BETTING LIMITS 39. Table stakes, (a) In any poker game except one with fixed limits, i.e., in any pot limit, doubling-up or no-limit game, a player who has not enough chips to call the preceding bets and who cannot obtain more chips may stay in for the showdown by betting all the chips he has left. If there are other players in the pot and they wish to continue betting, their bets above this amount go in a "side pot" in which the short player has no interest. Play continues normally until there is a showdown, when the player who was short competes on even terms for that part of the pot to which he contributed in full. (b) A player in a table stakes game may obtain additional chips from the banker, and add them to his stack on the table, only in the period between a showdown and the beginning of the next deal. He may at no time reduce the number of chips he has in front of him, by cashing them in or by removing them from his stack, except when he leaves the game. (c) A player who is tapped and calls remains in the pot until the showdown, drawing cards on even terms with the other players, without further contributions to the pot. If he has the best hand at the showdown, he takes the main pot. He has no interest in any side pots. (d) A player who drops rather than call a bet in a side pot must discard his hand and relinquishes his interest in all pots. POKER PROBABILITIES I said before that the higher mathematics of poker are not very important. It doesn't help a player much to know the chances of being dealt a straight flush or a full house or even a pair. Yet most of the published tables of poker probabilities are confined to that kind of information. It does help to know the odds against improving any particular hand. A summary of these odds is given on page 94. Memorize those odds. At the very least they will tell you when the pot is offering you good odds on a speculative play. In the following pages I give some special phases of poker mathematics. Possible Poker Hands in a 52-Card Deck Straight Flush ........................................................................ 40 Four of a Kind..................................................................... 624 Full House......................................................................... 3,744 Flush ....... _....................................................................... 5,108 Straight............................................................................ 10,200 Three of a Kind................................................................ 54,912 Two Pairs....................................................................... 123,552 One Pair....................................................................... 1,098,240 No Pair, less than above................................................ 1,302,540 Total ............................................................. 2,598,960 Possible Hands of Less Value Than One Pair IF ACE COUNTS HIGH IF ACE COUNTS LOW Ace High.................. King High........................... 502,860 King High................. Queen High ....................... 335,580 Queen High............... Jack High .......................... 213,180 Jack High.................. Ten High ........................ 127,500 Ten High................... Nine High ........................ 70,380 Nine High................. Eight High ........................... 34,680 Eight High................. Seven High ......................... 14,280 Seven High............... Six High ............................... 4,080 Total.............................................................. 1,302,540 Chances of Being Dealt Poker Combinations in the Original Five Cards Royal Flush....................................................... 1 in 649,740 Straight Flush ................................................... 1 in 64,974 Four of a Kind................................................... 1 in 4,165 Full House ....................................................... 1 in 694 Flush .............................................................. 1 in 509 Straight............................................................. 1 in 255 Three of a Kind................................................. 1 in 47 Two Pairs ........................................................ 1 in 21 One Pair ....................................................... 1 in No Pair ............................................ _............. 1 in 2
Blind-Opening Draw Poker Chance of beating one opponent who has not bet voluntarily (that is, chance of beating the blind raiser when you are the blind opener:) If you draw 5 cards................................... 9 to 1 against you If you draw 4 cards to an ace.................... If you draw 3 cards to an A-K.................... Z to 1 against you If you draw 2 cards to a flush..................... 8 to 1 against you If you draw 2 cards to a straight................. 8 to 1 against you If you draw 2 cards to a straight flush......... 6 to 1 against you If you draw 3 cards to a low pair (4, 3, 2).... Even If you draw 3 cards to a medium pair (5 to 9)........................................ 11/2 to 1 for you On any better hand than a medium pair you should raise. Comment: The pot usually offers 4 to 1. It will be seen that the usual plays stand to lose. However, the figures are complicated by the high cards in the hand that may pair—see page 58. The same principles apply to straight draw poker (page 54) when you are next-to-last man and everyone but the dealer is out. Every additional opponent reduces the odds in your favor on a particular hand. But every additional opponent has to put his money into the pot, thus increasing the odds you are getting for your own money. All poker calculations come to the same thing, though in varying degree: If you had the high hand to begin with, you figure to win. The more players there are against you, the fewer pots you will win but the more you will win each time you win the pot, and in the long run you still show a profit.
Chances of Improving in the Draw (Draw Poker) Draws to One Pair Drawing three cards to one pair—odds against making: Two pair or better................................... Aces up or better..................................... 6 to 1 against Three of a kind........................................ 8 to 1 against Full house............................................... 97 to 1 against Four of a kind.......................................... 359 to 1 against Drawing two cards to one pair and an ace kicker-odds against making: Two pair or better................................... 3 to 1 against Aces up or better..................................... 4 to 1 against Three of a kind........................................ 12 to 1 against Full house................................................ 119 to 1 against Four of a kind.......................................... 1,080 to 1 against Comment: It will be seen that if the player is sure he must have aces up or better to win, his chance is slightly better by holding the Ace kicker. Draws to Three of a Kind Drawing two cards to three of a kind—odds against making: Full house or better................................. 82/3 to 1 against Full house ............................................ 151/2to 1 against Four of a kind......................................... Drawing one card to three of a kind and any kicker— odds against making: Full house or better................................. 103/4to 1 against Full house .......................................... Four of a kind......................................... 46 to 1 against Comment: Holding a kicker to three of a kind decreases the chance of improvement and obviously can be advisable only for deceptive or tactical purposes. Other Odds The odds are 38 to 9 or With a double-ended straight-flush draw (such as
the odds are 2 to 1 against making a straight or better, 
to 1 against making a straight flush, 5 to 1 against making a flush, With a one-ended straight-flush draw (such as
Drawing four cards to an ace, the odds are 21/2 to 1 against making a pair of aces or better. (In stud poker the odds are 31/2 to 1 against pairing an ace if no other ace shows.) Drawing two cards to A-K, the odds are 21/2 to 1 against making aces or kings, or better. It is 23 to 1 against making a flush on a two-card draw and 22 to 1 against making a straight on a two-card draw (both ends open twice, as 10-9-8). It is 11 to 1 against making a straight or better on a two-card straight-flush draw such as Lowball The following odds apply to lowball played with the bug. In each case it is assumed that the bug is not in the hand. One card to 7-high......................................... 31/2 to 1 against One card to 6-high......................................... .51/2 to 1 against One card to 5-high......................................... …..9 to 1 against Two cards to any three cards under 7, to make 7-high or better................... 271/2 to 1 against One card to 8-high......................................... …..2 to 1 against One card to 9-high......................................... Even Comment: See page 61. The more players there are in the pot, the more low cards can be assumed to have been dealt originally and the worse the chances are for improvement. The same fact decreases the danger of pairing, but this does not alter the fact that the chances of improvement are lessened.
| ||||
Home Privacy Statement Site Map
|
