====================== Why Play Pot Limit Comparing PotLimit Poker's Ten You Playing Style How Deep Are You Taking The Initiative Drawing Hand's Psychology Reading The Opponent The Art of Bluffing Betting The Bully No Limit Play All In Coups ====================== 
KEY POTLIMIT CONCEPTSLondon lowball is an excellent game for studying mathematical models that illustrate key principles of potlimit play. The reasons are the last card dealt to each player is not visible to the others (as opposed to games with common cards like hold’em poker and Omaha), and it can be clear with one card to come that a hand is presently behind, but will certainly win if it improves. We will look at two related ideas in action. First, proper bluffing frequency; second, the leverage on the end that a drawing hand possesses.
Let us use a concrete example to illustrate this principle. Suppose there is a grand in the pot going into seventh street. Player A has the best hand right now, and player B will have the best hand in all cases where he improves on the last card. At the river player A should of course check. Suppose player B has ten winning cards he can hit. If B bluffs on five of the cards where he misses, then B is bluffing the precise amount that no matter what poker strategy player A adopts, the outcome will always be the same. If A always folds, he will not lose any additional money. If A always calls, he will lose $10,000 on the hands where B has hit, but gain back $10,000 on the five hands where B has run a bluff ($5,000 in B’s bluffs, plus another $5,000 that was originally in the pot). Another way to look at the situation is that when player B bets on the end using the proper game strategy of bluffing half as often as having the goods, then Player A getting 21 on the money will break even by always calling. Note that B is doing well on these fifteen hands despite bluffing, profiting by winning an equivalent amount to the main pot. A good poker player is going to do better than in our mathematical model. He will vary from the dictates of game theory by noticing whether his opponent is normally a caller or a folder, whether he has a tell when bluffing, and so forth. Here is another model, to tell us when the player with the best made should check going into the last card to deprive the opponent of the extra leverage gained from the bigger pot size.Suppose two players are contesting a pot with a grand in it. As previously, Player A is leading with one card to come, and Player B is trying to draw out. Assume there is enough money left for a bet and raise, or a bet now and a bet on the end. For a grand in the pot, this amount would be four thousand apiece. How much the best of it does Player A need to have for it to be correct to bet at the point there is one card to come? Remember, the bet now triples the amount that B can bet on the end. Is betting a good idea when you are increasing the leverage for the drawing hand on the end? Let us look at where the breakeven point between betting and checking is located. That point is when B has exactly a third of the available cards with which to improve. We illustrate this by seeing what happens in our thousand dollar pot when there are 30 unknown cards, B draws out with 10 of them, and A has his hand stand up with the other 20. (For most games, there would be more unknown cards than this, but the ratios are the same, and these numbers are easier to work with.) B will bet on his 10 winning cards, and 5 of his losing cards. In the case where A checks with one card to come, and always calls on the end (note that always folding yields the same result), A is going to break even on his action. A makes a profit of $2,000 x5=$10,000 on the five hands where B bluffs, plus $1,000 x15=$15,000 on the fifteen poker hands where B busts out and does not attempt to bluff. Thus A shows a total profit of $25,000 on all the pots that he wins. On the ten pots that A loses, he is out 10 x $1,000=$10,000. Thus, we see that A, by checking with one card to come, will win $15,000 on the longterm average, according to game theory. B will win $2,000 for each hand he completes and lose $1,000 for each hand he loses. Thus, he also wins 415,000. The total $30,000 is the original money in the pot on Card Six. The preceding discussion to prove out premise is quite involved, but the premise itself is easy to grasp. According to game theory, the breakeven point between betting and checking in the situation we have outlined is when the drawing hand is a 21 underdog. If the leading hand is a greater than 21 favorite with one card to come, it is correct for him to bet. If the leading hand is less than a 21 favorite, it is correct for him to check. Note that when A checks, B must not bet, or A will reraise him allin, which deprives B of any leverage on the end, leaving him a dog as a result.
We should mention the cases when A definitely should bet, to make everything crystal clear. Anytime you are the favorite and have the best hand, be sure to bet if you can thereby get the opponent allin before the last card. Now the drawing hand does not have any implied odds, and the made hand extracts the maximum from the situation. Second, do not try to apply this mathematical principle to games where the last card is dealt faceup, giving the made hand important information about when to call and when to fold should the drawing hand bet on the end. The drawing hand normally has less leverage in such a situation.
We should apply the information in our discussion to find out how big an underdog the drawing hand must be to fold when the opponent bets the pot with one card to come. He does not have to go strictly by the pot odds, as the implied odds help him because of his betting leverage on the end. When the opponent bets the size of the pot, you are getting 21 on the money for a call. So if you can bring your implied odds up to make you no more than a 21 underdog, you should call. As we have seen, the implied odds say the power of the drawing hand enhances the actual odds by a factor of fifty percent. So a player with a twoninths chance to win the pot is actually a threeninths contender for the money. Threeninths chance is the same as saying a 21 underdog. This means any time the drawing hand has two chances out of nine to win the pot, it is correct to call a potsize bet. As we have said, this applies only when the draw can bet the size of the pot on the end.
The same analysis cannot be applied as rigorously to nolimit, because we have been assuming a potsize bet. Suffice t say, if you intend to overbet the pot size each time, and want to play according to game theory, then you should bluff more frequently. Similarly, if you intend to underbet the pot size each time, you should bluff less frequently. 
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