Omgfriend

The bingo patterns shown on the screen are sort of a cover up of your bets, which will be paid out to you if you win, in accordance to the amount of your bet. You can watch these numbers being generated on a small bingo screen, while the full-screen display is there for spinning the reels or video icons. How to Win on Bingo Slot Machines?

You're right, according to my table of my probabilities in bingo the probability of any one person getting a bingo within 12 numbers drawn is 0.00199521.
Normally, if the probability of an event happening is p the probability that it will happen at least once in n times is 1-(1-p)ⁿ. In this case the probability that at least one person will get a bingo is 1 - 0.00199521⁷⁵ = 1 - .9980048 ⁷⁵ = 1 -.8608886 = .1391114.
However, in bingo we can't use the method above because all cards go against the same draw of balls. It is hard to explain, but because the cards are arranged in five columns of 15 possible numbers each, the expected number of balls is correlated. It would take a random simulation to properly answer your question. Without doing that, 13.9% is a good rough guess.

The probability of getting a bingo (5 in a row) is complicated to explain, mainly due to the free square. I used a computer to do it. Four corners is much easier. The probability of having 4 corners, given x marks on the card, is combin(20,x-4)/combin(24,x). In other words, it is number of ways to put 4 of the marks in the corners and the rest anywhere else divided by the number of ways to put all x anywhere on the card. The probability of getting four corners within y calls is the sum for i=4 to y of the product of the probability that given y calls there will be x marks on the card and the probability that these x marks will form four corners (above). The probability of getting x marks in y calls is combin(24,x)*combin(51,y-x)/combin(75,y). Following this logic, you should be able to see the math for a coverall.

Following is the expected number of calls before somebody gets a bingo according to the number of players.
1 player: 41.37
10 players: 25.51
50 players: 18.28
100 players: 15.88
200 players: 13.82
500 players: 11.56
1000 players: 10.13

The probability that any given card will have a coverall with 54 calls is combin(51,30)/combin(75,54) = 114456658306760/2103535234151140000 =~ 1 in 18738. The probability of 600 cards not winning are (1-1/18738)^600 =~ 96.79%. So the probability that at least one of the 600 players will hit is are 3.21%.

First let me explain that this is a rather old question that I put on the back burner, bingogala has now been in operation for two years according to their home page. The probability of a coverall within 54 calls for a single card is COMBIN(75-24,54-24)/COMBIN(75,54) = 0.000054. The probability at least one card in 600 will get a coverall in 54 call is 1-(1-.000054)⁶⁰⁰ = 0.032121. The expected number of winners over 380 days at 8 sessions per day is 97.65. The standard deviation is (380*8*0.032121*(1-0.032121))^1/2 = 9.72. So this is (97.58-76)/9.72 = 2.23 standard deviations south of expectations. The probability of 76 or fewer winners in a fair game is 1.30%. So this could either be explained by bad luck on the part of the players, or fewer than 600 players on average. Perhaps they didn’t get as many in the early days. So the evidence doesn't warrant an accusation of foul play in my opinion.

Another Mike S., what are the odds? Lots of racetracks permit what is called 'class 2' gaming, which must be lottery or bingo based. The way to offer slots under this rule is to have a lottery or bingo game going on behind the scenes and the outcome is displayed in the form of a slot machine win. For example if the lottery game determines that you win 20 times your bet it will display whatever slot machine symbols pay 20. So it is a clever illusion.

Oklahoma, and various other Indian casinos, have what is called 'class 2' slots. The outcome is actually determined by the draw of bingo balls. Players at different various different slot machines are linked together, each player has different cards but the draw of the balls is common to all players connected via the network. There is generally a 'game ending pattern' in which if some player completes it then balls quit drawing for all the other players. However with most manufacturers these game ending patterns are very hard to achieve so the element of competition is negligible. Unless the game ending pattern is achieved a certain number of balls are drawn, your cards are automatically daubed, and you are paid according the highest paying pattern you cover, and there are hundreds of patterns. A video representation of a slot machine is only to illustrate how much you have won. If done well, and they often are not, the games play almost just like a Vegas slot machine.

Thanks for the compliment. The answer depends on how the jackpot is determined by the bingo site. If it is a percentage of total cards sold, which is usually the case, then it wouldn’t make any difference. However, if there is a fixed prize for the winner, then it would be better to play one game at a time, lest you compete against yourself.

Yes, that is true. In some states like Oklahoma traditional “class 3” slots are illegal. A way to get around that law is to have a machine pick bingo cards and balls at random. Certain patterns will be mapped to certain wins and the outcome will be displayed to the player like a slot machine win. If done properly, and often they aren’t, the games play just like those in Vegas. If I recall correctly I saw some popular Williams slots like Reel ‘em In when I was at a casino in Tulsa, with just a little bingo card in the corner of the screen. Otherwise they looked the same to me. I don’t know what return they set their slots to in Oklahoma so I can’t help you with that question.

