Figuring Multiple player pot odds
I need some help in figuring odds against multiple players;
For example 1-2NL
You have a mid pair, EP is reraised all in for $56, and called by LP who has remaining $28 after $56 call
Pot has $148 so your getting close to 3-1
Your read is that your definetly racing against one player with two overs, the other your about 70% sure its a race and 30% he has a higher pair.
Do you call? How much needs to be in the pot to call?
What if?
If you KNOW that one is a race and the other is 4-1 pair, what odds do you need to call?
4-1? ignore the race an your against the pair?
5-1? Race and pair vs pair?
If you KNOW your racing against both players?
How much more then 2-1? If they dont have dominated hands Ie KJ and AQ?
How much less then 2-1? If they have Big aces but don't share kickers? AQ and AT?
For example 1-2NL
You have a mid pair, EP is reraised all in for $56, and called by LP who has remaining $28 after $56 call
Pot has $148 so your getting close to 3-1
Your read is that your definetly racing against one player with two overs, the other your about 70% sure its a race and 30% he has a higher pair.
Do you call? How much needs to be in the pot to call?
What if?
If you KNOW that one is a race and the other is 4-1 pair, what odds do you need to call?
4-1? ignore the race an your against the pair?
5-1? Race and pair vs pair?
If you KNOW your racing against both players?
How much more then 2-1? If they dont have dominated hands Ie KJ and AQ?
How much less then 2-1? If they have Big aces but don't share kickers? AQ and AT?
Comments
So 70% of the time the situation is like this:
You 8-8
Race one A-K
Race two Q-J
(I have assumed worst cace scenario)
In this situation the pot equity is as follows:
8-8 34%
A-K 38%
Q-J 28%
So in 70 trials you will win 32.8 pots
30% of the time the situation is like this:
8-8 19%
A-K 36%
Q-Q 45%
(also worst case)
In 30 trials you will win 5.7 pots.
In 100 trials you will win 38.5% of the time.
So assuming that you are all-in pre-flop you need about 2-1 to show a modest profit.
This is probably not the most elegant way to work this out, but it's (for me) a highly intuitive way of working through problems like this.
As a side note, if you have a small pair and you are against a bunch of over cards you equity is, generally, not as good as being heads up against a single pair of overcards.
I ran the numbers on poker stove as well, as no one gave me a quick (so I could be a lazy ass) answer.
But for a quick calculation at the table is there a simple forumla
equity (%) win (%) tie (%)
Hand 1: 41.4813 % 41.41% 00.07% { AcKc }
Hand 2: 26.8855 % 26.81% 00.07% { QhJs }
Hand 3: 31.6332 % 31.56% 00.07% { 8d8h }
So how do I twist it to come out that I need to see 3+ - 1
1/2 x 1/2 = 1/4 which is not right
1/2 + 1/2 = 1/1 oh oh I think Im calling really bad
1/2 - 1/2 = 0/1 I think my chances are a little better
Or even harder
equity (%) win (%) tie (%)
Hand 1: 45.0890 % 45.00% 00.09% { TcTd }
Hand 2: 37.4045 % 37.31% 00.09% { QhJs }
Hand 3: 17.5065 % 17.42% 00.09% { 8d8h }
1/2 x 1/5 = 1/10
1/2 + 1/5 = 6/10
etc etc
So is there a simple forumla?
its 1/2 x 1/2 = 1/4 but...
Each individual race is about 54/46 not 50/50, and given your opponents have some straight outs that the other needs, you could put your chances in the 56% area for each race... .56 x .56 = ~31%
You only need 2+ to 1 here.
When up against an over pair you win about 19% of the time... the only(a little simplified) way you beat the over pair is when you make a set, and when that happens you'll almost always beat the over cards in the second hand... unless he ends up making a straight, so take off a couple percentage points... voila ~17%
here you need almost 5 to 1
No.... but in this case, given your read of 70/30, it looks like you need (.31)(.7) + (.17)(.3) = ~.27 or about 2.7 to 1 to break even
If half the time you're racing when they have a dominated hand, we get (.31)(.35) + (.45)(.35) + (.17)(.3) = .32 or about 2.1 to 1