Special Thread For Chen-Ankenman Mathematics of Poker

[felson]

David,

The authors show that unexploitable strategies are often pure. So, they recommend always raising the same amount in each position when opening in NLHE (except for short stacks). This is very different from the advice in your NLHE book, where you recommend varying raise size with hand strength, with occasional mixups for deception. Could you comment on this?

[Artsemis]

[ QUOTE ]
DS,

We have a book forum.

[/ QUOTE ]

We have a sticky at the top of this forum as well.

[leaponthis]

Mr Sklansky,

Given the way the game is played in BLM casino's today is it possible to develop an optimal (holdem) poker stategy using game theory? Heads-up? NL? limit? If not what is the ultimate value of the use of game theory to a poker player? Also, is the reason that your No Limit holdem Book written with Ed Miller is so vague about strategy because you TWO really do not grasp the nonmathematical aspects of the game?

leaponthis

[kbinder]

I have a question about a computation on page 41. Specifically, for the 5-column chart on that page, I would like to have clarified how the entries under the column "p(A|B)" are derived.

In second paragraph, the authors write: "We cannot directly find the probability of a particular win rate being observed (because the normal is a continuous distribution.) We will instead substitute..."

Then the chart is displayed.

Could someone walk me through a calculation of one of the entries under the columns with the heading "p(A|B)"?

Thanks.

(Also note the typo where the heading of the 5th column of the chart should be "p(not(B))")

[Jerrod Ankenman]

[ QUOTE ]
I have a question about a computation on page 41. Specifically, for the 5-column chart on that page, I would like to have clarified how the entries under the column "p(A|B)" are derived.

In second paragraph, the authors write: "We cannot directly find the probability of a particular win rate being observed (because the normal is a continuous distribution.) We will instead substitute..."

Then the chart is displayed.

Could someone walk me through a calculation of one of the entries under the columns with the heading "p(A|B)"?

Thanks.

(Also note the typo where the heading of the 5th column of the chart should be "p(not(B))")

[/ QUOTE ]


Sure. If you have Excel handy, this'll be easy. If not, you can probably follow along anyway.

In cell A1, put a "true" win rate, say 0.

Now we want the probability that *given* that A1 is our true win rate, we would have observed a value of 1.15. We can't do this exactly, because the distribution is continuous. So we're going to use a proxy of any probability between 1.14 and 1.16.

In cell A2, put the value 1.16.
In cell A3, put the value 1.14.

In A4, calculate the standard deviation of the win rates. In this case, it's 2.1 bb/h, with a sample of 16900 hands, normalized to bb/100.

A4 = sqrt((2.1*16900))/100 which is like 1.615.

Using these, we can get two z-scores (one for 1.16 and one for 1.14) -- (A2-A1)/(A4) and (A3-A1)/(A4). Put these formulas into A5 and A6.

Now find the cumulative normal distribution phi(x) for these two:

A7: normsdist(A5)
A8: normsdist(A6)

Subtract them, and voila! The values from the table. Now you can just change the "true" win rate in A1 to see each row of the table.

Jerrod

[Lestat]

<font color="blue"> Also, is the reason that your No Limit holdem Book written with Ed Miller is so vague about strategy because you TWO really do not grasp the nonmathematical aspects of the game? </font>

Just how would you even think it possible that Sklansky would not grasp the non-mathematical aspects of the game?

I am NOT sucking up to DS!! The question just strikes me as insane.

[cardcounter0]

Your calculations are way off because you would not start counting such a thing until after you flopped your first set of ducks.

[creedofhubris]

I'm still trying to wrap my head around Chen and Ankenmann's suggestion of minraising preflop UTG with all hands that they care to play.

Let's talk full ring.

My guess is that minraising preflop will lead to an average of 4 players in a pot, with two opponents with position on you postflop.

It seems to me that if your opponents are good, and have 100 BB stacks, and your raising range is heavily oriented toward high cards and overpairs, that situation is quite unprofitable for you: opponents can use position and board texture to pummel you by raising hard when it's very unlikely that you can have more than one pair.

Obviously they could do this just as easily vs. a bigger raise, but with a larger raise you're giving them worse implied odds and will generally be up against fewer opponents.

If you mix a larger proportion of suited aces/suited connectors/small pairs into your UTG minraising hand frequency, then you sometimes hit unexpectedly strong hands on small boards, but you're making a lot of raises overall and you're vulnerable to the guy acting late who decides to reraise hard preflop to steal the dead money in the pot, which is also gonna happen a lot vs. an UTG minraise.

I just don't see a good way out of this situation with moderately deep stacks. I think with shorter stacks (30-50 BBs, say), where you can jam/fold in response to a preflop reraise or a flop raise, the minraising is a reasonable plan, but I see a lot of downsides for typical internet ring games.

In a live game with 100 BB stacks, the minraises give up a lot of value vs. live game fish who are happy to (exploitably) call 6 BB raises with trash.

[creedofhubris]

I'm still trying to wrap my head around Chen and Ankenmann's suggestion of minraising preflop UTG with all hands that they care to play.

Let's talk full ring.

My guess is that minraising preflop will lead to an average of 4 players in a pot, with two opponents with position on you postflop.

It seems to me that if your opponents are good, and have 100 BB stacks, and your raising range is heavily oriented toward high cards and overpairs, that situation is quite unprofitable for you: opponents can use position and board texture to pummel you by raising hard when it's very unlikely that you can have more than one pair.

Obviously they could do this just as easily vs. a bigger raise, but with a larger raise you're giving them worse implied odds and will generally be up against fewer opponents.

If you mix a larger proportion of suited aces/suited connectors/small pairs into your UTG minraising hand frequency, then you sometimes hit unexpectedly strong hands on small boards, but you're making a lot of raises overall and you're vulnerable to the guy acting late who decides to reraise hard preflop to steal the dead money in the pot, which is also gonna happen a lot vs. an UTG minraise.

I just don't see a good way out of this situation with moderately deep stacks. I think with shorter stacks (30-50 BBs, say), where you can jam/fold in response to a preflop reraise or a flop raise, the minraising is a reasonable plan, but I see a lot of downsides for typical internet ring games.

In a live game with 100 BB stacks, the minraises give up a lot of value vs. live game fish who are happy to (exploitably) call 6 BB raises with trash.

[leaponthis]

[ QUOTE ]
Just how would you even think it possible that Sklansky would not grasp the non-mathematical aspects of the game?

[/ QUOTE ]

Well of the two, David, it appears to me, is the theorist. Now it also appears to me that Mason is the poker player. They seem to compliment each other very well and look at a situation a bit differently. David seems mainly focused on the +EV (math) of a situation whereas Mason appears to have a better feel of how best to approach (play) in a situation. As for Ed Miller...who knows.

Of course I was just trying to piss Sklansky off with my remarks but as usual it didn't work.

[ QUOTE ]
I am NOT sucking up to DS!!

[/ QUOTE ]

Well that makes you different from most posters on this forum. Present poster excluded.

leaponthis