The probability two bingo cards have no numbers in common is (combin(10,5)/combin(15,5))⁴×(combin(11,4)/combin(15,4)) = 1 in 83,414. The probability two bingo cards have all 24 numbers the same is (1/combin(15,5))⁴×(1/combin(15,4)) = 1 in 111,007,923,832,371,000.

For the benefit of other readers, the Big 3 is a bingo side bet at all the Station Casinos and the Fiesta Rancho. The player is given a ticket, either paper or loaded into an electronic unit, with three random bingo numbers out of the 75 possible. If the first four bingo numbers called in that session contain all three of the player’s numbers, then the player will win a progressive jackpot. The jackpot starts at $1000 at grows by $200 a day until somebody wins. Every session, and property, has an independent jackpot.

The number of winning combinations is 72, because three of the balls must match, and the fourth can be any one of the other 72 balls. There are combin(75,4) = 1,215,450 possible combinations. Thus, the probability of winning is 72/1,215,450 = 0.000059. The player can buy 48 tickets for $10, thus the cost per ticket is 10/48 = 0.208333 dollars. The breakeven meter, where there is zero house edge, is (10/48)/(72/1,215,450) = $3,516.93.

Station Casinos indicate the Big 3 Jackpots on their Jumbo Bingo web site. There you will see the meter often will exceed $3517. When I answered this question on August 30, 2007, two of the eight properties had a player advantage, the Palace Station and Fiesta Rancho. This is one of the few bets in Las Vegas that often have a player advantage. Unfortunately, they limit the number of cards you can buy, making it not worth the bother to most people, including me, to make a special trip.

The cards are randomly printed, so if you purchased enough, you would get repeats. So there is no number where you would be assured of winning. The probability of each card winning is 0.00000000243814, or 1 in 410,148,569. Suppose you would be happy with a probability of winning of p, the number of cards you purchased is n, and the probability of winning per card is c. Let’s solve for n:

P = 1-(1-c)ⁿ
1-p = (1-c)ⁿ
ln(1-p) = n×ln(1-c)
n=ln(1-p)/ln(1-c)

For example, to have a 90% chance of winning you would need to buy ln(1-.9)/ln(1-0.00000000243814) cards, which equals 944,401,974.

Spend $1-$19 = 1 free card
Spend $20-$29 = 2 free card
Spend $30-$39 = 3 free card
Spend $40-$49 = 4 free card
Spend $50-$59 = 5 free cards
Spend $60+ = 6 free cards

Each card has five numbers, one for each letter in BINGO. The prizes are as follows:

Cover card in 5 numbers = $10,000
Cover card in 6 numbers = $3,000
Cover card in 7 numbers = $500

If nobody covers in 7 or less numbers, a consolation prize of $50 is paid to the first player to cover.

The following table shows the value of the base prizes to be 1/5 of one cent per card.

Expected Value of Mini X Card

The value of the consolation prize per card is 50/n, where n is the number of competing cards. For example, if there were 1000 competing cards, then the value of the consolation prize per card would be 5 cents.

It depends on how many cards there are in play. Assuming c cards in play, a good approximation for the probability for at least one set of identical cards is 1-e^{(-c/471,000,000)}. For example, with 10,000 cards in play, which I think is about right for a Vegas bingo session, the odds of at least one set of identical cards are about 1 in 47,000. To have a 50/50 chance of at least one set of identical cards, you would need to have about 330 million cards in play.

I won four jackpots in six bingo games. The requirement to hit the jackpot was a coverall within 50 balls. The casino then refused to pay, claiming there was a malfunction, and threatened to take my $100 deposit money too. This doesn't seem fair. What is your opinion?

The probability of a coverall within 50 balls on any given game is 1 in 212,085. The probability of getting one four out of six games is 1 in 134,882,670,482,530,000,000. That sounds like a malfunction if there ever was one. I think the casino has a legitimate case to decline the jackpots, as the games obviously didn't perform properly. However, I think it is just thievery to take your deposit money. I also have to question the integrity of the game, if it could gaff a win like this. Makes me suspect the draw may not be fully random.

This question is raised and discussed in my forum at Wizard of Vegas.

The casino in Milwaukee, which started as a bingo hall, had a record 290 bingos in one game this week. The pattern was the letter I, either up and down (3 on top and bottom and all the Ns) or sideways (3 Bs and Os with the middle). It took 43 calls for the first G ball to be called, resulting in mass winners. Each person got $25.

Here is an article about it: Bingo! Record set at Potawatomi for number of winners in single game.

My question is what are the odds of going 43 calls without calling any numbers of a particular letter?

I've been in similar situations where most people were waiting on a particular letter, but the most winners I've ever seen at once is around 25.

I show the probability of going 44 calls and avoiding any one letter (not just G) is 1 in 1,517,276. Here is a formula to that probability: 5*combin(60,44)/combin(75,44) - combin(5,2)*combin(45,44)/combin(75,44)

In the document titled bingo pattern probabilities (PDF) on your site, you indicate the expected number of calls to find a winner, assuming 300 cards in play, is as follows:

• Four corners: 8.43
• Small diamond: 11.833

Both patterns require four marks only and have only one way to win. Why are the expected number of balls to find a winner different?

