Wednesday, January 21, 2004

Posted by Dr Fro 2:47 PM
From the mail bag:

From: "Mark"
To: Dr Fro
Subject: Good post
Date: Wed, 21 Jan 2004 09:03:25 -0600

I came across a good post for your site (if you're interested)

Here is text from a chat board with poker pro Andy Bloch:

I am curious as to how you weave numerical odds and calculations into
your game. I am assuming you have quite a strong grasp on this dimension
of poker since you graduated from MIT with an engineering degree. So,
when you see your hole cards or a flop, do you start calculating the
odds of you winning the hand (let's say by counting how many hands your
opponent could beat you with)?

I am struggling to find a profitable way to use my own knowledge with
regards to probability at the poker table. I know general odds (like a
low pair versus overcards, for instance) and rules of outs... but should
I try to go further? I am not a human calculator, nor do I have the
patience to try to do excessive math in my head before I act. I was
wondering if you could lend me some advice for this aspect of the game.

Andy Bloch's Answer:
Most of the hard core calculations I do away from the table. Then I take
the results and try to form some general rules or simpler procedures for
estimating my odds.

I've written several different programs of my own and use them and some
programs that others have written, (such as ) for calculating poker odds and solving
simplified poker games. I've done enough calculations of pre-flop
situations that I don't have to do much calculation. For example, if
it's heads up I know that I have odds to call an all-in raise or reraise
with practically any A if I'm getting pot odds of better than 3:1 --
even if my opponent will only make that play with QQ, KK, or AA. ("Pot
odds" is the size of the pot divided by the size of the bet that has to
be called. For example, suppose the pot is 1000, my opponent bets all-in
for 500 more. The pot is now 1500, and I have to call 500, so the pot
odds are 3:1. If I have a 25% chance of winning or better, the correct
play is to call.)

Well, to be exact, if the pot odds are exactly 3:1, I should throw away
A2, A3, and A6 through AQ offsuit. But if the pot is just slightly
larger, or if my opponent might also have JJ or AK, then I'm supposed to
call. In fact, getting exactly 3:1 against an opponent whom you know has
either QQ, KK, AA, or AK, you're getting the right pot odds to call with
quite a lot of ugly-looking hands. Any pair. Any AK. Any suited cards
except K2s through K9s, Q2s, and J2s. Offsuit 43 through JT, 53 through
T8. And offsuit AT, A5, A4, and A3.

At the table, do I calculate exactly what my probability of winning is
pre-flop? No. What I do know is that if I raise preflop I will almost
never fold to a single all-in reraise when I'm getting 3:1 or even 2:1,
if I had something worth stealing with.

On the flop, I know that I'll win half the time if I have 13 outs
("outs" are all the cards that you win with against a better hand). A
good approximation for your chance of winning is 2% per out on the turn
and twice that, 4% per out, on the flop. This will usually underestimate
your probability of winning, but being a little conservative is OK,
especially since one or more of your outs might be in your opponent's
hand or might help him also.

The next step is to think about the hands that your opponent is likely
to hold and assigning some rough probabilities to them. Total the chance
of winning against each of them weighted by their probabilities. Maybe
your opponent is bluffing or semi-bluffing, or maybe you think you've
picked up a tell that makes you think your opponent has a strong hand --
adjust accordingly. You don't need to do a perfect calculation, just
close enough so you're only making at most a small mistake. Thinking too
hard to get a more exact answer will make it harder for you to
concentrate on other important things like looking for tells and
remembering your opponents' tendencies.

If you're playing against a strong opponent, you might want to use game
theory to determine whether you should call or fold, especially on the
river. If you have a medium-strength hand, game theory says you should
call often enough to make your opponent almost indifferent to bluffing
with clearly losing hands. If your opponent bets the pot on the river,
you should call roughly half the time. If he bets a fraction X of the
pot, you should call roughly 1/(X+1) of the time (or call if your hand
is better than X/(1+X) of all the hands you could have). So ask
yourself, is my hand in the top X/(X+1) of the hands I might have in
this situation? If it's close, or if you think your hand is too
well-defined by the betting, you can even resort to flipping a coin.

Also, your hand gives you some information about what your opponent can
have, so in some situations, you should call with a hand that is worse
than a hand you'd fold with -- if you have cards that suggest your
opponent is more likely to be bluffing. For example, you might be more
inclined to call a big bet on the river when the board is A2568 with A7
than with AT, because the 7 makes it less likely that your opponent has
a straight. Top lowball A-5 draw players will sometimes call with a pair
of aces (aces are low) but fold a K-high, even though the K-high would
beat any pair, because the second ace makes it less likely that your
opponent made his low hand.

That's pretty much all the math you need to do while at the table. It
may seem like too much to some, but after a while you should get used to
it. If you can't do it while you're at the poker table, practice doing
it away from the poker table. After a time, most situations will become
second nature.

-Andy Bloch

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Random thoughts from a lawyer, an accountant, a commodities trader, an ex-Marine and a WSOP Main Event money finisher that don't know as much as they wish they did...



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