The Poker's Fundamental Theorem

We have Fundamental Theorem of Algebra and a Fundamental Theorem of Calculus. Now it's time to present the Fundamental Theorem Of Poker. Like all other card games, Poker is a game of curtailed information which has a distinct feature from other board games like checkers, backgammon and chess where what your opponent is doing can be seen by you. At all times, if the cards are shown by everybody, there would always be an accurate mathematically, for each player, the correct play. If the correct play is diverged from any player, he would reduce his mathematical expectation and increase the expectation of his opponent.

Of course, there wouldn't be a game of poker if all cards were interpreted at all times. Filling the gaps in the curtailed information provided by your opponent's betting and interpreted cards in open handed games is the art of the poker but at the same time avoid your opponent from detecting any more than what you want them to know about your hand.

Let's go further to the Fundamental Theorem of Poker

When you play a hand differently every time from the method that you have played it and could see all your rivals' cards, they gain; and every time when you play a hand in the same method that you have played it and could see all your rivals' cards, they lose. On the contrary if your rivals' play their hands differently every time from the method they had and could see all your cards, you gain; and every time when they play a hand in the same method they have played and could see all your cards, you lose.

The Fundamental Theorem is applied unanimously when a hand has been reduced between you and one rival to a contest. It is also applied to multi-way pots but there is an exception case, which will be discussed at the end of the chapter.

What do you mean by the Fundamental Theorem? Think that if anyhow your rivals know your hand then for him it would be a correct play to make. For example: In a draw poker game, if your rival has seen that you had a pat flush before the draw, the correct play for him would be to throw a pair of aces when you bet. There would be a mistake if you make a call but such mistake is of a special kind. It does not mean that your rival has played the hand badly by calling with a pair of aces; it means that he played differently from the method you would play it if he had seen your cards

The example of flush is quite clear. In fact, the entire theorem is clear which its beauty is, yet its function often is not so clear. You can make a correct call because of the amount of money in the pot, even if you had seen your rival's hand is better than yours. Let's take various examples of the Fundamental Theorem of Poker effectively.

The Fundamental theorem of poker and its examples

Example # 1

Let's say when you bet in poker game, your hand is not as good as your rival. When your rival calls for your bet, you tend to lose. But, indeed if you do not lose, you gain! Why? Because the correct play of your rival would be to raise only if he knew what you are having. And so consequently, if he does not raise, you will gain and if he folds, you will gain a huge amount.

This example may seem to be clear for serious argument but it is a common declaration of some highly complicated plays. Suppose in no-limit hold'em you hold the

and an offsuit is hold by your rival

The flop comes to

You call when you check and your opponent bets. Now, it comes the ace of diamonds on the fourth street, you bet, attempting to show aces. The rivals' correct play would be to raise you if he knows what you have, so that it would cost to draw to a flush and on the last card for a straight and so you will have to fold. Therefore, you will gain, if your rival just calls. You have gained because your rival did not made the correct play and not because that you are getting a comparatively cheap final card. If your rival folds and throws away the best reading hand, you have gained enormously.

Example # 2

Suppose you are having two pair and there is $80 in the pot. You are playing draw poker and we shall assume that $10 is the amount all you can bet. Your single rival is having a four- flush which is four cards to a flush. The question would be that are you delving for him to call or fold? Obviously, you will make him to do that thing which is most profitable to you. The Fundamental Theorem of Poker states that making the incorrect play by your rival based on entire information about both hands will be more profitable for you. As your rival gets 9-to-1 odds (he can win $90 with $10 call) and is about a 5-to-1 loser to make a flush, to call is correct for him because a call has positive expectation. As for him it is correct to call, using the Fundamental Theorem, you are therefore delving for him to fold.

Such situation occurs regularly. You are having the best hand but your opponent is getting good odds to make the call correct only if he knew what you are having. Hence you want your rival to fold. Likewise, when you are getting adequate pot odds it would be correct for you to pursue. You will consequently, make money for your rival if you do not pursue and as such you yourself will cost more money.

