LottoCalc

Lottery, Bingo and Keno Calculation FAQs

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How do I use LottoCalc?

You will be asked about various details of a lottery, such as how many numbers are drawn. This site calculates odds, payoffs and other crucial information that is important to casinos, lottery managers and bettors. You should have this information on hand before starting:

The range of numbers from which players make their choices.
The number of choices players may make.
The number of balls (or numbers) that are drawn.
The details of any bonus number.
Optionally: Financial information, such as ticket sales and parimutuel pool allocations.

What is exactly is a lottery?

Lottery (frequently marketed as Lotto) is the general term for a game in which players choose from a series of numbers and hope that they match similar numbers drawn by the lottery managers, who are known as the “house”. The more matches, the better the payoff.

What is Keno?

Keno is a special case of lottery where 80 numbers are in play and 20 are drawn by the casino. Players may pick up to 10 numbers. Casinos favor Keno because of its many betting permutations, low operating costs, extremely high odds and relatively low payoffs.

What are odds?

Odds are simply the ratio of winning combinations to the number of possible ways that losing lottery numbers can appear. To use dice as an example, two dice can produce 6x6 or 36 combinations, but there is only one way to roll "2": each die must display one dot. Thus the odds of rolling 2 with two dice are 1/36 and can be stated variously as:

35 to 1 (or 35:1)
36 for 1
1 in 36
1/36
.02777

The math is simple division, although the numbers can get quite large when dealing with lotteries. Note that 35:1 is not a typo; the number of losing combinations is on the left, and the number of winning combinations is on the right. Many bettors confuse this term.

What is the house percentage?

The house percentage, also known as “the vig,” is the percentage of a winning payout that the house keeps as its commission, to cover overhead, profit and such.

The house percentage in certain craps bets can be as low as 1.414% (usually the lowest in a Las Vegas casino game) to a high of 50% or more with lottery-type games. In other words, if you are playing a game with odds of 100:1, but winners are paid only $50 For each $1 bet, the house percentage is 50%. Any house percentage above 10% is generally known to professional gamblers as a “sucker bet,” which includes virtually all lotteries.

Strange as it seems, the house only makes a profit when bettors win, since it is the house percentage that generates casino and lottery income.

What is parimutuel betting?

Parimutuel or pari-mutuel is short for Paris Mutuel, a French horse race betting system that pools all of the bettors’ money and distributes it to winners based on a percentage of ticket sales, minus overhead costs. Most American race tracks and lotteries are based at least in part upon parimutuel betting. For example, a lottery might determine that the jackpot will be funded with 50% of all ticket sales; all winners of the jackpot must share that pool. The more winners, the lower the share each person takes home.

What is a negative pool?

Casinos and lotteries sometimes guarantee minimum jackpots for lesser prizes, and occasionally this means that they pay out more money than the total amount available in the parimutuel pool. This happens most frequently at horse racing tracks, when bettors overwhelmingly back the winning horse.

This phenomenon is called a negative pool or negative bank. Prudent casinos, race tracks and lotteries stash a bit of all bets in a reserve fund or contingency pool and use the money to pay off negative pools. If there is no reserve fund, the lottery must either reduce its profit or use a parimutuel loss carryover to recoup the lost money from future games.

What is a bonus ball?

Although more balls can be drawn than the number of balls chosen by the player, bonus balls are distinguished by one of these two features:

The ball is drawn from the same set of balls as the normal draw, but can only be matched with players’ numbers that were unmatched in the regular draw.
The number is drawn from a separate set of balls, as in Mega Millions.

The payoff chart says that my winning ticket should pay off $500, but I only got $400. Why?

The financial analysis is based on the long run; that is, on average what will happen if you play a game several hundred times. It assumes, for example, certain ticket sales patterns. Humans, however, don’t pick random numbers. For example, players tend to shun 13 while betting heavily on 7 and 11. Certain dates are also favored. This means that ticket sales patterns are not evenly distributed, skewing the parimutuel pool.

The odds chart sometimes says that it’s easier to get one or two numbers right than to get none right. How can that be?

This is the marketing beauty of carefully crafted lotteries, and it is why Keno is so popular. Drawing extra balls gives the odds chart a "U" shape instead of a steady upward curve, with very high odds at either end and relatively low odds in the middle.

Players believe they come close to winning because they match two or three numbers and, perhaps, only four are needed to win. But matching one more number involves a huge jump in odds. Some casinos even offer money-back guarantees if players fail to match any numbers, because the odds against it can be astronomical.

How can the actual winning jackpot ticket be worth more than the calculated jackpot pool?

In many cases, the chances of someone winning the jackpot are considerably less frequent than once per game. This is how a jackpot rolls over to the next game, and sometimes for several games more. The calculation chart estimates, on average, how much the jackpot ticket will be worth when it is won, excluding any rollovers. Remember that these are long-term averages, and that real winners will end up with either more or less money.

Can’t I be certain to win the jackpot if I place a bet on each possible combination?

Yes, but you’ll most likely lose a ton of money. Lottery managers retain anywhere from 10% to 60% of all bets, which means that all of the payouts totaled up can represent less than half of all the money that was bet.

Even if you win a jackpot with a large rollover from previous weeks, there is a possibility that more than one person will share the jackpot, meaning that you could end up with half or even one-third of the expected jackpot. Bettors who invest in every combination stand to lose millions.

What are the best numbers to pick?

It’s random, so pick any numbers you wish. Really. It doesn’t matter one whit whether the numbers have appeared recently or not, or whether they are lucky numbers or not. Pick whatever makes you happy.

What is the relationship of Bingo to Lotto and Keno?

Like Keno, Bingo is a special case of a lottery. There are five sets of numbered balls, each with a different letter prefix (B I N G O, of course) and each letter has its own series of 15 numbers. The letters themselves actually have no effect on the game, the odds or the rules of play, but merely serve to allow winners to call out “Bingo!”

The 75 numbered balls are divided into five groups, which are reflected on the player’s cards:
B: 1 – 15
I: 16 – 30
N: 31 – 45
G: 46 – 60
O: 61 – 75

The game proceeds just like Lotto, except that players’ winning combinations are chosen for them on printed cards and the house draws balls continuously until one of the players gets four or five numbers vertically, horizontally or diagonally. Calculating Bingo odds using a variation of the Lotto calculations is straight forward, but must take into account the free space in the middle of the N column on each player’s card. LottoCalc does not do Bingo calculations.

Unlike Lotto or Keno, many number combinations (e.g. 15-16-17-18-19) cannot possibly win, but the printed playing cards never include those combinations; 15 will always be in the B column, for example. Every card has an equal chance of being a winner.

On average, it takes roughly 41⅓ balls draws to determine a winner playing one card of the basic game. Variations, such as requiring that two lines of numbers be filled in, greatly alter the odds.

Where can I learn more?

See Scarne’s New Complete Guide to Gambling by John Scarne (Simon & Schuster). To determine rules and parimutuel pools, visit lottery web sites such as the New York Lottery and the Multi-State Lottery Association.