Bingo Strategy

The probability that a given bingo card will win a game is difficult to assess. To be sure, math helps a player calculate the odds of obtaining a winning pattern in X number of calls. As the number of calls goes up, the odds of winning improve. The problem is that if a card belonging to another player obtains a winning pattern in fewer than X calls, it will win instead, and the card being analyzed will lose. The probabilities associated with being beaten by another card are bound up in the number of other cards in play. This number is often hard to obtain, particularly if the game is being conducted by closed circuit with other venues. By keeping multiple cards in play, the probabilities improve by a multiple of the probabilities for one card.

Once a game begins, it is simply up to chance whether a given card is a winner or not. The only way to improve the edge is to be selective about the venue, the game to be played, and to pay as little as possible for the cards.

The probability of winning is heavily influenced by the number of other cards in play in comparison to the number of cards a player is using. This factor is slightly under the control of the player in two respects.

First, a player can simply refuse to play when the competition is too plentiful. By choosing “off” hours and days to play, and by going to bingo halls with fewer people in them and no closed-circuit connections that confuse the issue, competition can be reduced. A player should be mindful, however, that serious bingo players make up a large percentage of all the players in the house, and each of them is aware of this principle. In addition, the prizes offered in off-hour games with predictably low competition may be smaller than at other times, thus pushing the advantage in the wrong direction.

The precise probability of winning is almost never knowable. The closest approximation is to estimate the cards in play, multiplying the number of players or tables by a sample of cards per table or cards purchased by each player. When unseen players are in the game, too, there are several imprecise methods of estimating the number of cards in play. One common method is to take the speed of bingo (number of calls) and work backwards to estimate approximately how many players there must have been in the game.

Serious bingo players estimate competition by keeping records of dates, times and places they play, how much was won, and in how many calls. Often players note how close to bingo they were before they lost to someone else. If there’s a big gap, then a lot more cards are in play than when the player is “care cased” (lacking only one mark for a win). When machines are in use, other players’ “case alerts” will also tip off a player about how many other cards are in play. A lot of beeps when the player is still far from a win will indicate that there is too much competition. Other indications of the degree of competition are the distribution of calls across the five columns and if there are a lot of ties for a win.

The other influence the player has over the probabilities of winning is the choice of the number of cards to play. The higher the percentage of the player’s cards out of the total number of cards in play, the better the player’s chances. As the only real skill involved in playing bingo is recognizing numbers quickly on the cards, a player who is not reliably capable of identifying all the numbers called out is hurting his or her advantage by adding to the cost of play without increasing the chances of winning.

Given the probability of winning, whatever it is, what else can a player do to improve the advantage? There are really only two other variables in a wager, going back to first principles. Once the “physical expectation” (probability of winning) is known or given, the only other elements are the reward offered (the prize) and the cost of the bet. A player can be selective about the games entered, thus having some pre-game control over how big the prize is. The problem is that the size of the prize is inversely proportional to the probability of winning, so that a serious player may have to do a lot of shopping around for the best combination.

If casinos must clear around 5% or more on a given bingo game without playing directly against the players, then the relationship of the prize to the chance of winning is most likely to result in a negative edge for the player. To illustrate, imagine that a casino sells 1,000 cards for a dollar each. The chance that any given card will win the game is 0.1%. Total cash in will be $1000. If the prize is $950 (95% of the take), the casino makes its 5% to pay for running the game. But the players’ edge is negative as a result. The formula for edge is true odds (physical expectation) times the payoff divided by the cost of the bet, all minus 1 (or 100 in the case of percentages). In this case, the calculation is (0.1% * $950/$1)-100%, which yields -5%. This could obviously be done by inspection, but it is always a good idea to check things with the formula.

The cost of the bet is really the cost of a card; therefore, one way to improve the situation described above is to reduce as much as possible the cost of a card. This is possible, within limits. The most straightforward is to buy cards in packs of large numbers, where the per-card cost is reduced because of the quantities sold. Sometimes this is presented as getting a certain number of cards “free” with the purchase of some quantity. If more than one “level” of card is available, be sure the increase in the reward for the increase in the cost of the level is proportionate. “Premium” cards may improve the size of the prize more than the increase in the cost of the card. If not, avoid them. Also, if they participate at the same level with other cards in a big jackpot or progressive jackpot, they may not be a bargain, either.

“Cash Ball” jackpots and similar wagers should be avoided unless the jackpot is high enough to make “validation” a positive edge bet. Side bets of all other kinds should be avoided, as they are almost without exception “sucker bets.”