Gap concept and pot odds

Question

In his book "The Theory Of Poker", David Sklansky states that in order to call an early open/raise you should hold at least the same or a tighter range than the open/raiser opponent.

Sklansky called this the "Gap Concept". But as the first round of bets go ahead, players are faced with better pot odds that can lead a villain to call with a wider range of starting hands.

As an example look at this scenario:

The blinds are 0.5xbb and 1xbb, now the pot is 1.5xbb.
The first to open is Alice with 3xbb, now the pot is 4.5xbb.
If Bob would call needs at least an equity of 3/(4.5+3)=0.4.
If the Alice range is R1, Bob needs a range R2 such that R1 vs R2 is at least 60% vs 40% in orther to achieve that equity.
Now the action is on Charlie who needs to commit 3xbb to gain 7.5xbb. So he needs a 0.28 equity against the other players. In order to achieve that equity, Charlie needs a distribution R3 such that R2+R1 vs R3 is 70% vs 30%.

How can we unify these two points of view? Or in other words, where does the gap concept come from?

Answer 1

Sklansky's statement is nothing more than just statistics. Looking at your stats in PokerTracker you will see that in most cases preflop callers have better hands than preflop raisers. If your raise has two calls preflop, then the second call will be "stronger" than the first on the distance.

Really, better pot odds can make someone call with boundary hand (like small pair) and join the multipot, and you will dominate him. But in most cases you are playing against one opponent. Especially with respect to the later stages of MTT.

Answer 2

The gap concept is a little dated. In a completely sterile poker world with perfect information about each others' ranges, it makes sense that the calling range of a middle position player is stronger than the calling range of a late position player, and since we don't know whether the hand was at the bottom or the top of his calling range, you may actually be playing against someone who has called with a hand at the top of his calling range. Because of this, your calling range needs to raise so that the middle of YOUR calling range is BETTER than a hand at the top of his range, something like 99.

Of course, this discounts everything from position to exploiting opponents to forcing mistakes. These days it's really only applicable in a Limit Hold'em game where everyone is playing at a very high level.

Answer 3

I think the correct answer is this (all the equity are tested with a equilab functionality "equity at least"), is an empirical rules due required equity against ranges.

Suppose Alice opens with 10% of hands, this means hands: 77+,A9s+,KTs+,QTs+,AJo+,KQo

Now Bob have to call with hands that have at least 40% of equity. These range can be computed with equilab and is: 44+,A9s+,KQs,AJo+.

If Charlie calls, he needs at least a 28% equity against Alice and Bob. The hands that have at least this equity are: 77+,AQs+,AQo+

As you can see the range become smaller and smaller although the equity become smaller.