"Theory of Poker " extrapolations?

[AmericanAirlines]

Hi Everyone,
The "TOP" paraphrased seems to say to me, "If you play any different for how you would (should?) if you could see your opponents cards, you lose".

This leads me to believe, after game selection that the most important things are:

1. Hand Reading

2.(This is the point of the post) Knowing what to do if you *did* know the opponent(s) cards.

Assuming for a moment that you did know the opponents cards (your reads were good), you would still have to know how to play the cards.

This is easy to do for specific cases after the fact. Go to twodimes or run some monte carlo sim, or even figure it out long hand.

But, has anyone every compiled "hand against hand" or "hand against many hands" odds of winning? Particularly in a class of conflict sort of way. I.e. Not so much 2d3s vrs. 5h7d (because there's just too many once you get to the flop) but rather... "two pair vrs. trips", "straight draw against pair", etc. At least that way you could remember the guidelines while actually at the table.

After all, if I don't know what the correct play is, even if the game was played cards face up, I don't really know what I'm doing, do I ?!?!

Seems like truly basic info that should be figured out and maybe should already be publishes and I just haven't found it yet.

Granted, I could go looking through all my poker books and start to compile a draft list. Many of the books I have show "favorite vrs. dog" odds for various situations. For example, I believe I saw that one match up that indicated AA vrs. KK, made KK a 4 to 1 shot. Knowing that in advance would let me say, "Geez he's probably go AA, but the pot *really* is/is not big enough for that situation."

The hard part to me seems to be determining the most frequent conflicts, so you could start with the most meaningful ones.

Let me know what y'all think.

(I think there's value in cataloging as many useable rock solid facts about the game as possible.)

Sincerely,
AA

[pudley4]

This is pretty much what you do when you figure out your number of outs and then determine the pot odds you are getting.

For example, if I have 2 pair on the turn and I put my opponent on a straight, I know there are 4 cards that can help me (out of 44 cards remaining), so my odds are 10-1 against making my hand and winning.

If I have top pair on the flop, but I put my opponent on 2 pair, my outs will depend on which 2 pair he has - I could be anywhere from a 1.8 - 1 favorite (K /forums/images/icons/spade.gif Q /forums/images/icons/spade.gif vs J /forums/images/icons/diamond.gif T /forums/images/icons/club.gif , board is K /forums/images/icons/club.gif J /forums/images/icons/spade.gif T /forums/images/icons/spade.gif ) to a 110 - 1 dog (K /forums/images/icons/diamond.gif 2 /forums/images/icons/club.gif vs K /forums/images/icons/spade.gif Q /forums/images/icons/spade.gif , board is K /forums/images/icons/heart.gif Q /forums/images/icons/heart.gif 8 /forums/images/icons/spade.gif )

[tewall]

You raise a good point, about the importance of knowing how to play the cards. While it's helpful to know your probabilities of success against a given hand, this alone cannot tell you the proper way of playing your cards as this is dependent on your opponent's play.

[AmericanAirlines]

Hi Tewall,
I agree, it doesn't tell me how to play, in the sense of maximizing profit. But it certainly would tell me when there's not enough in the pot to continue.

I believe the sort of data I'm talking about would be the starting point of strategy, because it would represent the actual mathematical facts. Hence the profit potential.

From there one should be able to decide what the correct action in a given situation would be.

For example, "You're the dog?"... try to play cheap if the pot odds are there. "You're the favorite?"... try to maximize the pot.

But if you really don't know what situation you're in... you're guessing... or going by reccomendations you read/heard somewhere... and don't know if they are true or not.

So ultimately, I'm saying that the objective data is the absolute starting point, ground zero. Then reading hands to try to figure out what objective situation your are in is next. Then the "Play the Player" stuff is needed to achieve the goal that the Hand vrs. Hand odds dictate you are after.

Sincerely,
AA

[tewall]

I agree with all of this.

The FTOP is all about inducing mistakes. One way of going about your analysis is to consider the value of mistakes. For example, in a heads up situation chasing with 6 outs is a small mistake at worst, chasing with 3 outs is a fairly bad mistake, folding when you have the best of it and your opponent has 6 outs is very bad and folding with the best of it and your opponent has 3 outs is terrible. This would mean, for example, that folding a hand like 88 when your opponent holds A7 would be a terrible mistake (assuming a flop that missed both of you).