Example # 3

When your rival is getting adequate pot odds, it is correct for him call, but you can also sometimes make him to fold incorrectly by showing strength than you have on an early betting round. Let's say in the seven-card stud you bet with

and your rival calls with

You are confident that he is having kings. Now, you continue to make a pair of 6s on board and you make a bet. Your rival will fold a pair of kings, as he is scared that you have made aces up.

Some people may say that why don't I want my rival to call as long as my two small pair is better than his pair of kings? The answer would be that if there are cards to come and your rival is getting correct odds, you would definitely win the pot. A pair of kings against your two small pair needs very short odds to give good reason to make a call. Since your rival is correct to call, you gain when you make him fold.

Example # 4

In razz, a seven-card stud lowball game where the lower hand wins, we shall see in another example of showing more strength than you can make a rival to fold incorrectly. Suppose your rival has

You are having

If you think your rival is having a four-card 8 and you are having a pair of a four-card 8-7, it is important to bet even if you know you would be called. The bet will make you gain some extra fairness. Do you want to perceive a little card on the sixth street providing you an 8-7 low? If your rival chases a big card or a pair, still to draw a better 8 than yours, he will fold, as your previous bet specify you have an 8 made already. You have made a 7 low suggesting to a little card, which makes your rival to think that he has no chance to win.

Even though you have the best hand, you once again want your rival to fold. You are having 8, 7 low and want to draw to a 7, while your rival has to draw a better 8. Though, you gain by his folding because had he known that you are having only 8, 7, he will get correct odds to call in the anticipation of drawing out on you. He made a mistake of not to call and therefore you gain. (You would have gained more if you had made two pair on the sixth street card and that your rival folds the best hand.)

Example # 5

As you are delving for your rival to fold when he gets sufficient pot odds. Therefore it is normally correct to play an effective hand once in a weak on an initial round - the reverse of your plays in the earlier two examples - so that your rival makes a bad call when you improve. Take a glance at the following two hands from seven-card razz.



To make a good play some people with this hand would check and if your rival bets, he will just call. Most of the player would set you on a pair or a bad card in the hole. If you do chase a 4, 5 or 7 on board which will give you a 6 or 7 low, your rival would still call, even if your rival is drawing dead because he will think of your play along with his pot odds that it is worth calling. Exactly, this is what you are looking for. Your early misleading play has affected your rival to play poker incorrectly on the later round.

Example # 6

If sometimes, a rival does not get closed to proper odds against you, you are delving for him to call, even if it calls, he has a chance to draw out on you. At the beginning, in the example of flush, the pot were $20 in place of $80, you will delve with your rival with the four flush to call for your $10 bet because he gets 3-to-1 for his money instead of 5-to-1 underdog. Their will breaks if he calls and makes a flush. However, he had a negative expectation and so his play was incorrect, you would have gained anytime when he had made it.

When you are having a hand that is delving for a call, do not try to make your rival to fold by betting an excessive amount in a pot-limit game or in no-limit game. One day when I was playing no-limit hold'em such a matter aroused. One card was about to come and I was having a straight, which was nuts that is the best possible hand. I bet with $50, the player to my left called and the player after him called $50 and raised the rest of his money that is, $200.

As I had the best possible hand, should I raise or just call was only the question? There was about $500 in the pot. Because the third man was all-in, I just had to think of the player who is behind me. If I re-raised say $400, making it $600 to him, I knew that he would definitely fold; truly speaking, if I raise any amount, he would fold. Instead if just call $200, he would possibly call.

What did I want him to do? He had two pair that I was quite sure. If I call $200 there would be around $700 in the pot that will give him 7-to-2 odds to call $200 with his two pair. Thus, the odds against to make a full house with two pair were 10-to-1 (it did not worked it out with the 40 cards in the deck and 4 that did). Hence, if he knew that I am having straight, it would be incorrect for him to take 7-to-2 odds on a 10-to-1 shot. So I just called $200 he did the same as I required and wanted.

The sad ending to this story is that full house was made by him and bet a lesser amount, which I had to pay. Many online poker players disputed that I was wrong to let him in rather than raising him out, but actually they all were wrong. I gave him a chance to make a mistake where I succeeded in doing so because whenever my rival made a mistake, I gained in the long run.

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