Remembering back to when I first discovered the depth of strategy involved in poker – and things seemed quite complex. After years at the tables and in the webmaster business, I can’t help but feel that some people like to publish complex sounding articles, simply to show off their skills!
Today I decided to take 3 advanced concepts, and show you how easy the fundamental principles behind them really are. These are Reverse Implied Odds, Combinatrix and Prize Pool Equity Models.
#1 – Reverse Implied Odds
To understand the concept of reverse implied odds, it is useful to start with the general implied odds concept first.
Implied Odds account for the extra bets you can win on future betting rounds if you make your hand. For example a small pair pre-flop can call a bet, since those times you hit a set you will often win a big pot. Likewise on the flop, you can call with a straight draw, since you can make more money those times you hit to make up for the times you do not. So, implied odds are the extra money you can win on later streets, this can make your call profitable even when your hand is not the best at the moment you call.
Let’s now reverse this logic.
Reverse implied odds refers to the money you stand to lose on future streets by calling a bet now. This can occur when you have a hand which is likely to be either a small favorite, or completely crushed – or when you make your draw (say a small flush) and get beaten by a better hand.
For example, you have top pair (no hearts) on a board which is 6-7-9 of hearts, your opponent bets, and you call. Now, in the event you have the best hand, any heart, a lot of straight cards and even an over-card could leave you in bad shape. There is also a strong possibility your opponent already has you beaten.
You might have the best hand now, but your reverse implied odds (money you can lose on later streets if you are either already beaten or outdrawn) are big here… depending on your reads it can be better to fold and wait for a clearer spot.
An even more dangerous situation with reverse implied odds is where you are hoping to hit a draw like a low straight or flush, and your opponent hits a bigger hand. Here you are often busy calculating the implied odds – how much extra you can make if you hit your hand. Unfortunately, your opponent’s flush is ace-high, and you end up losing a huge pot instead. On a paired board your reverse implied odds are bigger, you could be hoping to hit a flush when an opponent is already sitting with a full-house.
These kind of situations will happen occasionally, and are very hard to prevent without playing so tight you never get any value at all from your made hands. The best way of dealing with this is to ensure that you make a little extra those times you are ahead (by ensuring stacks are deep compared to your initial bets).
#2 – Combinatrix
Combinatrix refers to the math of being dealt certain types of hands in poker. You can use it to work out the probability of an opponent having certain hands when they bet.
For example, if you know that your opponent only ever re-raises with aces, kings or ace-king – then you can work out the likelihood of him having each one.
This is done by looking at the 1326 ways in which 2 cards can be dealt from a 52 card deck.
For any pair there are 6 possible ways they can be dealt. So, Ace(h) + Ace (s), Ace(h)+ Ace(c), Ace(h)+ Ace(d), Ace(s)+Ace(c), Ace(s)+Ace(d) and Ace(c)+ Ace(d).
When it comes to ace-king, there are a lot more possible ways of this hand being dealt, in fact twice as many as with a pair with 16 possible combinations.
So if you think that an opponent only makes a certain bet with aces, kings or ace-king, then probability shows that he will have an ace-king hand more than half the time (57%), aces 21.5% and kings 21.5%... most players mentally give equal weighting to those hands in these situations, which can cost money over time.
There are a ton of uses for this, for example, if you have an ace in your hand, the numbers change significantly. You can also use the chances of different hands to work out whether your bet is profitable. For example, if your opponent will fold ace-king to a low flop, but not the other hands, you know he will fold more than half the time and can size your bet to take advantage of this.
You can get more info on this type of probability from the Wikipedia, this is a great starting page. This subject is worth looking into!
#3 – Prize Pool Equity Models
The Independent Chip Model (or ICM) used to be a specialist niche of Sit N Go players about 5 years ago. Nowadays it is required knowledge for SNGs and MTTs of all shapes and sizes.
Here, the idea is that you make decisions based on the value of your chips based on the average share of the prize pool you will win over the long run. A silly example is a $100 prize pool, and 4 players with 3500 chips each… over time, they each get to win $25 (all else being equal).
Now, if the prizes are distributed 50% / 30% / 20% (like in a Sit and Go), then doubling your chip stack with 4 left will not double your long term wins – since that means you would need to win 100% of the time you doubled up with 4 left… and that is simply not going to happen.
Instead you can recalculate your new equity… in this example it would be somewhere around $35 over the long run.
Back to the initial decision.
Someone puts you all-in at the bubble of a Sit N Go. If you call, you are risking your $25 in equity to win $10 more… and that is the key to understanding ICM!
You do not just need to have a better hand, you need to have a hand which is good enough to compensate for the risk being bigger than the possible reward.
You will need a specialist calculator to run through examples of this to get a feel for how it affects your ranges in SNGs and MTTs – if you specialize in these games it is well worth the effort though.
Taking advantage of mistakes your opponents make with prize pool equity is central to my free Sit n Go course, the SNG Blueprint, find out more about it here.
If anyone has more poker concepts they would like to be simplified – please let me know!
Gl at the tables, Mark
Submitted by Planet Mark on Tue, 11/19/2013 - 10:05