Albright article and propokertools.com

[catlover]

There is a very subtle error in the Albright article.

When you flopalyze T987ds vs. AAxy as the article does, what the flopalyzer does is the following:

1) deal out a random flop
2) pick at random an AAxy hand
3) compute your pot equity.

It then repeats those steps a whole bunch of times, and graphs the resulting equity distribution.

The problem is that as the person with T987ds, you really want steps 2 and 3 in the above process to be reversed. That is, when AAxy puts you all in on the flop, you don't know what x and y are. You need to make your call or fold decision without the benefit of this information.

The upshot is that the situation the flopalyzer allows you to analyze is different from the situation that occurs in actual play. The flopalyzer assumes knowledge of your opponent's sidecards. In actual play you don't have that knowledge. So using it in the way the article did is unfortunately not correct.

If it's any consolation to the author of the article, the author of this note misused the flopalyzer in exactly the same way for quite a while before he realized what was going on.

[bachfan]

[ QUOTE ]
There is a very subtle error in the Albright article.

When you flopalyze T987ds vs. AAxy as the article does, what the flopalyzer does is the following:

1) deal out a random flop
2) pick at random an AAxy hand
3) compute your pot equity.

It then repeats those steps a whole bunch of times, and graphs the resulting equity distribution.



[/ QUOTE ]

I'm not sure I understand your criticism yet - could you elaborate? I can tell you the operations of the tool for sure, though, as i am the author.

1 - If any board cards were specified, they are dealt. Since the article analyzes before the flop situations, this step does not apply.
2 - Random hands are picked for each player from the set of legal hand n-tuples. It is as if all such n-tuples were generated, and one
was picked at random. (Example for illustration, three player holdem
race, [AA] vs [KK] vs [AK, AQ] - legal tuples are AA-KK-AK and AA-KK-AQ (suits
are properly accounted for in actual simulation, of course))
3) Random board cards are dealt (in this case, three) from the deck
4) Exact equity is computed for everyone
5) Bucket counts are incremented (data points for the graph)

[catlover]

Here is the problem. In your algorithm, you have step 2 (pick random hand) before step 4 (compute equity).

But when I am making my call/fold decision, I don't know which hand my opponent has within his range. What I am interested in is my equity against his range as a whole.

To give me this information, the flopalyzer would need, for each flop, to compute my equity against my opponent's range, rather than picking a random hand within the range and computing my equity against that.

As the author of a tool, this brings up some tricky issues for you, because different people will use the tool for different purposes, and for some of those it may be great as is. We can get into that discussion if you like.

[greg nice]

in regards to the article itself, what if you are the player holding aces. how do you determine what flops to commit to? if you put in 10-15% preflop and bet the flop, youve got half your stack in and it would be terrible to fold then. so your decision comes in whether or not you should bet the flop.

an example, one limper, you raise ~20% of your stack with A[img]/images/graemlins/diamond.gif[/img] A[img]/images/graemlins/club.gif[/img] 3[img]/images/graemlins/diamond.gif[/img] 3[img]/images/graemlins/heart.gif[/img] before the flop, it comes T[img]/images/graemlins/spade.gif[/img] 6[img]/images/graemlins/club.gif[/img] 5[img]/images/graemlins/spade.gif[/img] , your decision is whether or not to bet the flop, and if you dont, what are you gonna do when someone leads the turn?

[creedofhubris]

[ QUOTE ]
in regards to the article itself, what if you are the player holding aces. how do you determine what flops to commit to? if you put in 10-15% preflop and bet the flop, youve got half your stack in and it would be terrible to fold then.

[/ QUOTE ]

Don't put in 10-15% preflop, put in more or less

[bachfan]

[ QUOTE ]
Here is the problem. In your algorithm, you have step 2 (pick random hand) before step 4 (compute equity).

But when I am making my call/fold decision, I don't know which hand my opponent has within his range. What I am interested in is my equity against his range as a whole.


