Odds
Poker is a
mixture of Mathematics and Psychology, while the latter is quite qualitative
and based on judgements, the maths side is usually a lot more black and white.
Therefore learning the maths side of poker can help to improve your game. The
majority of the maths involved in poker revolves around odds and there are
plenty of articles on Outs, Pot Odds and Implied Odds which you should
familiarise yourself with if you haven’t already.
I don’t like
to write about topics that have been covered to death and written better than I could hope to, so I am going to
briefly talk about a couple of related concepts that I use rather than using
Pot Odds or Implied Odds, these may or may not help but I always think it’s
useful to look at things from a different angle, I will try to keep the maths
to a minimum but some is required!
Maximum Return
One thing you
can always do is calculate your Maximum Return; that is the maximum amount you
can win from a pot if everyone still in the hand at that point went all in. Let
us say we are on the cut-off with 18bb and it is folded to us, before blinds
were posted the button has 12bb, the SB has 22bb and the BB has 17bb, assuming
no antes in play our Maximum Return is 12bb + 18bb + 17bb = 47bb (we can only
win 18bb from the SB since we only have 18bb ourselves). Even in a dream
scenario where everyone behind us went all in and we won the pot we would only
show 47bb profit and of course this is extremely unlikely, for example, if the
button folds preflop our MR drops to 35bb.
Taking
another scenario we are in a pot which is on the flop and there is already 12bb
in the pot, we have 20bb behind and have a 22bb and a 13bb stack still involved
in the hand, here our MR is 12bb + 20bb + 13bb = 45bb.
Maximum
Return is useful as it is a definite known quantity which may help us quickly
identify that we are not getting the implied odds required as there are not
enough chips in play to make it ever worth chasing that flush draw.
Target Amount
All these
different numbers and definitions can be confusing but when involved in a hand
and making an odds decision I usually calculate things in a slightly different
way than Pot and Implied Odds, I call this Target Amount (TA) and I will give
an example to demonstrate how I might do this as this will make it clearer than
any explanation could.
I am dealt
ThJh on the button and a TAG player opens from early position, we have reached the turn and the board read AhQd2h 7s, the pot is 2,000 and we both have 8,000
behind, the TAG player bets 1,500 on the turn, what is the best move here? Well
if I call and miss my flush and straight draws on the river I am folding and
investing nothing else in the pot, I am also going to rule out raising
(although that may be a valid play in some circumstances I am ruling it out
here for illustration) so our options here are either to call or fold, if we
make our draw we will try to get value on the river, if we miss we will fold.
It costs me 1,500
to call here, to make things easier I am going to assume we know the villain
has AcKc so I have 11 outs and this equates to roughly 25%, which means I need
to win 3x whatever I call in order to break even (3 to 1 – if you are unsure of
how this figure is reached then google the subject and you should find some
handy articles to help). This means I need to win a total of 1,500 x 3 = 4,5000
to break even therefore 4,500 is my Target Amount at this point in the hand,
note the TA may change at different points in a hand as action unfolds.
As there is
3,500 already in the pot (2,000 plus my opponents 1,500 bet) I need to make at
least another 1,000 on the river when I make my hand to hit my target amount
and thus for the call to be profitable (do not make the mistake of adding the
cost of your call into this equation, you haven’t called yet so it cannot be
added into the pot and as such it is not profit).
So the
question to ask is if I call this turn bet how likely is it that I can make at
least 1,000 on the river when I make my hand. If I call on the turn the pot
will be 3,500 + 1,500 = 5,000 so it is reasonable to assume that when I make my
hand I can make at least 1,000 on average, e.g. if I bet 2,500 when I make my
hand and only get called 50% of the time then in the long run I make 1,250 on
the river when I hit my hand, calling the turn therefore is profitable, the
river bet of 2,500 is only half the pot and so is a reasonable river bet and
the villain has 8,000 behind so it is putting about a third of his stack at
risk so he is more likely to feel he can call and still have a playable stack.
Of course if
you are playing a good player they may put you on the flush draw and may fold
more than 50% of the time to a 2,500 bet so you may not be able to reach that
target amount no matter what bet size on the river you choose and so would not
be able to call the turn bet, similarly if stack sizes are short you may never
be able to reach your Target Amount as your opponent does not have that many
chips behind (this is where Maximum Return is used). If in the example above
the villain only had 3,000 behind then it is probably going to be much harder
to get them to call a value bet when we hit so the TA is harder to make and so
calling should be less appealing.
Notice that I
didn’t calculate pot odds or implied odds, I looked at how much I had to call
and determined what amount I needed to win if I made the call, if this Target
Amount is reasonably achievable in the long term then the call can be deemed
profitable, this doesn’t always mean it is the best play of course!
In another
hand we get dealt pocket deuces in mid position, we have 28bb and UTG + 1 makes
it 3bb to go from his 30bb stack. Should we set-mine here? Well we will flop a
set 1 in 8 times, so 7 times we lose the value of our call which makes a total
of 7 x 3bb = 21bb. This means that the 1 time in 8 that we flop the set we need
to make a profit of 21bb just to break even, so we need to make 24bb (since we are putting 3bb in by calling) the original raise was 3bb and
there is another 1.5bb in the pot from the blinds, so we need to make a further
24 – 3 – 1.5 = 19.5bb postflop when we flop the set, this is over half of our remaining
stack! This means we would need to double up at least 50% of the time we flop
our set and this is usually an unrealistic assumption as the original raiser
may fold as they missed the board or they may get it in with us but either have
a better hand or hit a draw to improve to the better hand. Add this to the fact
that if we do flat preflop there is always the chance that someone squeezes and
we might not even see a flop. This means we should aim for above our Target
Amount (how far above depends on how likely we feel we are to be squeezed off
the pot) and so this makes the decision a pretty easy fold if we are purely set
mining. Of course we may have reads on the villain that mean we are happy to
call here as we know they will always stack off if we hit the set or they never
c-bet without a good hand which may allow us to win the pot without a set.
These last 2
or 3 points cannot be quantified and our opponents range may not always be well
defined and so there will always be a grey area when it comes to calling based
on a Target Amount but it can be a useful guide and as shown above can often
illustrate a spot that is a clear fold or a clear call, if you are not
confident of making these kind of calculation during a hand then you could even
create a spreadsheet with common bet sizes (either in number of blinds or as an
amount of the pot, e.g. ½ pot etc) and chances of winning to get grids of
target amounts based on typical situations (such as flush draws, small PPs etc)
using this you would always have a figure that closely resembles the situation
you are in which you could refer to in play to help your decision making. Of
course there will always be grey areas and this is where you will need to use
your experience to make a decision that may override any calculations you make.
This will
probably be my last blog this year so I wish you and your families a Merry
Christmas and a Happy New Year J
