Odds

The odds in favor of an event or a proposition are expressed as the ratio of a pair of integers, which is the ratio of the probability that an event will happen to the probability that it will not happen. For example, the odds that a randomly chosen day of the week is a Sunday are one to six, which is sometimes written 1:6, or 1/6. In probability theory and statistics, where the variable p is the probability in favor of the event, and the probability against the event is therefore 1-p, the odds of the event are the quotient of the two, or p/(1-p). That value may be regarded as the relative likelihood the event will happen, expressed as a fraction if it is less than 1, or a multiple if it is equal to or greater than one of the likelihood that the event will not happen. In the example just given, saying the odds of a Sunday are one to six or, less commonly, one-sixth means the probability of picking a Sunday randomly is one-sixth the probability of not picking a Sunday. While the mathematical probability of an event has a value in the range from zero to one, the odds in favor of that same event lie between zero and infinity. The odds against the event with probability given as p are (1-p)/p.

The odds against Sunday are 6:1 or 6/1 = 6: it is 6 times as likely that a random day is not a Sunday. Hence 'odds' are an expression of relative probabilities. Generally 'odds' are quoted in this format odds against rather than as odds in favor of, because of the possibility of confusion of the latter with the fractional probability of an event occurring. E.g., the probability of a random day of the week is a Sunday is 'one-seventh' 1/7. A bookmaker may for his own purposes use 'odds' of 'one-sixth', but the overwhelming everyday use by most people is odds of the form 6 to 1, 6-1, 6:1, or 6/1 all read as 'six-to-one' where the first figure represents the number of ways of failing to achieve the outcome and the second figure is the number of ways of achieving a favorable outcome: thus these are odds against. In other words, an event with m to n odds against would have probability n/ m + n, while an event with m to n odds on would have probability m/ m + n. Even in probability theory, odds may be more natural or more convenient than probabilities. This is in particular the case in problems of sequential decision making as for instance in problems of how to stop online on a last specific event, which is solved by the odds algorithm.

In some games of chance, using odds against is also the most convenient way to understand what winnings will be paid if the selection is successful: the winner will be paid 'six' of whatever stake unit was bet for each 'one' of the stake unit wagered. For example, a winning bet of 10 at 6/1 will win '6 × 10 = 60' with the original 10 stake also being returned. Betting odds are skewed to ensure that the bookmaker makes a profit—if true odds were offered the bookmaker would break even in the long run—so the numbers do not represent the true odds.

Odds on means that the event is more likely to happen than not. This is sometimes expressed with the smaller number first 1:2 but more often using the word on 2:1 on meaning that the event is twice as likely to happen as not.

Decimal presentation

Taking an event with a 1 in 5 probability of occurring i.e. a probability of 1/5, 0.2 or 20%, then the odds are 0.2 / 1 − 0.2 = 0.2 / 0.8 = 0.25. This figure 0.25 represents the monetary stake necessary for a person to gain one monetary unit on a successful wager when offered fair odds. This may be scaled up by any convenient factor to give whole number values. For example, if a stake of 0.25 wins 1 unit, then scaling by a factor of four means a stake of 1 wins 4 units.

Ratio presentation

Fixed odds gambling tends to represent the probability as fractional odds, and excludes the stake. For example, 0.20 is represented as 4 to 1 against written as 4-1, 4:1, or 4/1, since there are five outcomes of which four are unsuccessful. Thus, the stake returned must be added to the odds to compute the entire return of a successful bet. In craps, the payout would be represented as 5 for 1, and in money line odds as +400 representing the gain from a 100 stake.

By contrast, for an event with a 4 in 5 probability of occurring i.e. a probability of 4/5, 0.8 or 80%, then the odds are 0.8 / 1 − 0.8 = 4. If one bets 4 units at these odds and the event occurs, one receives back 1 unit plus the original unit 4 units stake. This would be presented in fractional odds of 4 to 1 on'' written as 1/4 or 1–4 , in decimal odds as 1.25 to include the returned stake, in craps as 5 for 4, and in money line odds as −400 representing the stake necessary to gain 100.

Fixed odds are not necessarily presented in the lowest possible terms; if there is a pattern of odds of 5–4, 7–4 and so on, odds which are mathematically 3–2 are more easily compared if expressed in the mathematically equivalent form 6–4. Similarly, 10–3 may be stated as 100–30.