Some mistakes are worse than others. Think about situations where you can induce your opponents to make the bad mistakes and improve your chances of avoiding them.

[AmericanAirlines]

Hi Tewall,
Certainly seems valid. First step is to know what a mistake is. So I'm still stuck trying to know what is/is not correct. So I'd still need to have the basic knowledge of what I should do when my read of the opponents hand is 100% correct.

Any thoughts on that?

Seems like it's a question of totaling your winning outs vrs. his winning outs. Or stated another way, knowing the odds of winning in situation X. If the odds are totally your way, perhaps slowplaying is correct. If they are little closer, raising... If your the dog, go for the cheap play.

'course you have to throw in the occasional bluff or semi-bluff when it presents itself to be not predictable.

But I find myself coming back to feeling the need to know the actual odds of various classes of common hand conflicts. And worse yet, trying to figure out what those classes are!

Guess I should get Wilson's TTH and start running simulations or something. You probably couldn't come up with a "Poker Basic Strategy" like 21, but you could come up with basic strategies for typical situations.

Sounds to me like we need two or three threads or forums:
1. Hand Reading, 2. Odds of Winning, 3. Deceptive Plays

Perhaps some others as well, broken out along the lines of strategic issues/considerations similar to the above 3.

Sincerely,
AA

[AmericanAirlines]

Hi Pudley4,
So do you do this in real time, or do did you figure out common scenarios away from the table?

The mechanics of determining an answer for a particular situation aren't lost on me. However, doing it fast at the table is.

I was hoping that common situations were published already.
Otherwise I'll end up gathering all the odds I can find and organizing them for memorization.

However most tables of odds out there are such that they tell you the outs/odds of making hand X, rather than winning against hand X. Then there's the problem of multiple opponents.

Anyway, the idea was to find out if the reference info already exists somewhere, of if I and other poster's here ought to simply start cataloging them as a tool for our own use.

I'm essentially arguing that we should. To further the science of the game... and our profits. :-) (By mechanizing as many decisions as possible, to leave mind share for other things, such as "playing the player".)

Sincerely,
AA

[The _Grifter]

" Sounds to me like we need two or three threads or forums:
1. Hand Reading, 2. Odds of Winning, 3. Deceptive Plays "

Not a bad idea !

[pudley4]

I do it real time at the table.

First you determine what hand you have or what draw you have. Maybe you have top 2 pair. Maybe you have a gutshot. Then calculate how many cards will make your draw, or improve your hand.

Then you try to figure out what your opponent has. This is based on previous experience with the opponent, the betting that has happened this hand, etc. Now you know whether you are ahead or behind.

Finally, you look at the pot odds, implied odds, etc, and determine what you should do.

It sounds more difficult than it is, especially once you start playing. It becomes easier the more you do it.

As far as hand-vs-hand odds, I haven't heard of these being published anywhere. Like I said before, there are so many different combinations (even within the same "grouping") that it would seem easier to learn to calculate them out as they come, rather than try to memorize them.

[davmcg]

If you have already worked this out , sorry - I may have missed your point /forums/images/icons/smile.gif

The problem with TOP is that you can usually only put your opponent on a range of hands. Let's say you have KK in the BB and an UTG player raises. You know that he only raises UTG with AA KK QQ and AK. So 6/21 times he will have AA. You should still re-raise because 14/21 times you are a big favorite. When the flop comes you can narrow the range depending on your knowledge of the player and perhaps on the turn you would be able to precisely identify your opponent's hand. So it is virtually impossible to avoid mistakes only to minimise them.

[AmericanAirlines]

Hi Pudley4,
Hmmm... your brain is faster than mine!

My hope was that someone had done enough simulations to make a statement like, "All underpairs are roughly from 4:1 to 5.2:1 underdogs to an overpair" etc.

My intuition says that even though there are a myriad of matchups, that bands of probabilities would be found, and thus "close enough for gov't work" estimates could be memorized.

Truth, is when I lived in Nevada and played regularly I was faster at these things. Now I'm in Colorado and have a hard time justifying playing those $5 games vrs. the rake.

Anyways, I'll have to break out a deck of cards and practice. In the mean time I'll keep my eyes open for generalities.

If I ever break down and by TTH, maybe I can do some exhaustive sims as well.

