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So let’s make it difficult ;-) and let’s start speaking of:
Fundamental Theorem of Poker and Morton’s theorem
Recently on Poker Engineering I wrote about the benefits of playing a non-optimal strategy in poker. I also briefly illustrated the Fundamental Theorem of Poker, introduced by David Slansky, the father of modern poker:
“Anytime you are playing an opponent who makes a mistake by playing his hand incorrectly based on what you have, you have gained. Anytime he plays his hand correctly based on what you have, you have lost.”
Here I’d like to show the limits of the theorem and the support given by what is nowadays known as the Morton’s Theorem with some maths.
Against Fundamental Theorem of Poker, Morton’s Theorem states that in multi-way pots, a player’s expectation may be maximized by an opponent making a correct decision.
But actually David himself intended to apply his theory to head-to-head situations, which involve only two players. So when one theorem falls, another comes in support.
The most common application of Morton’s theorem occurs when one player holds the best hand, but there are two or more opponents on draws. In this case, the player with the best hand might benefit from the absolutely “correct” decision of her opponent to fold to a bet.
Morton proposed an example very similar to the following one to prove his thesis.
Consider in a limit texas hold’em game the following situation:
Flop –> K93
Player A –> AK (top pair and best kicker)
Opponent B –> AT (9 outs for the flush draw)
Opponent C –> Q9 (4 outs — not the Q which gives the flush to the opponent B)
Turn –> 6
The pot size at that point is P, expressed in big blinds.
When the player A bets the turn, opponent B, holding the flush draw, will call having the correct pot odds to call the player’s bet.
Once opponent B calls, opponent C must decide whether to call or fold. To understand what is the right path for her, let’s calculate her expectation in the two cases. Mathematical expectation is the amount a bet will - on average - win or lose. In our case the expectation depends on 2 factors: the number of cards among the remaining 42 that will give her the best hand and the size of the pot when she is deciding.
Expectation of C when she decides to fold = E( opponent C | folding ) = - (1/3) * P that means that C, folding, will lose what she has put into the pot so far.
Expectation of C when she decides to call = E( opponent C | calling ) = (4/42) * (2/3*P+2) - (38/42) * (1/3*P+1) that means that C, calling, will win 2/3 of P + 2 big blinds with probability 4/42 and will lose what she has put into the pot so far + 1 new big blind with probability 38/42
Setting these two expectations equal to each other and solving for P we may easily discover that for a pot size (P) = 7,5 big blinds it is indifferent for the opponent C calling or folding: that means that when the pot is larger than this, opponent C should call, otherwise fold.
Now let’s try to understand what is the best move of opponent C from the point of view of the player A.
Let’s calculate the player A’s expectations:
Expectation of A when C decides to fold = E( player A | C folds) = (33/42) * (2/3*P+1) - (9/42) * (1/3*P+1) that means that the player A will win 2/3 of the pot + 1 big blind with probability 33/42 and will lose 1/3 of the pot + 1 big blind with probability 9/42
Expectation of A when C decides to call = E( player A | C calls) = (29/42) * (2/3*P+2) - (13/42) * (1/3*P+1) that means that the player A will win 2/3 of the pot + 2 big blinds with probability 29/42 and will lose 1/3 of the pot + 1 big blind with probability 13/42
Once again setting these two equal we find that for a pot size (P) equal to 5,25 big blinds, the player A is indifferent to any decision of the opponent C: that means that when the pot is smaller than this, the player profits when opponent C calls instead of “correctly” folding, but when the pot is larger than this, the player A would benefit from B’s folding.
It results clear that there is a range of pot sizes included between 5,25 and 7,5 in our example where it is “correct” for C to fold and at the same time the player A would benefit from the “correct” play of C. And hence there is a range, a blindside, where the Fundamental Theorem of Poker is no more applicable.
Morton’s theorem From Wikipedia, the free encyclopedia
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Know How to Bluff when Playing 7 Card Stud Poker
When engaged in a game of 7 card stud poker you have to be well aware of all the actions you make. It is not an easy game to play, that's for sure, and with each and every unfolding of the cards there are different approaches to consider. According to these approaches, you can end up being a winner for most of the times or a loser.
This will also relate to the way you consider placing the bets, of course, since this is part of your actions and your decision-making. 7 card stud poker games will require patience, focus and a good memory along with skills of knowing when and how to include your action approaches. It can be a game that asks a lot from its players, but there is as well a lot of excitement added to it.
Now, when it comes to the approaches used, you might as well be tempted to use bluffing, but you have to be careful because this type of 'taking action; is not for every player. Actually, bluffing belongs mostly to players who like to take their chances on the risk venue, but once you perform it with care, it may not be that risky after all.
Let's take a look and find out in what way you can venture on approaching this course of action:
- First of all you must be aware that this action requires a good timing, this means that you cannot simply choose to bluff all the times when there is not a good hand to rely on. So, with a poor timing you will have a poor bluffing, hence losing more often.
- Knowing the way your opponents play, is the next thing to take into account. This requires paying attention to their way of gambling prior to consider bluffing. Once you have a good feel on what they are about to do next, then you can think of bluffing as your next move, if your cards and all those on the table indicate this.
- Make sure that you foresee when the opponent-s is/are folding, because they should be the best 'victims' for your bluffing. So, player who are tighter usually fall for the bluff.
- Take also a good look at your board and once it appears to be threatening, then you can consider bluffing. You see, this is exactly as if you mislead the opponents into believing you have a strong hand. Your opponents will be intimated by the cards on your board and they will probably not go any further. Not the same can be said if your board shows weak cards.