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Introduction

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Calculating bingo odds is similar to calculating keno odds. From a probability standpoint, bingo is basically a game of keno where you don't win anything for partial matches. Of course, I am solely talking about the probability of matching a particular pattern as opposed to winning a game of bingo because the probability of winning a bingo game is dependent on how many other people you are competing against.

Calculating bingo odds

Here is the equation for calculating the probability (p) of matching a particular pattern made up of (x) numbers when (y) numbers were drawn out of (z) total numbers (i.e. - 'What is the probability of hitting a pattern made up of 4 particular numbers (e.g. 'corners') when 20 numbers are drawn out of 75?').

p(x,n) = (((combin(x,(x-x)))*combin(z-x,y-x))/combin(z,y))

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To calculate different bingo odds, you can download my odds spreadsheet by right-clicking and selecting 'Save target as' to calculate the casino's edge of the keno game you play.

Bingo Odds Table

# of CallsCover AllFour corners'X' pattern
1---
2---
3---
4-0.00008%-
5-0.00041%-
6-0.00123%-
7-0.00288%-
8-0.00576%0.000000006%
9-0.01037%0.000000053%
10-0.01728%0.000000267%
11-0.02715%0.000000978%
12-0.04073%0.000002934%
13-0.05883%0.000007628%
14-0.08236%0.000017800%
15-0.11230%0.000038142%
16-0.14974%0.000076285%
17-0.19581%0.000144093%
18-0.25176%0.000259367%
19-0.31889%0.000447998%
20-0.39862%0.000746663%
21-0.49241%0.001206149%
22-0.60183%0.001895377%
23-0.72854%0.002906244%
240.000000000000000004%0.87424%0.004359366%
250.000000000000000097%1.04077%0.006410833%
260.000000000000001261%1.23000%0.009260091%
270.000000000000011347%1.44391%0.013159077%
280.000000000000079426%1.68456%0.018422708%
290.000000000000460671%1.95409%0.025440883%
300.000000000002303355%2.25472%0.034692113%
310.000000000010200573%2.58875%0.046758935%
320.000000000040802291%2.95858%0.062345246%
330.000000000149608400%3.36665%0.082295725%
340.000000000508668560%3.81554%0.107617487%
350.000000001618490874%4.30787%0.139504149%
360.000000004855472621%4.84635%0.179362478%
370.000000013819422074%5.43379%0.228841782%
380.000000037509859915%6.07306%0.289866257%
390.000000097525635779%6.76712%0.364670453%
400.000000243814089448%7.51903%0.455838066%
410.000000588022215727%8.33189%0.566344264%
420.000001372051836696%9.20893%0.699601738%
430.000003105169946207%10.15344%0.859510706%
440.000006831373881656%11.16879%1.050513085%
450.000014638658317834%12.25842%1.277651050%
460.000030608103755472%13.42589%1.546630218%
470.000062546994630747%14.67481%1.863887699%
480.000125093989261493%16.00889%2.236665238%
490.000245184218952526%17.43190%2.673087724%
500.000471508113370243%18.94771%3.182247290%
510.000890626436366014%20.56029%3.774293298%
520.001654020524679740%22.27364%4.460528443%
530.003022865096828490%24.09190%5.253511277%
540.005441157174291290%26.01925%6.167165412%
550.009653665954387760%28.05998%7.216895695%
560.016893915420178600%30.21844%8.419711644%
570.029180399362126600%32.49907%9.794358443%
580.049778328323627800%34.90641%11.361455794%
590.083912039174115500%37.44506%13.143644939%
600.139853398623526000%40.11971%15.165744160%
610.230569116649597000%42.93513%17.454913090%
620.376191716638816000%45.89617%20.040826140%
630.607694311493471000%49.00777%22.955855397%
640.972310898389554000%52.27496%26.235263310%
651.541468497446850000%55.70283%29.917405529%
662.422307638845060000%59.29656%34.043944223%
673.774293297735320000%63.06142%38.660072253%
685.832998732863680000%67.00276%43.814748554%
698.943931390390970000%71.12600%49.560945086%
7013.610330376681900000%75.43667%55.955905742%
7120.560286313711000000%79.94035%63.061417582%
7230.840429470566500000%84.64272%70.944094780%
7345.945945945945900000%89.54955%79.675675676%
7468.000000000000000000%94.66667%89.333333333%
75100.000000000000000000%100.00000%100.000000000%

COMMENTS:

Hey! Thanks for all this great info! I'm a fan.
I have a question, what would be the equation if I needed to make it dynamic in a way where the odds react to the number of real players in the room and the # of bingo cards they each have keeping in mind that I want a balance between AI odds of winning and player odds.

dandan on September 7, 2016

How would this formula change if the number chosen was put back into the hopper instead of kept out (ie with replacement)

DaveG44131 on September 11, 2014

HPG ADMIN on February 27, 2013

  • Racing (1935), Lottery (1971), Bingo (1971), Casinos (2012)
  • $971 million
  • $4.8 billion
  • Lottery, bingo, and racing: 18 Casinos: 21
  • Smoking is not permitted in any indoor business in Massachusetts. This does not apply to tribal land.
  • Horse racing is legal at licensed sites.