Sincerely,
AA

[AmericanAirlines]

Hi Davmcg,
Agreed. As I play more HE I suspect my reads will get better. I feel comfortable reading stud hands.

But even so, I "ought" to know what to do with my read. So it seems knowing what to do if the cards were face up is a good starting point.

I have no illusions that I won't make mistakes. But at least they should be mistakes on the read, not what to do in the supposed scenario.

Of side interest. I'm wondering if there's some strategy for the game, that though not optimal, gaurantees a profit no matter what the opponent does? An interesting idea, though I have no idea how to approach it.

Sincerely,
AA

[AmericanAirlines]

Hi Pudley4,
I was reviewing your post again. You mentioned in the last paragraph that you would be anything from a 1.8:1 favorite to a 110:1 dog.

How'd you go about getting those two answers. Those are clearly different from the idea of "I have 4 outs and 44 cards left".

In the case of 4 outs... you've calculated odds of improving. Pretty straight forward.

In the second case you determined you dog or favorite status. I'm particularly interested in that computation and if you do this at the table?

Straight pot odds are meat and potatoes poker. Dog/favorite values I could probably do with a piece of paper at best!

Sincerely,
AA

[pudley4]

The reason I used "outs" in the first hand is because there is only 1 card to come. The only way I can win is with the straight, so it's simple.

For the second hand, I went to twodimes.net for the results. Because there are 2 cards to come, there are thousands of possible final boards. Nobody wants to calculate them all by hand, and no one can do it at the table /forums/images/icons/smile.gif

Those scenarios took me a while to come up with. I tried to figure out the best and worst possible ways you could have top pair against 2 pair. I had a few mistakes at first, but I'm pretty sure those are the best and worst.

[pudley4]

</font><blockquote><font class="small">In reply to:</font><hr />
My hope was that someone had done enough simulations to make a statement like, "All underpairs are roughly from 4:1 to 5.2:1 underdogs to an overpair" etc.


[/ QUOTE ]

Unfortunately it's not that simple. The probability of winning vs a certain type of hand greatly depends on other draws that each player has as well as on the board itself. Like I showed above, top pair can be a favorite over 2 pair if it has enough draws, while it can also be so far behind that it has less than 1% chance of winning.

[davmcg]

I am not sure about a strategy that guarantees a profit, but in heads-up limit HE play you can eliminate strategies (not playing enough hands pre-flop and folding too often post flop) that guarantee a loss against most players. The better strategies would be among what was left.

I seem to remember that there was a lengthy discussion in one of the forums about computers and "perfect" heads up strategy. I think that David Sklansky commented that he thought that even if such a strategy existed it probably wouldn't maximise profits against bad players.

[VOC]

Of the first situation I manage to calculate the 1.8 to 1. 20 cards (9 spades, 4 Aces, 4 nines, 2 Kings and 3 Queens minus the Ace of spades and the Nine of spades) in the deck will improve your hand. With two cards to come this means 1-25/45*24/44=0.697=69.7%. Your opponent, however, makes a full house with a probability of 1/11 if you manage to improve yours. This reduces the chances of ending up with the best hand to 63.4%, which means you're about a 1.7 to 1 favourite.

In the second situation the only way of improving your is if you get twos on the last two cards. This means 3/45*2/44=0.3%, which means you're a 329 to 1 underdog. Am I missing something?

VOC

[pudley4]

First, there are only 3 possible winning combinations in hand 2, not 6, because we don't care what order the cards come in. For the same reason, there are only 990 possible boards.

Second, there are 11 possible combinations where the 2 hands end up in a tie (example: aces on the turn and river would give both players aces over kings w/queen kicker)

I got the actual numbers from twodimes.net

[cero_z]

AA,
Theory of Poker explains how to calculate odds with 2 cards to come in hold'em. In the example above, you can only win with 2 running deuces, and you can tie if it comes A, A, or K, Q. I'll do the 2, 2, scenario 'cause it's simpler. this is a slightly different method from Sklansky's, but we only need to estimate, and this gets us close. The odds of a 2 on the turn are 2/45=about 4.5%, and another 2 on the river comes 1/44= about 2%, so .045 x .02 = .009, or .9%, or about 110 to 1. Is that clear?

[AmericanAirlines]

Hi Cero_z,
No I don't think you missed anything. Perhaps I was unclear.

I was looking for the odds of (Hand A beating Hand B) or (Hand A beating Board X).

