Lee Jones SAGE Article -- Is the Content Correct?

[JNash]

I tried to find out whether anyone on 2+2 had reviewed the <u>content</u> of the Lee Jones SAGE article. I found the threads where David and Mason (rightly) took issue with Lee's attacking Dan Harrington, but not a discussion of the actual strategy.

The article mentioned that a game-theory solution has been discussed on 2+2. If yes, can someone please provide the reference? I thought that the only solution that's in the public domain is the Borel mini-game on the [0,1] interval, but that the solution with cards had not been published.

Being a game theory nut, I've actually worked out the equilibrium strategies on my own (unpublished). My solution is directionally similar to the SAGE solution, but the details (calling thresholds and range of cards) are fairly different at times. Is there any 2+2er out there who can confirm/deny the correct solution to the game?

If I am correct, then on top of the objectionable rhetoric, the underlying content of the article is flawed too.

[sarsen]

I think there was an article in either December of November 2+2 magazine that wasn't directly about SAGE, but was an article about game theory and HU strategy. Either the General forum or the news-views-gossip forum had some discussions on SAGE and this article as well.

I think you'd have to email Tysen Streib to get a copy of the article from November. I believe he's the one who wrote it.

[trojanrabbit]

[ QUOTE ]
I think you'd have to email Tysen Streib to get a copy of the article from November. I believe he's the one who wrote it.

[/ QUOTE ]

Yeah, I wrote the article in November. I've talked in person with James Kittock (the guy who actually invented the SAGE stuff) and we compared our systems. Mine turned out to be slightly more accurate, but his is easier to remember. Send me a PM if you want me to email you a copy of the orginial article.

Tysen

[JNash]

Thanks -- I'll send you a PM.

[Pokertini]

I've studied the SAGE article and look forward to implementing it. Since you've done some research on your own, I'm interested in your opinion regarding playing the BB HU in the event the SB simply completes, or raises but does not go all-in. With a mediocre hand in the BB but one that meets criteria to call an all-in raise from the SB, should you then re-raise to force the SB all-in?

[trojanrabbit]

[ QUOTE ]
I've studied the SAGE article and look forward to implementing it. Since you've done some research on your own, I'm interested in your opinion regarding playing the BB HU in the event the SB simply completes, or raises but does not go all-in. With a mediocre hand in the BB but one that meets criteria to call an all-in raise from the SB, should you then re-raise to force the SB all-in?

[/ QUOTE ]

Unfortunately there is no easy answer to this as it's very opponent specific. If the short stack is &lt;7BB or so I'd usually push myself. You'll win on those occassions when he just made a weak action with a weak hand. If stacks are larger, you can just call with a medium-good hand and see the flop. It also might be a good opportunity to try a stop-n-go.

Tysen

[Mason Malmuth]

Hi Tysen:

What you're saying about accuracy is actually quite interesting. I suspect that James Kittock was probably cringing when he got to read that Harrington at 31 had it wrong since the calculated number is 29.

Best wishes,
Mason

[Central Limit]

question about the big blinds response in the SAGE article:

Are the hands that the big blind calls with determined by the range of hands that the small blind pushes with? Hmm, that's a confusing way for me to put it. Let me try again.

I'm guessing that the small blind's push or fold strategy is based on the assumption that the big blind can hold any two cards. Okay, that's reasonable. But does the big blinds response assume that the small blind could have any two cards? Or does the BB assume the SB has only the range of hands that SAGE says you should push with? It seems to me, this should influence the optimal strategy. Also, does the SB strategy assume the BB will fold when he has a below threshhold hand?

None of this is clear from the article.

[binions]

[ QUOTE ]
[ QUOTE ]
I think you'd have to email Tysen Streib to get a copy of the article from November. I believe he's the one who wrote it.

[/ QUOTE ]

Yeah, I wrote the article in November. I've talked in person with James Kittock (the guy who actually invented the SAGE stuff) and we compared our systems. Mine turned out to be slightly more accurate, but his is easier to remember. Send me a PM if you want me to email you a copy of the orginial article.

Tysen

[/ QUOTE ]

Tysen

Care to weigh in on the maligned HOH example? If your system is more accurate, it would be interesting to know whether it concurs with SAGE re: what they say is an easy call (and Mason interprets as a close call).

[trojanrabbit]

[ QUOTE ]
Or does the BB assume the SB has only the range of hands that SAGE says you should push with? It seems to me, this should influence the optimal strategy. Also, does the SB strategy assume the BB will fold when he has a below threshhold hand?

[/ QUOTE ]

I can't speak for the SAGE article, but I assume so. It is so for my studies. If either player deviates from the assumed strategy they will lose more and their opponent will win more. It might no longer be the most exploitive play, but you will still be better off if you just stick to the given strategy.

Tysen

[trojanrabbit]

[ QUOTE ]
Care to weigh in on the maligned HOH example? If your system is more accurate, it would be interesting to know whether it concurs with SAGE re: what they say is an easy call (and Mason interprets as a close call).

[/ QUOTE ]

Take a look at my response in this other thread (http://forumserver.twoplustwo.com/showthreaded.php?Cat=0&amp;Number=4694902).

[JNash]

I agree with Tysen that the jam-or-fold strategy is "best" for the SB only if R (the ratio of small stack to the big blind) is fairly small -- 7-8 sounds about right.

The problem with multiple betting rounds--just completing, or making a small raise--is far more complex, and I do not know the mathematical solution to it. There's an academic paper by Chris Ferguson and his dad Tom out there that combines the Borel and VonNeuman models for the [0,1] mini-game, but it's not for the mathematically faint of heart. The pdf can be found at http://www.math.ucla.edu/~tom/

I am not aware of anyone extending this from the [0,1] mini-game to "real" poker with 169x169 possible starting hands.

[JNash]

[ QUOTE ]

Are the hands that the big blind calls with determined by the range of hands that the small blind pushes with?

[/ QUOTE ]

Definitely not. The equilibrium solution of the game is defined as the one where the SB's range is optimal given the BB's range and vice versa. For example, the SAGE article states that if R=3, then SB pushes with the top 74% hands, knowing that BB will call with the top 70%, and BB calls with the top 70% because he knows SB pushes with the top 74%.

And yes, the BB folds if the hand is below the threshold.

Hope that clarifies it.

[trojanrabbit]

I'm getting a lot of PM's for people who want a copy of the article I wrote for November. Please remember to include your email address in your PM.

Also in response to several of the common questions I'm getting... Take a look at my current (http://www.twoplustwo.com/magazine/current/streib0206.html) article. It talks about some of the assumptions and dangers. But probably more importantly look at next month's (March) article where I'll be talking about what happens when your opponent is not using a game theory strategy and how we should adjust.

Tysen