Massachusetts casinos were very slow to appear in New England. For years, its residents went to Rhode Island or Connecticut for casinos. The first Massachusetts casino, Plainridge Park Casino, opened in Plainridge in June 2015. It has not performed as well as expected. This left concerns about the other three Massachusetts casinos that are set to launch in the next few years.

Massachusetts gamblers will find a few other options beyond casinos. Charities may offer bingo and similar games. There is a state lottery that sells tickets for scratch-offs, lotto drawings, keno, and electronic horse races. There is live horse racing and off-track betting as well.

Paying Gambling Taxes in Massachusetts

Do you have to pay taxes on your gambling winnings? Yes! OnlineUnitedStatesCasinos has gathered everything you need to know about paying taxes straight from a Certified Public Accountant. For more information please visit our exclusive Gambling Taxes article.

Massachusetts Casinos Map & Guide

  • Plainridge Park
  • Wynn (2017)
  • MGM Springfield (2018)
  • Project First Light Resort (2018)
  • 1
  • 0
  • 0

Types of Massachusetts Online Gambling Allowed

There are two types of legal Massachusetts online gambling. Off-track betting on horses is permitted. These are simulcast races with pari-mutuel pools through associated venues. TVG, TwinSpires, and BetAmerica are the most popular sites that accept this type of action from Massachusetts residents.

Daily fantasy sports are the other type of gambling legal in Massachusetts. The law does not explicitly permit daily fantasy sports sites. State Attorney General Maura Healey determined the contests to be legal under state law. Healey did not give the sites a free pass. She proposed regulations that will help protect players. DraftKings, one of the largest fantasy sites in the world, is located in Massachusetts.

Despite these advances, there is still no legislation on legalizing online casinos currently.

Types of Live Massachusetts Gambling

  • Slots: Yes
  • Blackjack: Yes
  • Poker: Yes
  • Craps/Roulette: Yes
  • Horses: Yes
  • Lottery: Yes

The newest form of live gambling in the state are the Massachusetts casinos. The first casino opened in June 2015, with three more Massachusetts casinos are under development. The only casino games that Plainridge Park Casino offers are slots, video poker, and electronic table games. When other Massachusetts casinos and resorts launch, they will be able to offer more games including live poker, craps, roulette; with a different card and table games as well.

There are two Massachusetts racetracks. These venues may offer horseracing. Greyhound racing was outlawed in 2009. Suffolk Downs and Plainridge Park are the two racetracks. Live and simulcast racing are available. Charities in Massachusetts may spread bingo and beano games. Raffles, casino nights, and poker tournaments are also legal for charities to spread in Massachusetts.

The Massachusetts Lottery holds a wide variety of drawings. Traditional scratch-off and lotto drawings are held. There is keno drawing every four minutes from 5 am to 1:15 am daily. There are also virtual horse races every four minutes. Venues include bars, restaurants, and bowling alleys. Lotto buyers can purchase subscriptions to games over a 13, 26, or 52-week period.

Massachusetts Gambling Laws

Massachusetts gambling laws allow for a wide variety of gambling options. It allows its state lottery and charities to spread more games than most states. Massachusetts casinos and racing are the typical types of businesses that can also be found in other states.

The Massachusetts Lottery was created through a state constitutional amendment. It is permitted to sell tickets for games of chance involving pull-tabs or numbers. This includes scratch-off tickets, lotto drawings, keno and virtual horse racing. The Massachusetts Lottery is permitted to join interstate drawings like Powerball and Mega Millions. Subscriptions may be sold for as long as one year out for specific games. Lottery tickets may not be sold over the Internet.

Educational, charitable, religious, fraternal and veterans may hold games of chance and in some cases skill. This includes bingo, beano, and raffles. Raffles or bingo games with a buy-in of $10 or more or with a grand prize of over $10,000 require special rules available through the state attorney general’s office. Bingo and beano games are regulated by the lottery board.

Casino nights are also permitted. These require special permission from the state. Craps, roulette, blackjack and TexasHold’em tournaments are allowed. Cash awards are limited to $25. Casino nights may only be held three times per year.

New Casino Licenses

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Massachusetts casinos were approved by voters, with three resort casinos and a racino. The three resorts have yet to open, as they are still under development. When full-scale gambling goes live, slots, video poker, live poker, craps, roulette, blackjack, Three Card Poker, Four Card Poker, Ultimate Texas Hold’em, baccarat and Pai Gow Poker are among the games that will be available. The racino may only offer slots, video poker, and electronic table games.

List of Massachusetts Casinos

There are dozens of charities that hold bingo and casino nights. Hundreds of convenience stores sell scratch-off and lotto tickets. Bars and similar businesses sell virtual racing and keno tickets.

There are two racetracks in Massachusetts. They are PlainridgePark and SuffolkDowns. Both of these tracks offer live horse racing and race books. Plainridge Park is located in Plainville. Suffolk Downs is in Boston.