For example, I hold KK and Read opponent to have AA, what are the odds of KK winning? Or I hold KK against 10 players and board comes x y z, what are odds of winning.

In other words, rather than the odds of making a hand, what are the true odds of winning in a given spot. Seems to me that's the real number one is interested in.

My hope was that someone had done this, and various common situations had reasonably easy to rememeber values.

Just an attempt to know more often, when I'm in a +EV or -EV situation.

Sincerely,
AA

[SoBeDude]

Of side interest. I'm wondering if there's some strategy for the game, that though not optimal, gaurantees a profit no matter what the opponent does? An interesting idea, though I have no idea how to approach it.

In the January issue of Card Player magazine there is an article by Alan Shoonmaker, Ph.D. that says Mason Malmuth calculated it is possible that a good players could have a 4,000 hour losing streak, or about 2 years full-time play.

He also says Mike Caro said someone who plays full time for 20 years will have a 1,000 hour losing streak.

(Quoted with respect, but not permission. I hope this is OK)

Given this, it seems unlikely then there is a possible strategy that would always make money.

-Scott

[SoBeDude]

Of the first situation I manage to calculate the 1.8 to 1. 20 cards (9 spades, 4 Aces, 4 nines, 2 Kings and 3 Queens minus the Ace of spades and the Nine of spades) in the deck will improve your hand. With two cards to come this means 1-25/45*24/44=0.697=69.7%. Your opponent, however, makes a full house with a probability of 1/11 if you manage to improve yours. This reduces the chances of ending up with the best hand to 63.4%, which means you're about a 1.7 to 1 favourite.

I'm probably doing this wrong, so I'm posting it for help getting it right:

If I have 20 outs, the numerator in the above math should be a 20, not a 25 and 24. also, since I can get my winning card on either the turn or the river, but I don't need a runner-runner hit, I should be adding the two together, not multiplying them.

So I come up with
20/45 + 20/44 or .89% of improving. thats about a 1.1 to 1 advantage by my calculator.

But as I said i'm probably making a mistake.

Also how do you calculate how many of those times that you DO make your hand, your opponent makes the full house and beats you?

Thanks for your help!

-Scott

[pudley4]

</font><blockquote><font class="small">In reply to:</font><hr />
If I have 20 outs, the numerator in the above math should be a 20, not a 25 and 24.

[/ QUOTE ]

No - notice the equation is:

1 minus 25/45*24/44.

This equation is correct. He is calculating the odds of not hitting and then subtracting it from 1.

When you add all the probabilities together for all possible outcomes, it always equals 1. So to figure out the probability of something happening, you can do it one of two ways:

1-Figure out all the possible ways of this outcome happening and then add them all together

or

2-Figure out the probability of this outcome not happening, and then subtract that result from 1. This is what the poster chose to do. In many cases it's easier to figure it out this way.

</font><blockquote><font class="small">In reply to:</font><hr />
also, since I can get my winning card on either the turn or the river, but I don't need a runner-runner hit, I should be adding the two together, not multiplying them.

[/ QUOTE ]

This is correct if you were figuring the chances of hitting on either the turn or river.

</font><blockquote><font class="small">In reply to:</font><hr />
So I come up with
20/45 + 20/44 or .89% of improving.

[/ QUOTE ]

This is not correct. The chance of hitting on the turn is 20/45. The chance of hitting on the river if you first miss on the turn is 25/45 * 20/44. Add those two together and you get about 69% chance of improving.

</font><blockquote><font class="small">In reply to:</font><hr />
(.89)thats about a 1.1 to 1 advantage by my calculator.


[/ QUOTE ]

no, .89 is actually an 8-1 favorite. the formula is: (.89)/(1 - .89)

[cero_z]

I'm a little embarrassed to say that I don't recall many of these, but no one else responded, so I'll tell you what I know. A pocket pair is a 13 to 10 favorite vs 2 overcards (QQ vs AK), and a pocket pair is favored over a smaller pocket pair by (I think) 5 to 1. In confrontations between 2 non-pair hands, the one with the highest card is always favored (Q2 is favored over JT), and it's closer than 13 to 10.
Hopefully someone will correct me where I'm wrong above, and as far as sources for this type of info, I remember reading some of these comparisons in a Caro Card Player article several years back called "a few matchups" or something like that. Sorry, but that's the best I can do.
Cero