Gambling odds versus probabilities

In gambling, the odds on display do not represent the true chances that the event will occur, but are the amounts that the bookmaker will pay out on winning bets. In formulating his odds to display the bookmaker will have included a profit margin which effectively means that the payout to a successful bettor is less than that represented by the true chance of the event occurring. This profit is known as the 'over-round' on the 'book' the 'book' refers to the old-fashioned ledger in which wagers were recorded, and is the derivation of the term 'bookmaker' and relates to the sum of the 'odds' in the following way:

In a 3-horse race, for example, the true probabilities of each of the horses winning based on their relative abilities may be 50%, 40% and 10%. These are simply the bookmaker's 'odds' multiplied by 100% for convenience. The total of these three percentages is 100%, thus representing a fair 'book'. The true odds against winning for each of the three horses are 1-1, 3-2 and 9-1 respectively. In order to generate a profit on the wagers accepted by the bookmaker he may decide to increase the values to 60%, 50% and 20% for the three horses, representing odds against of 4-6, 1-1 and 4-1. These values now total 130%, meaning that the book has an over round of 30 130 − 100. This value of 30 represents the amount of profit for the bookmaker if he accepts bets in the correct proportions on each of the horses. The art of bookmaking is that he will take in, for example, $130 in wagers and only pay $100 back including stakes no matter which horse wins.

Profiting in gambling involves predicting the relationship of the true probabilities to the payout odds. Sports information services are often used by professional and semi-professional sports bettors to help achieve this goal.

The odds or amounts the bookmaker will pay are determined by the total amount that has been bet on all of the possible events. They reflect the balance of wagers on either side of the event, and include the deduction of a bookmaker’s brokerage fee vig or vigorish.

Computer poker players are computer programs designed to play the game of poker against human opponents or other computer opponents. They are commonly referred to as pokerbots or just simply bots.

These bots or computer programs are used often in online poker situations as either legitimate opponents for humans players or a form of cheating. Whether or not the use of bot constitutes cheating is typically defined by the poker room that hosts the actual poker games. Most if not all card rooms forbid the use of bots although the level of enforcement from site operators varies considerably.

Player bots

The subject of player bots and computer assistance, while playing online poker, is very controversial. Player opinion is quite varied when it comes to deciding which types of computer software fall into the category unfair advantage. One of the primary factors in defining a bot is whether or not the computer program can interface with the poker client in other words, play by itself without the help of its human operator. Computer programs with this ability are said to have or be an auto player and are universally defined to be in the category of bots regardless of how well they play poker.

The issue of unfair advantage has much to do with what types of information and artificial intelligence are available to the computer program. In addition, bots can play for many hours at a time without human weaknesses such as fatigue and can endure the natural variances of the game without being influenced by human emotion or tilt. On the other hand, bots have some significant disadvantages - for example, it is very difficult for a bot to accurately read a bluff or adjust to the strategy of opponents the way humans can. In addition, bot operators have to beat the rake in addition to their opponents. For this reason, many bots can only be reasonably expected to generate a reliable profit at the lowest stakes.

House enforcement

While the terms and conditions of poker sites generally forbid the use of bots, the level of enforcement depends on the site operator. Some will aggressively seek out and ban bot users through the utilization of a variety of software tools. The poker client can be programmed to detect bots although this is controversial in its own right as it might be seen as tantamount to embedding spyware in the client software. Another method is to use CAPTCHAs at random intervals during play.

House bots

The subject of house bots is even more controversial due to the conflict of interest it potentially poses. By the strictest definition, a house bot is an automated player operated by the online poker room itself, although some would define more indirect examples for example, a player operating bots with the knowledge and consent of the operator as house bots as well. These type of bots would be the equivalent of brick and mortar shills.

In a brick and mortar casino a house player does not subvert the fairness of the game being offered as long as the house is dealing honestly. In an online setting, the same is also true. By definition, an honest online poker room, that chooses to operate house bots, would guarantee that the house bots did not have access to any information not also available to any other player in the hand the same would apply to any human shill as well. The problem is that in an online setting the house has no way to prove their bots are not receiving sensitive information from the card server. This is further exacerbated by the ease with which this can be accomplished in a digital environment without being detected. For the house to even prove they are not using any house players to begin with is essentially impossible - probably the only real way that could be done would be to disclose the confidential personal information of every player and that obviously cannot be done due to privacy considerations.

Poker Jacks Back

Draw Poker Jacks Back

Draw Poker Jacks Back is played with a standard 52-card deck and one Joker. The Joker may be used as an Ace or as any card that completes a straight, flush, or a straight flush. All players place their ante in the pot.

Players are dealt five cards face down, one at a time, in rotation. A round of betting begins (check, bet, call, raise, or fold). If no player has a pair of Jacks or better (higher) after the initial deal, the game converts to the game of Lowball, i.e., California or Kansas City Lowball.

If a player has a pair of Jacks or better after the initial deal, the remaining players may discard any number of their original cards and have the same number of cards replaced by the dealer. Another round of betting occurs. The player with the highest ranking five-card poker hand wins. Five Aces is the best possible hand (four Aces and the Joker). In the event of a tie, the pot is split equally.