Sunday, February 03, 2008

The Other Side Of Pot Odds - Part #2 (Numbers!)

Time to continue looking at poker Pot-odds and how they relate to all-in situations in the mid to end portions of MTTs today.

In case you missed it... here is part #1: The Other Side Of Pot Odds - Part #1 (Intro)

Today's post will concern the numbers behind a seemingly simple scenario - you raise and are re-raised all in by a smaller stack (of various sizes). We will look at how hand ranges and the odds on offer affect your decision... the next post in this series will look at situational factors - for now we will cover only your expectation in terms of chips.

Throughout his tournament books, Dan Harrington suggests that when being offered 2/1 you should be inclined to call. Colin Moshman summed it up well in his SNG book too - when getting 2/1 you need a good reason not to call!

We will start with a pair of 8's which you raise from later position... in each case a smaller stack re-raises all-in from the button and everyone else folds. To keep things simple we will use 2 ranges for the small stack... Fairly loose and fairly tight.

The fairly loose range = Pairs 55+, A7+, KJ+ and QJ suited
The fairly tight range = Pairs 88+, A10+ and KQ suited

So, the first question to answer is how does our pair of 8's do against these ranges?

88 vs Loose = 52% wins for the 8's
88 vs Tight = 42% wins for the 8's

(as an aside you need to know this stuff... or at least to have a good idea - get yourself the free tool called Poker Stove and compare hands to ranges at least until you have a general idea!)

Next we bring the pot-odds into the equation.

That is to say, how many chips do you need to call to see a showdown. Again we will simplify things a little, you have 10000 chips in each case, the blinds are 200 / 100, which means that the pot pre-flop is your raise + 300... now some stacks for the smally.

Scenario #1 - Smally has 2000 chips, you raise to 600 and face an all in.

So, there are 600 (your raise) + 300 (blinds) + 2000 (smally all-in) and you need to call 1400 more chips to see a showdown. Your pot-odds here are 1400/2900 = just under 2.1/1.

This means that to break even on this call you need to win just under 1/3rd of the time. Here it does not matter whether the small-stack is tight or loose... calling will win you more chips than folding... now let me ask a question: How many players do you see folding their hands in exactly this situation??

Scenario #2 - Smally has 3000 chips, you raise to 600 and face an all in.

So now there are 3900 chips in the pot and it would cost you 2400 chips to call. Here your pot-odds are 1.6/1 (rounded down a little). You now need 40% winning chances to call and have a positive expectation... well, as you know you have it against either loose or tight players, here your edge against the tighter range is small... situation and other factors might come into play.

Scenario #3 - Smally has 4400 chips, you raise to 600 and face an all in.

Now we have 5300 chips in the pot and you have to call 3800... the pot-odds are thus down to 1.4/1... meaning we need to win around 43% of the time to make this a positive expectation call... well, now we have a clear fold against the tight range and still a call against the looser range. Though it seems like a big bet to call here our expectation is still positive vs the loose range.

That is enough scenarios for now!

The idea of this post was to illustrate the critical role of pot-odds in deciding whether your call would have a positive or negative expectation in terms of chips... the things to think about here are:

- Do you have a basic understanding of the equity of certain hands against possible ranges of opponents hands?
- Can you then relate these ranges to the odds being offered and make positive expactation calls or fold when required?

It's a tough poker world out there... we all need every edge we can get!

GL at those tables, Mark

Copyright 2008 - Online Poker Blog - Plan3t Gong


Mat said...

Hey Mark, great blog.

But your maths regarding pot odds and whether or not you should be making the call at the mid to end stages of a MTT are off.
When deciding whether to make a call, you have to factor in the payout structure and how far off it you are. It is a crucial determinant and changes the odds with which you should be calling... Its basically to do with ICM (something with which you are very familiar :))

I recommend Lee Nelson's "Kill Everyone"... It is excellent at explaining the proper calling ranges.

Mark said...

Thanks for the kind words Mat.

Sure, you have a point about ICM, this is going to be part 4 of my pot-odds series... really not sure that it makes too much difference in an MTT though.... the reason this is such a big thing in SNGs is the jump from 0% to 20% of the prize pool. In an MTT chips do change value, but the effect is less marked due to the shallow start to the prize distribution.

Good point though - will crunch some numbers on it soon.

Cheers, Mark

Mat said...

yeah, it isn't as big of an effect as at the bubble of an STT, but its effect is still significant and more impotantly, it is always there.

In "Kill Everyone" Nelson introduces the concept of 'bubble factors', and states that you should make decisions based on pot odds divided by your individual 'bubble factor'.
For example, the average stack with 4 to go in an STT has a bubble factor of 1.88. But at the beginning of the STT the average stack has a bubble factor of 1.2!!! This is still significant and cannot be ignored.
Likewise, in a MTT, bubble factors start close to 1 and gradually increase until the money bubble bursts (in the Sunday Millions the average stack at the bubble has a bubble factor of 1.55). Average bubble factors then drop off once in the money, and eventually rise again when approaching the final table.

The only time when you can use pot odds without adjusting is when you are a long long way off the money or in a cash game.

Basically, the non-linearity of chip values play havoc with the decisions you make not only at the bubble, but throughout any tournament (and the effects are often more significant than you'd think)

peace out... Keep up with those posts.
I've learnt a lot (and i'm still learning) :)