TD last-draw strategy tool

[MarkGritter]

Suppose on the last draw you have a one-card draw to a 7432 (discarding a Q), and the button, while your opponent has a one-card draw to 8642 (discarding a K.) The pot has 5.5 big bets. Can you describe a game-theoretical optimal last-round strategy?

Such a strategy should specify, for each card you receive, a "line" such as "bet when checked to and call a raise" or "fold to any bet" or "raise and cap."

Here's a tool (toy) I wrote:

http://gritter.dsg.stanford.edu/strategy.html

It lets you specify a complete "pure" strategy for each player and evaluate the resulting EV for each player, given a specified pot size. (I've only tested it in Firefox.)

Can you come up with good strategies for the two players?

If there is no further action in the situation I described, A's expected value is 2.514 and B's is 2.986. It seems hard in practice to get A (acting first) to achieve this much against a good B strategy.

Further features that should be added but probably won't:

1. Evaluate other hand matchups. (Currently I work it out on a spreadsheet and import the probabilities and winning hands as a fixed table.)
2. Allow mixed strategies where a line is taken only some % of the time. (For example, bluffing every pair of 8s might be too much.)
3. Easier save/restore of strategies.

[2461Badugi]

I can come pretty close against what I think of as a "standard" B. And if B starts folding kings and aces A can do quite a bit better. There are some interesting counterintuitive plays, though.

I think the resolution isn't high enough to construct a truly optimal strategy, however. For instance, kRF, kRC, and kRR are in my bag of tricks, but I would never assign them to a whole card, much less a whole rank.

ETA: and 2.955 against the "standard" Stars player by bet-folding 2-8 (even #6!) and check-folding 9-A.

[DeathDonkey]

I could play with this thing for hours. Ok first I put in what I think my strategy would be as player B in the 5/10 stars games against an unknown. I don't do any bluff raising and simply call when I think my hand is ok, raise when its good and fold when its bad. Then I started tweaking player A's strategy to maximize his EV against me. Very interesting to see that he should be bluffing every time and not 3 betting even strong 8's. Also noteworthy is he should check and fold Q's and K's but bet/fold everything worse and many things better (for bluffs or value) but the Q's and K's specifically do best when we both check. Can't wait to see other tidbits people come up with using this awesome tool.

-DeathDonkey

2BF 3BC 4BF 5BC 6BF 7BC 8BF 9BF TBF JBF QKF KKF ABF : 2.599
2kK/bF 3kK/bF 4kK/bF 5kBRC/bRR 6kBRC/bRR 7kBF/bF 8kBC/bRC 9kBC/bC TkBC/bC JkBC/bC QkBC/bC KkK/bC AkK/bF : 2.901

[gergery]

I would think you could use some of Chen/Jerrod's 0-1 toy game results and plug in range values to find optimal results.

Certainly one of these handles a game where A can check/bet/fold, B can do same, and optimal values have been determined (ie. A bets with .78 or better and .15 or lower and check calls with .5 to .78 etc). then you can translate .78 or better into pat 7's to 85x etc.

http://groups.google.com/group/rec.gambl...arch+this+group

I haven't read thru it all but it should be there, yes?

Edit: I'm playing around with this now, holy [censored] this is cool

-g

[Guruman]

Devastation occurs when our hero folds too much!

If A bet/folds every pair and AQK8, check/calls 9TJ, and checkraises better hands he actually comes out ahead if player B folds his paired up hands, goes nuts with sevens, calls down 89TJ (betting 8 and 9 when checked to) and folds AKQ.

2BF 3KRC 4BF 5KC 6BF 7KC 8BF 9KC TKC JKC QBF KBF ABF : 2.855
2kK/bF 3kK/bF 4kK/bF 5kBRC/bRR 6kBRC/bRR 7kK/bF 8kBF/bC 9kBF/bC TkK/bC JkK/bC QkK/bF KkK/bF AkK/bF : 2.645

WOW!

This would lead me to believe that it can be correct to bluff a hell of a lot on the river - and also correct to look people up with all kinds of trash. Man, river folds can wreck you in this game.

[Munga30]

Mark,

I'm finding that Player A is indifferent to kRF and kRC against DD's player B above. I'm definitely ignorant about the game, but this seems likely to be a software problem.

Player A: 2BF 3KRF 4BF 5KRF 6BF 7KRF 8BF 9BF TBF JBF QKF KKF ABF : 2.726
Player B: 2kK/bF 3kK/bF 4kK/bF 5kBRC/bRR 6kBRC/bRR 7kK/bF 8kBC/bRC 9kBC/bC TkBC/bC JkBC/bC QkBC/bC KkK/bC AkK/bF : 2.774

and

Player A: 2BF 3KRC 4BF 5KRC 6BF 7KRC 8BF 9BF TBF JBF QKF KKF ABF : 2.726
Player B: 2kK/bF 3kK/bF 4kK/bF 5kBRC/bRR 6kBRC/bRR 7kK/bF 8kBC/bRC 9kBC/bC TkBC/bC JkBC/bC QkBC/bC KkK/bC AkK/bF : 2.774

[HOWMANY]

[ QUOTE ]

Man, river folds can wreck you in this game.

[/ QUOTE ]

The biggest reason why the 5/10 game is so easy is because the vast majority of players let you play almost perfectly against them on the river which is the most important betting round.

They also manage to screw up the other three rounds fairly often, which is quite perplexing since it's pretty difficult to screw up automatic decisions, but that's a topic for a thread I'd rather not start.

[MarkGritter]

Good catch. The winner was not being awarded the extra bet in the check-raise/call case (2 bets instead of 3 in the code.)

I have fixed this and uploaded a new version.

Check/raise + fold:
2BF 3KRF 4BF 5KRF 6BF 7KRF 8BF 9BF TBF JBF QKF KKF ABF : 2.726
2kK/bF 3kK/bF 4kK/bF 5kBRC/bRR 6kBRC/bRR 7kK/bF 8kBC/bRC 9kBC/bC TkBC/bC JkBC/bC QkBC/bC KkK/bC AkK/bF : 2.774

Check/raise + call:
2BF 3KRC 4BF 5KRC 6BF 7KRC 8BF 9BF TBF JBF QKF KKF ABF : 2.688
2kK/bF 3kK/bF 4kK/bF 5kBRC/bRR 6kBRC/bRR 7kK/bF 8kBC/bRC 9kBC/bC TkBC/bC JkBC/bC QkBC/bC KkK/bC AkK/bF : 2.812

[gergery]

This is as close to optimum as i can get so far


2KF 3BC 4KF 5BC 6BF 7BC 8BF 9BC TKC JKC QKC KKF AKF : 2.467

2kK/bF 3kK/bRF 4kK/bRF 5kBRC/bRR 6kBRC/bRR 7kBF/bRF 8kBRC/bRC 9kBC/bC TkBC/bC JkK/bC QkK/bC KkK/bF AkK/bF : 3.033

-g

[F8thless]

FYI, the dates at the bottom of the page say '05, not '06