and he is still drawing. It would make sense to me to put up our hand against an equally good drawing hand and find out how it performs. It seems like it does pretty well and I would think it would do even better against lesser hands like 2568.

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gallopingael

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7/24/08 2:12 PM

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Quote
Originally posted by: sp1ke36

It would make sense to me to put up our hand against an equally good drawing hand and find out how it performs. It seems like it does pretty well and I would think it would do even better against lesser hands like 2568.

Since the calcs for 2-7 (like 2dimes) don't allow you to input ranges, the only real way to do it and get a more "accurate" assessment of equity would be to input ALL the possibilities by hand.

That's a pain in the ass.

Second best option is to do exactly what you did. Figure out the worst case scenario for you and then draw conclusions. Obviously your equity in the case of him drawing to the 8 with more bad cards is going to be greater than the "worst case" scenario you concocted. If a play is good in the worst case scenario then it's still going to be good over the range of his possible holdings.

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"Here is wisdom. Let him who has understanding calculate the number of the beast, for the number is that of a man; and his number is six hundred and sixty-six."

Edited: 7/24/08 at 2:13 PM by gallopingael

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7/25/08 12:02 PM

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Quote
Originally posted by: gallopingael

Second best option is to do exactly what you did. Figure out the worst case scenario for you and then draw conclusions. Obviously your equity in the case of him drawing to the 8 with more bad cards is going to be greater than the "worst case" scenario you concocted. If a play is good in the worst case scenario then it's still going to be good over the range of his possible holdings.

I'm not sure that's completely true. With the opponent's holding spike outlined, it is right to redraw a Q and stick a J (assuming spike's numbers are correct, which I did not verify but have no reason to doubt). Thus redrawing a Q is good and sticking a J is good. However, if we redefine our oppoent's 4 cards he holds as 568T (as the most extreme case), there are now 12 cards that could pair him instead of 9. This *might* make it the right play to hold the Q.

And all of this still ignores the fact that even if we win 55% by holding, we might win 60% by redrawing. I don't know the answers, but I don't think we can say we've reached a conclusion. (not to suggest that we can necessarily reach a conclusion, but assuming we don't know is better than thinking we do know and being wrong.)

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7/25/08 3:41 PM

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Siuation 1: You are up against a solid player who would draw to sevens, eights, and nines

Lets say you decide to break the J

cards win %win lose %lose tie %tie EV
5s 3c 2d 7h 807 46.86 906 52.61 9 0.52 0.471
7s 2s 4c 3h 906 52.61 807 46.86 9 0.52 0.529

compared to if you didnt break the J

cards win %win lose %lose tie %tie EV
5s 3c 2d 7h 19 45.24 23 54.76 0 0.00 0.452
7s 2s 4c Jd 3h 23 54.76 19 45.24 0 0.00 0.548

not much difference either way.

Situation 2: You are up against a donk who is still in the hand on the third draw w/ 568T

Breaking the Jack

cards win %win lose %lose tie %tie EV
6s 8c Td 5h 663 38.50 1059 61.50 0 0.00 0.385
7s 2s 4c 3h 1059 61.50 663 38.50 0 0.00 0.615

Keeping the Jack

cards win %win lose %lose tie %tie EV
6s 8c Td 5h 16 38.10 26 61.90 0 0.00 0.381
7s 2s 4c Jd 3h 26 61.90 16 38.10 0 0.00 0.619

Maybe my numbers lie.
Feel free to do the calcs on your own:2-7 lowball calulator

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7/26/08 11:13 AM

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Maybe these articles will helpLowball stuff

Some of this stuff is very technical. I don't regularly play the game enough for the math to make sense to me, but the conclusions in the articles seem pretty straightforward.

The two articles that may be of use is one on the bet-call-break line and standing pat when you are not the favorite.

Take it or leave it.

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Edited: 7/26/08 at 11:14 AM by sp1ke36

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