[/ QUOTE ]

I think I understand what you are getting at, but I think my way is more practical. Here's a rough outline of my thinking:

current way
-----------
pick random hand tuple, generate board, compute equity, repeat

your suggested way
------------
pick random board, compute equity using range of hands, repeat

(* note that in an exhaustive simulation, these are equivalent*)

I'm still not convinced that it matters which way you do it in terms of the quality of data produced. However, there is a practical consideration which makes me think my way is best, at least for now. The problem is, doing a range of hand simulation takes a long time, especially in omaha. How many trials should be done for each board generated using your method? (Exhaustive will most definitely not be practical in almost all cases) Let's pick 10,000 as a minimum. My typical limit on omaha sims for compute time is 600,000 flops. So, that would give us 60 boards to work with. Not really enough, in my opinion - there will be significant differences from graph to graph if there are only 60 datapoints. Using my method, I typically get 2,000-10,000 flops, depending on server load.

[catlover]

[ QUOTE ]


current way
-----------
pick random hand tuple, generate board, compute equity, repeat

your suggested way
------------
pick random board, compute equity using range of hands, repeat

(* note that in an exhaustive simulation, these are equivalent*)

[/ QUOTE ]

No they aren't. Perhaps the point would be clearer if we look at the river instead of the flop. I looked at the equity graph for the following sim:

Ah As Kh Ks vs. ****, board 2s 4d 8h Qc.

What I got was a bunch of buckets at 0% and 100%, and a few at 50%. That is because in the end, the AAKK hand has either won, tied, or lost. It doesn't have a "30% probability of winning" or anything like that. With my way, it would.

[catlover]

To clarify my previous post:

The two methods are equivalent if all you are interested in is your overall pot equity. However, if you are interested in the curve of your different equities vs. your opponent's range for different boards, they are not equivalent.

[bachfan]

[ QUOTE ]
Perhaps the point would be clearer if we look at the river instead of the flop. I looked at the equity graph for the following sim:

Ah As Kh Ks vs. ****, board 2s 4d 8h Qc.

What I got was a bunch of buckets at 0% and 100%, and a few at 50%. That is because in the end, the AAKK hand has either won, tied, or lost. It doesn't have a "30% probability of winning" or anything like that. With my way, it would.

[/ QUOTE ]

Aha, finally getting somewhere, thank you.

1) I see how they are different now, but I'm not sure if one is superior - requires more thought.

2) I still don't see how it affects the conclusions of the article, although I leave it for the authors to comment on that.

3) There is a subtle difficulty in proceeding the way you described. Imagine a game consisting of 13 cards, the spades from ace to king, with each player getting one card, and a 5-card board ala hold'em.

Let's set our simulation to run a two-player race:

Player 1 range of hands: A, K, Q
Player 2 range of hands: K, Q

Here's the thing - we cannot deal a random board of three cards, because each board has a different probability given our players ranges of hands (the ace is 1/2 to appear in someone's hand, and k is 3/4, q is 3/4). And I don't know a procedure that would either a ) compute the probability for each board
or b ) let me roll dice and generate boards with the correct probability (that is, without visiting every possible n-tuple of hands, which is not practical in omaha). I'll have to think about it.

[Troll_Inc]

Before I address the two issues raised thus far, I'd like to acknowledge several people who helped with this article. Firstly, the idea for the topic of the article stemmed from a discussion with a friend on how the hand in the article should be played. Second, ProPokerTools made the whole analysis possible, and the author (2+2 poster 'bachfan') has been very helpful throughought, including making software adjustments, which now makes this type of analysis easier. Also, 2+2 contributor BluffThis reviewed this manuscript and provided constructive criticism that provided me the opportunity to make this manuscript better. Lastly, I started reading 2+2's Omaha Hi forum in the past year and have learned a tremendous amount. If PLO isn't in your normal rotation of games, give it a shot, and the forum is a great place to learn how to play the game.

Regarding greg_nice's question about how to play aces correctly. To cover that issue, you'd need a couple of full articles or even a book. From my analysis, I'd like to point out that the whole assumption is that you can definitely put the villain on aces. So one of the basic keys to playing aces correctly is to disguise them. Optimally, you'd like to raise with at least your top 10% hands when you have position. The same holds true for re-raising. (Also, in my example, the villain reraised from the small blind.)

Regarding the issue brought up by catlover, and answered and discussed very well by bachfan. "I have nothing further to add."