Pre-millenial post: 27 lowball research problems

[LearnedfromTV]

I'd really like to figure out how to calculate equity vs range on the early rounds for both games. Easier in badugi than td, but pretty complicated in both.

[BBQbowser]

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I thought of saving this for my 1000th post, but the list was ready and I had some downtime at work...

Research problems in lowball (TD2-7, Kansas City Lowball, or Badugi)

or

"27 challenging problems"

1. (TD) Nontrivial 1st-round hand equities, hot + cold. For example, if you push all-in with 23xxx, what are your chances of winning the pot vs. a player who calls with a range of two-card draws?

2. (Badugi) Nontrivial 1st-round hand equities, hot + cold.

3. (TD) Nontrivial 1st-round hand expected values. Is it actually profitable to play three-card draws from the button? From SB? This can be attacked from either a theoretical or a measurement perspective.

4. (TD) Game-theoretic optimal 3rd round play on the button. What is the appropriate mix of call + break, raise for value, raise to induce a break, fold, call and stand pat (freeze), etc.?

5. (TD or KCL) Quantify the increased fold equity from having paired cards first to enter.

6. (TD) Describe a strategy for beating 'Sheiky draw' (one player gets six cards before the first draw but must call all bets in the first two rounds.)

Alternately, quantify the increased equity from being the Sheiky.

7. (KCL) Develop an analogue of S-C numbers for SB vs BB matchups.

The S-C number for a Hold'em hand tells you when it "cannot be correct to fold" because if you push all-in with a stack smaller than the S-C number, you guarantee a profit even against a BB who plays perfectly.

8. (TD) Calculate S-C numbers for NL 2-7 triple draw.

9. (TD) Determine in what ways the optimal last-round play in triple draw diverges from the optimal play in the [0,1] game.

10. (TD) Quantify the negative value of drawing to a flush on the first draw (compared with a non-flush.)

11. (Badugi) Quantify the notion of a "median badugi". The following definitions are arranged in assumed increasing strength:
Dealt pat badugis
Badugis made after the 1st draw drawing to any badugi
Badugis made after the 2nd draw drawing to any badugi
Badugis made after the 3rd draw drawing to any badugi
Badugis made by discarding any card if a favorite to get a better replacement
Badugis made by drawing to a specific range (e.g., 8 or better)
Badugis made by drawing optimally against a known opponent or opponents

12. (Studugi) Quantify how likely you are to get a badugi in 7 cards. What is the median strength of this badugi?

13. (TD) Describe a game-theoretical snowing frequency on the first draw. (i.e, when you stand pat on the 1st draw you should have a mix of decent to strong pat hands and complete bluffs. How often should you be on a complete bluff?)

14. (TD) Describe a game-theoretical snowing frequency on the second draw.

15. (KCL) Describe a game-theoretical optimal solution for push-or-fold NL single draw 2-7.

16. (TD) Provide bounds on the net EV gain of being in position rather than out of position in a limit game.

17. (TD) Demonstrate or refute, using collected data, the "big pots are won by big hands" maxim for TD.

18. (TD) Does any non-pat triple draw starting hand or 2nd round hand benefit from having additional players in the pot?

19. (TD) Does observation of how often a player stands pat on the 2nd or 3rd draw provide a faster or more accurate estimate of his hand range than observing showdowns? Quantify this.

20. (TD) Describe the "expected" distribution of draws by round (i.e., number of cards) for a winning player. Describe how to exploit deviations from this distribution.

21. (TD) Describe TD statistics that correlate well with win rate. (i.e, what should "poker tracker TD" measure?)

22. (TD) Completely characterize all the "degenerate" cases in perfect-information last-round triple draw decisions.

For example, I described a case in "2-7 theory: strange and disturbing" where it is correct to draw to 29T instead of 289T when the deck contains just 6's and 8's. A degenerate case involves discarding a card other than the highest one(s) in your hand, or discarding two cards even though you would be drawing live drawing one card.

23. (KCL) Your arch-enemy offer you a deal. He will play no-limit single-draw lowball with you heads-up. You may have the button 100% of the time, but you will have to pay a bigger blind predraw. Note that if you pay the only blind it's a losing game for you since he can just wait for the nuts and shove. What ratio of small blind to big blind produces a fair game?

24. (Chinese Poker) Describe the optimal strategy for Chinese Poker with 2-7 rankings in the middle. (Bonus: Would the game be improved by some requirement about the strength of the 2-7 relative to front or back?)

25. (Chinese Poker - Badugi) Invent and solve a Chinese Poker variant using badugi rankings in the middle.

26. (TD) It seems likely that showdown hand strength improves as the game contains more drawing rounds. Come up with a model describing this relationship.

As an easy first step, determine (for a limit game) how many rounds of drawing make it unprofitable to draw to anything but the nuts. Is three rounds some sort of optimum?

27. (TD) Develop a bot capable of playing winning triple draw.

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Great post. I like the way you think Mark and want to have your babies.

1. Determine a way to illustrate a baby(s) using characters on the keyboard.

[MarkGritter]

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bump b/c i just found this via lowballgurus and think it's pretty cool.

Progress?

I've been doing some td and badugi research, will add some of these to the list.

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I did some work on Chinese Poker with 2-7 in the middle (#24) described occasionally here and in my LiveJournal. I wrote a couple articles about it for the 2+2 Internet Magazine, but Dynasty isn't in the habit of sending out acceptance notices. [img]/images/graemlins/smile.gif[/img] So either they'll show up there in a month or two, or I'll post the full articles elsewhere.

#4: Game-theoretic optional 3rd round play in TD2-7. I have a program which calculates this for a pair of known 1-card draws. But I really haven't analyzed the results in any detail, nor really validated them. I think it should be feasible to expand this tool to calculate ranges of draws instead of single draws; I did so for 4th round play.

#15: I solved push-or-fold single draw 3-card lowball. 5-card lowball (either A-5 or 2-7) is lots harder but probably within reach.

#7: I calculated a few S-C numbers (they're in the lowball wiki) but there are lots of gaps to be filled in. [img]/images/graemlins/smile.gif[/img]

Nobody has told me about results on any of the other problems.