Poker: A Guaranteed Income for Life

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V
Odds (9)

1. Card Odds (10)

The card odds are the probabilities of being dealt or drawing to various hands. These odds are reviewed in most books about poker. Table 4 is based on the card odds and shows the statistical frequency with which different poker hands occur.

TABLE 4
CARD ODDS

^* A fifty-three card deck with the joker has 2,869,685 possible hands.

(+) No straights or flushes. Ace is high.
(++) Including straights and flushes.Ace is low.

There are 2,598,960 different poker hands in a fifty-two-card deck. If a player is dealt 100,000 hands in his lifetime, he will never hold (on his first five cards) more than 4 percent of all the possible hands.

Other poker probabilities based on the card odds are tabulated in Appendix D.

The card odds can reveal interesting information. For example. how many pat straight flushes will Sid Bennett get during his lifetime? To determine that number, the expected number of hands that will be dealt to him during his life is estimated by the following calculation:

From this estimation, the number of pat (on the first five cards) poker hands that Sid should get during his lifetime is calculated from the card odds and tabulated below:

So statistically, Sid should get a pat straight flush on his first five cards once or twice during his life. He will, of course, catch straight flushes more frequently on the draw and in seven-card stud.

. . . Sid wins a big pot with a full house. He throws back his massive head and shouts, "I'm on a spinner! I'm going to break this game!" His head drops; he shakes his finger at the players and continues, "Just watch my luck. I'm getting a whole round of pat straight flushes...starting next deal."

"That won't happen till the sun burns out," Quintin Merck snorts.

Statistically, Quintin is right. Sid will be dealt five consecutive straight flushes once in every 1.7x10²⁴ deals, or once in every 700,000,000,000,000,000,000 years. Yet his five consecutive straight flushes could start coming with the next deal.

Let him hope, John Finn says to himself.

2. Investment Odds (11)

Investment odds are the estimated returns on money that is bet. These odds are approximated by the following formula:

[Note: If you are a beginner or are not mathematically inclined, do not be discouraged or get bogged down by this formula. Forget the formula for now and read on. With experience, you will realize that accurate estimations of investment odds are achieved by the proper thinking methods and not by mathematical problem-solving. This formula is merely a shorthand expression of the thought process required for properly evaluating a bet.]

For example, if a player estimates that a $80 potential pot would require a $20 betting investment (his potential loss), and if he estimates that his probability of winning that pot is .4 (40 percent),[ 7 ] then his investment odds would be calculated as follows:

Investment odds are important for making correct betting and playing decisions. Most players rely only on card odds, which often lead to wrong decisions. For example, investment odds sometimes favor drawing to an inside straight. At other times, investment odds favor folding three aces before the draw. In both cases, the wrong play may result if the decision is based on the card odds.

Determination of investment odds is not a mathematical problem. Numbers plugged into the investment-odds formula are quick estimations or guesses derived by gathering together and then objectively evaluating the facts of the game, players, and situation. Those estimations become more valid with increased thinking effort and experience. While the good player may never actually use or even think about the investment-odds formula, it does express his thought process for evaluating bets.

Quintin, Ted, and Scotty each draw one card. John Finn holds two low pair, tens and fours. What does he do? He considers the card odds, the past betting, probable future betting, his observations (e.g., of flashed cards), and his reading of each opponent ... and then estimates the following investment odds:

Draw one card to his two pair. . .

Draw three cards to his pair of fours . . .

So instead of folding his two pair (and often the investment odds favor folding the two small pair), he breaks up his hand and draws to the pair of fours at favorable investment odds. The low $20 estimate of his potential loss is the key to making this play favorable. John figures his chances for catching and having to call the last bet are small.[ 8 ] When the high probability of a no bet or a folded hand (zero dollars) is averaged into the numerator, the potential loss becomes relatively small--even though the last-round bet may be large if he improves his hand. In other words, he will fold with no additional cost unless he catches three of a kind or better, which would let him bet heavily with a good possibility of winning.

In another hand, Sid and Ted draw three cards. Again John has two low pair. After objectively weighing all factors within the framework of the investment-odds formula, he estimates his most favorable play is to stay pat and then bet the last round as if he had a straight or a flush:

Play pat . . .

The advantages of this play are: If either Sid or Ted catches two pair or even trips, he may fold and let John win on a pat bluff. If either catches a strong hand and shows any betting strength, John folds with no additional cost. Also, neither will try to bluff into John's pat hand. And finally, if Sid and Ted do not improve, John Finn wins additional money if either one calls.

John Finn is the only good player in the Monday night game. He works hard, thinks objectively, and adapts to any situation. By applying the Advanced Concepts of Poker, he wins maximum money from the game.

To overcome mental laziness and restrictive thinking, he forces himself to think constantly and imaginatively about the game. That effort lets him make more profitable plays. For example, he breaks up a pat full house[ 9 ] to triple the size of the pot while decreasing his chances of winning only slightly (from 98 percent down to 85 percent). But that play increases his estimated investment odds from

3. Edge Odds or Edge Percentages (12)

Edge odds indicate the relative performance of a player in a poker game. These odds are calculated by the following formula:

average winnings (or losses) of player, $ x 100% = Edge Odds % [ 10 ]
average winnings of the biggest winner, $

For example, if the biggest winner of each game averages plus $150, and if a player averages plus $75 per game, then the edge odds for this player are +75/150 x 100% = +50%. The more games used to calculate edge odds, the more significant they become. Edge odds based on ten or more games should reflect the relative performance of a player fairly accurately. The good poker player usually maintains edge odds ranging from 25 percent to 65 percent, depending on the game and abilities of the other players. An approximate performance grading of poker players based on the edge odds is tabulated in Table 5.