You can check out the details of each casino by looking at their websites. For those planning a trip to any of the casinos once they have opened, you can check our Massachusetts casinos map to help guide you to your preferred location.

CasinoSizeAddressWebsite
MGM Springfield3,000 Slot Machines1441 Main Streetwww.mgmspringfield.com
Plainridge Park Casino1,250 Slot Machines301 Washington Streetwww.plainridgeparkcasino.com
First Light Casino Resort3,000 Slot MachinesRoutes 24 & Route 140www.projectfirstlight.com
Wynn Casino3,000 Slot Machines1 Horizon Waywww.wynnineverett.com

Plainridge Park also has a racino where slots, video poker, and electronic table games are available. There are three more Massachusetts casinos on the horizon. Wynn plans on building a casino in Everett. MGM will build a casino in Springfield. Project First Light Resort and Casino will be in Taunton.

History of Massachusetts Gambling

Horseracing was legalized in Massachusetts in 1935. Its roots run much earlier than that. That is just the year that racing became a regulated industry. There were once seven regulated tracks in Massachusetts. There are only two today.

Greyhound racing was once legal in Massachusetts. The Massachusetts Greyhound Protection Act sought to ban the practice by 2010. It passed by a 56-43 margin. Wonderland Greyhound Park operated its last greyhound race on December 26, 2009.

Raynham Park was another greyhound track. It took another approach. The track tried to claim exemption under the state’s casino night part of its charity gaming law. Raynham Park opened twice a week to offer roulette, blackjack and poker games. The proceeds of the gambling went to charity. The activity gave the establishment a way to sell other items to patrons. State law only permits casino nights three times a year. The maximum prize is $25 under charity gambling laws. Raynham Park agreed to stop casino nights after pressure from the state attorney general’s office.

Voters approved having three new casinos in Massachusetts in a statewide referendum to amend the constitution in 2012. An initiative to repeal casinos hit the ballot two years later and failed. Local jurisdictions must approve of each Massachusetts casino. Only four casino licenses were approved by the referendum and the Massachusetts Gaming Commission. One is on tribal land. Another is at a track. The other two were resorts. Wynn and MGM won the resorts licenses in Everett and Springfield, respectively. Suffolk Downs lost the racino license to Plainridge Park.

Boston seemed unhappy about this and challenged Wynn and the potential traffic the casino in Everett would bring to Boston. This caused a back and forth between Boston mayor Marty Walsh and Steve Wynn. Walsh accused Wynn of improprieties in obtaining the land where the casino will be located. Wynn accused Mayor Walsh of defamation. The war finally ended after Wynn Resorts agreed to give Boston impact fees to help with its traffic situation.

Plainridge Park was the first casino in Massachusetts to open. That occurred in June 2015. It only hosts slots, video poker, and electronic blackjack. After a big opening, gaming revenue has declined. This has left industry observers wondering if the same issue will affect the three full-service casino-resorts under construction.

Looking into Fantasy Sports

Massachusetts Attorney General Maura Healey announced in 2015 that her office would investigate the daily fantasy sports industry. Healey is on record as being antigambling but determined that daily fantasy sports were legal in the state by declaring it a game of skill. This was a relief to DraftKings as it is based in Boston. Healey proposed a number of regulations to protect consumers and sports. Raising the minimum age to 21 years, eliminating college sports and capping the number of entries a participant may place in a pool were among her suggestions. These have yet to be implemented by any state or site.

Massachusetts Casinos & Gambling FAQ

Yes. It has been regulated since 1935.

Yes. It was approved by voters in 1971.

What games are operated by the Massachusetts Lottery?

Scratch-off tickets, lotto drawings, virtual horse racing and keno games are spread by the Massachusetts Lottery.

Can you buy subscriptions for Massachusetts Lottery drawings?

Yes. They are sold in 13, 26 and 52-week packages.

Can you buy lottery tickets over the Internet in Massachusetts?

Tickets

No. Lottery sales are only available at retail stores.

Are daily fantasy sports contests legal in Massachusetts?

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Yes. State Attorney General Maura Healey ruled the games legal in 2015.

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Which daily fantasy sports sites operate in Massachusetts?

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DraftKings and FanDuel are the largest. CBS Sports, Yahoo!, Star Fantasy Leagues and BetStars are among the others.

Yes. It is spread by Suffolk Downs and Plainridge Park.

Can you bet on horses over the Internet in Massachusetts?

Yes. Major sites that accept this action include TVG, TwinSpires, and BetAmerica.

As of 2016, there was only one casino in Massachusetts. It is at Plainridge Park.

What is the minimum gambling age in Massachusetts?

The minimum Massachusetts gambling age is 21 years for casinos, and 18 years for lottery, bingo and racing.

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What games are available at Plainridge Park Casino?

Slots, video poker, and electronic table games are the only games live at this time.

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What resort casinos are under construction in Massachusetts?

B And Q

Wynn in Everett, MGM in Springfield and Project First Light in Taunton are the three casinos under development in Massachusetts.

What games will be available at Massachusetts resort casinos?

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Slots, video poker, live poker, craps, roulette, blackjack and other card games banked by the house will be legal once resort-casinos launch.