Morton’s Theory

We all have heard many times the term “Poker takes a day to learn and a life time to master”. There is a lot of truth to this statement. It takes many hours of experience to gain the ability to evaluate what the correct tactics and strategies are, but experience alone does not bring this ability. It also requires spending time studying and training.

While online technology has changed the game of poker in a number of ways, not only has Texas Hold ‘em, seven-card stud, and Omaha poker moved online, but also the ability to find any thing you want to know about the subject has evolved to a greater degree. Most tactics for beginners or intermediate poker players are clear or pretty cut-and-dried. Most top poker article writers and poker book authors agree that playing a well rounded poker game making rational decisions, thinking positive, paying attention, playing good starting hand, playing the percentages, mixing up your play and a combination with bankroll management will make you a winning player certainly!

But, is this always true? Some instances, yes, in low-limit games, but on the other side of the coin there are constantly players who practice these exact tactics and complain at the end of the day as they actually fall short of their planned goals.

Why is this? Let’s take a step back and find out where you might be possibly failing. Thinning the field, this is a reference in poker where some big hands (KK, QQ, AK) make more money when the whole table of opponents isn’t chasing them to the river trying to catch a miracle card. When you have too many players trying to draw to flushes, straights and two pairs, the profit expectation can be significantly reduced. Many quality hands earn more profits on average when targeted by fewer competitors than when targeted by many competitors. This sounds reasonable, does it not? But, I wanted some game mathematical theory to back this tactic up.

After a brief time of pottering through most online card rooms, online poker bonuses, hand evaluations, live poker tourneys among other things, I found what I was looking for, which sort of intrigued me quite a lot. A well-written article by an author named Andy Morton. If you do not know Andy Morton, he is well known in southern California for his poker playing and blogging on newsgroups all over the Internet. On this newsgroup, he made some excellent points to the discussion of thinning the field in multi way pots called “Morton’s Theorem”.

His theorem was based on his quote “What I’m going to tell you is that if you bet the best hand with more cards to come against two or more opponents, you will often make more money if some of them fold, even if they are folding correctly, and would be making a mistake to call your bet. Put another way, you want your opponents to fold correctly, because their mistaken chasing you will cost you money in the long run”.

For example:
You’re holding Ace of diamonds and King of clubs in limit Hold ‘em, the flop (first three community card) is King of spades-Nine of Hearts-Three of hearts (Ks9h3h), now you have flopped top pair with the best kicker possible.
After the betting on the flop is complete, you have two opponents remaining. Player A is holding the top flush draw (Ace of hearts and Ten of Hearts), giving him nine winning cards (Kh-Qh-Jh-8h-7h-6h-5h-4h-2h).
The second player, player B, holds Queen of clubs and Nine of clubs, this player has flopped second pair with four outs (9s-9d-Qs-Qd). You exclude the Queen of hearts, because even though it makes two pair against you and gives him a winning hand but doing this he loses to player A making a flush.

Here comes the turn card (Six of Diamonds) and both drawing players, A and B miss totally!
Player A with the nut flush draw is most defiantly calling for a single big bet. Player B must make a decision whether to call or fold his hand.
Player B expectations are the following:
• Player B folding = 0
• Player B calling = 4/46 * (P+2) – 42/46 * (1)
*P=pot size
Setting these two expectations equal to each other and solving for P lets us determine the pot size at which he is indifferent to calling or folding:

• E(player B>folding) = E(player B>calling) => P’ B = 8.5 Big bets
What this means in simpler terms, when player B decides to fold, he does not lose any thing. But if he calls, he will win 4/46 of the times minus the one big bet the remainder of the time. Basically the pot should be larger than 8.6 times the big blind amount to call the bet to get a positive expectation.
Your expectations are the following:
E(you>B folds) = 37/46 * (P+2)
E(you>B calls) = 33/46 * (P+3)
*P=pot size
E(you>B calls) = E(you>B folds) => P’ you = 6.25 Big bets.
What this means in simpler terms is that when the pot is smaller than 6.25 big bets, you profit when player B is chasing, but when the pot is larger than this, your expectation is higher when B folds.

There are two things you have to remember:

If B calls incorrectly, you’re not the only one that benefits, player A will stack his chips when he makes his flush. In fact, player A is benefiting more from B’s call – since you are also losing expectation due to B’s call.

However if player B folds, your expectation heads up against a flush draw climbs and you have a more positive expectation than if player B called.
So you ask, “What is the breaking point in which you want player B to call or fold”, it dictates in the graph below:

The “X” dictates the region in big bets you want him to fold correctly if the pot turns a blank

Why is this article a diamond in the rough? This goes against every thing we have been taught by other respected authors like David Sklansky who wrote “Fundamental Theorem of Poker”.

Well, here’s my job: to keep learning all the time, and use it to the best of my ability on the tables! I’m sure you would agree.