TABLE 5
EDGE ODDS

Edge odds are estimated for an average seven-man game.

The good player is a very expensive person to have in a poker game, as indicated by the sharp decreases in everyone's edge odds when he plays.

In a black leather notebook, John Finn keeps records of every player. After each game, he estimates their winnings and losses. After every ten games, he calculates their edge odds, as shown below:

^* The biggest winner for each game averaged +$445.

By reviewing his long-term edge-odds data (shown below), John notices slow changes in the players: Quintin is gradually improving, Scotty and Ted are deteriorating. while Sid remains stable.

The steady increase in profit for the biggest winner also reflects John Finn's progress in driving up the betting stakes and pace.

VI
Betting (13)

Few players differentiate between the betting stakes and the betting pace. The betting stakes are the size of bets and raises permitted. The stakes are established by the house rules. The betting pace is the tempo or frequency of bets and raises. The pace depends on the games played and the willingness of players to bet. Both the stakes and pace determine how expensive the game is . . . or how much money can be won or lost.

The good player is seldom characterized as a tight player. His betting pattern is generally [but not always) aggressive,[ 11 ] and often lopsidedly aggressive. Pushing hard whenever he has an advantage (i.e., at favorable investment odds) and quickly dropping against stronger hands let him maximize his wins and minimize his losses.

When the good player bets, he generally bets aggressively. For the good player, increased aggressiveness advantageously quickens the betting pace, while lopsided aggressiveness advantageously creates confusion and fear in his opponents.

As the stakes increase with each round of betting, the losses of the poor players will increase faster than the potential losses of the good player. Indeed, the investment-odds formula in Concept 11 suggests that a steeper and steeper betting progression within a hand (causing the numerator to increase more rapidly than the denominator) permits greater and greater betting aggressiveness, which in turn allows the good player to bet with poorer and poorer hands. In other words, the good player not only tries to drive up the betting stakes and betting pace within a game, but also tries to create a steeper betting progression within a hand.

1. Betting Stakes (14)

Most players think only of the betting stakes when they consider the size of the game.

The betting stakes in John Finn's Monday night games are as follows: In draw, $25 is the maximum bet or raise on the first round of betting. This maximum increases to $50 in subsequent rounds of betting. In stud, the maximum bet is $5 on the first up card. The bet then increases in $5 increments on each subsequent round of betting to $10, $15, $20, and so on. Only three raises are allowed except when only two players remain, and then raises are unlimited. Check raising is permitted.

2. Betting Pace(15)

The betting pace is often more significant than the betting stakes in determining the size of the game. The good player knows the betting pace of both the game and of each individual hand. The betting pace of the game (game pace) is determined by comparing the betting done on various hands to the betting normally done on these hands. The pace may differ markedly in different poker games. In a fast-paced game, for example, two pair after the draw may be worth two raises. In a slow-paced game, those same two pair may be worth not even a single bet.

The betting pace of each hand (hand pace) is determined by comparing the extent of betting, calling, raising, and bluffing to the size of the pot. Often the pace is too slow during certain phases of a hand and too fast during other phases. The good player controls his offensive and defensive game by altering his betting pace at various phases of a poker hand. The ratios shown in Table 6 reflect the betting pace during the various phases of a poker hand.

TABLE 6
BETTING PACES

Few hands are played at the optimum betting pace. And if, for example, the betting pace is relatively slow, the optimum pace will be somewhat faster. A person increases his investment and edge odds by playing closer to the optimum pace.

In the Monday night game, John realizes that the betting in seven-card stud moves at a fast pace during the early rounds, but slows considerably in the late rounds of big bets. He takes advantage of that imbalance by laying back during the early rounds as players get drawn in and disclose their betting tendencies. Then in the later rounds, he quickens the pace by betting aggressively. But while playing closer to the optimum pace himself, John is careful not to correct the imbalanced pace of other players.

The following ratios illustrate how John Finn estimates and influences the hand pace of the Monday night, seven-card stud game.

The techniques for applying the Advanced Concepts of Poker are described in Part Two of this book.

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[ 7 ] How does a player estimate the probability of winning a pot? He does this by assessing his own hand and position against the behavior and betting of his opponents. Initially, the estimates may be little more than guesses. Accuracy will improve with practice, experience, integrated effort, and application of various concepts described in this book.

[ 8 ] The weakness of hands such as small pairs, four flushes, and four-card straights after the draw increases the investment odds because failure to improve those hands causes an immediate fold, thereby reducing the potential loss.

[ 9 ] The opportunity to profitably break a full house by drawing to three of a kind rarely occurs. The above case results when several players with weak hands would fold if the full house were played pat, but would call if a draw were made. Also, the full house would be broken to draw to four of a kind if sufficient evidence existed that the full house was not the best hand.

[ 10 ] If you are not mathematically inclined and do not understand this or other formulas and ratios presented in this chapter, do not worry. Just skip over the formulas and read on. for these formulas are not necessary to understand and utilize the concepts identified in this book.

[ 11 ] Good players are confident in their betting and generally play aggressively, Poor players are either too loose or too tight in their betting and seldom play aggressively.

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