This is a difficult answer to explain. Let me start by saying that expected number of calls in a single-card game would be the same. However, there is a correlation effect with more than one card.

It's hard to give a quick answer to this one, but if forced, it's because the four corner pattern requires a concentration of balls in the B and O columns. The small diamond pattern is more likely to be hit with a flatter distribution of balls over the B, N, and O columns.

Let's simplify the game to one where there are an infinite number of cards in play and the balls are drawn WITH replacement. Here is the number of balls required to get a winner in both games:

• Four corners: 2.5+2.5+((1/2)*10+(1/2)*(2.5+5)) = 13.75
• Small diamond: =(5/3)+((1/3)*((5/3)+(5/2)+5)+(2/3)*((5/2)+((1/2)*((5/2)+5)+(1/2)*(5+5)))) = 12 + 2/9

This shows that the four corners takes 1.53 more balls.

Running this through a simultion under normal bingo rules, assuming infinite cards, here are the results:

Bingo Patterns On Slot Machines

• Four corners: 12.8289
• Diamond: 11.3645

This time a different of 1.46 balls.

What I hope to have shown is patterns are more likely to be covered quicker if the marks are distributed over more columns. For this reason, I think that in a single-bingo game you usually see the winning bingo is horizontal.

This question is asked in discussed in my forum at Wizard of Vegas.

If you’ve ever visited a Native American casino, chances are you’ve seen a Class II slot machine. They’re the games that display a bingo card somewhere on the screen.

So what are Class II slots and how are they different from the slot machines you’d find in Las Vegas?

A Brief History

In 1988 the United States enacted the Indian Gaming Regulatory Act (IGRA), establishing the framework governing Native American gaming laws. The act established 3 classes of gaming:

• Class I: traditional and social games for minimal prizes
• Class II: games of chance based off bingo
• Class III: a catch-all category of games that can’t be considered Class I or II, like slots, roulette, blackjack, etc.

Knowing the hurdles Native American casinos faced to allow Class III slots, gaming companies began developing Class II gaming machines: games that play like regular slots but are technically fancy versions of bingo.

Difference between Class II Games and Regular Slots

Regular (class III) slots use a random number generators (RNG) that generate thousands of random numbers each second. When you hit spin, that RNG locks in the value at that moment. Then the slot assigns reel positions to parts of the random number and evaluates your win (if there is one). We covered this in more detail here.

To be legally considered as such, class II slots have to be based on bingo. This is where class II game developers have been creative, often implementing different approaches. On some, like WMS and Multimedia Games, your machine’s “bingo card” remains constant and the drawn numbers change each time. On others (like VGT), you stay in the same game while your card randomly changes each spin.

The implementation doesn’t especially matter. What matters is that the game has the necessary elements required to be bingo: more than 1 player (class II slots must be networked together) and a set of numbers drawn that must match a pattern to result in a win that ends the game (a game-ending pattern).

The fact is Class II slots still rely on RNG to generate the cards and drawn numbers. It doesn’t matter if the RNG is creating simulated bingo cards/numbers on a class II game or virtual reel positions on a class III slot – the results are still random. Payouts are determined on regular slots by adjusting the reels and likelihood of landing on any position. Payouts on class II slots are defined by specifying the bingo patterns that must be matched and within what number of numbers drawn.

Why NA Casinos Prefer Class II

While many modern NA casinos have a mix of class II and III games, the numbers almost always skew heavily towards class II games. Why?

For one, the IGRA granted tribes the power to self-regulate Class II gaming, whereas tribes have to enter state compacts to offer class III games.

But the big reason NA casinos prefer class II games is that tribes don’t owe taxes on class II revenue like they do on class III games.

Licensed slots and most of the fancy new, popular games aren’t available in class II form, so NA casinos keep a mix. However, slot manufacturers are taking an increased interest in offering Class II games. Aristocrat bought Oklahoma-based bingo game developer VGT and used their technology to start offering some Aristocrat favorites in Class II form.

The Bottom Line on Class II Games

Modern class II games can look, act, sound, and feel like typical class III, Vegas-style slots.

Class II games are sometimes criticized for their mysterious nature, leading some to believe they can be rigged. They’re networked together as a central server determines the wins.

Class III slots go through rigorous third-party and government testing to ensure their randomness and resistance to rigging. Class II slots go through some of the same tests, but the self-regulating nature and lack of transparency of NA casinos have historically raised questions about their fairness.

Though their back-end operates different, both class II and class III games still ultimately rely on RNG. Casinos don’t need to rig the machines because the games’ math is already in their favor. That’s not to say their games’ programmed payout percentage is going to be to your liking, but the notion of some casino worker selectively deciding who’s going to win and lose on class II games is just a myth that doesn’t make sense.

Your Take

Do you love or hate class II slots? Tell us about your experiences in the comments below!

Bingo Card Patterns On Slot Machines Play