The mathematics of lotto 6/49 are much the same as for cash in hand 7/31. The player must pick 6 numbers and has 49 to choose from. The jackpot for getting all 6 right keeps growing until somebody wins. The player may choose from an annuity or a lump sum if they win the jackpot and must choose at the time they buy the ticket. At the time of this writing the next drawing was for March 15, 2000 with a lump sum prize of $3,650,000.

Unlike all other Maryland lottery games with lotto 6/49 the player gets two plays for $1. This table shows the prizes per game but the return is based on a per dollar bet basis. In other words the return is the product of the prize, the probability, and 2.

 

I will not repeat all the derivations but present the probability table below. It should be stressed that this table was for a the jackpot at a point in time and does not reflect the long term return. According to Howard Benjamin with the Maryland lottery the long term return of lotto 6/49 is about 51%.

 

Lotto 6/49

Match Combinations Probability Pays Return

3 246820 0.0176504 2 0.07060162

4 13545 0.00096862 40 0.07748958

5 258 0.00001845 1500 0.0553497

6 1 0.00000007 3650000 0.52203204

Total 0.01863755 0.72547293

I was surprised that the return of 0.72547293 was as high as it was, about the same as keno in any casino.

 

The Big Game

This game is similar to cash in hand 7/31 and lotto 6/49. The player must select 5 numbers out of 50. The player must also choose a specific “big money ball” from 1 to 36. The “big money ball” is chosen from a separate set of balls. The math is similar to cash in hand 7/31 or lotto 6/49 but the probabilities must be multiplied by 1/36 if the player matches the big money ball and 35/36 otherwise.

Below is the probability table for this game. At the time of this writing the next jackpot for March 14, 2000 was for a lump sum of 4.5 million. It should be stressed that this table was for a the jackpot at a point in time and does not reflect the long term return. According to Howard Benjamin with the Maryland lottery the long term return of lotto 6/49 is about 51%.

 

The Big Game

Match Big Money Ball Combinations Probability Pays Return

0 Yes 1221759 0.01601774 1 0.01601774

1 Yes 744975 0.00976692 2 0.01953383

2 Yes 141900 0.00186036 5 0.00930182

3 No 346500 0.00454275 5 0.02271376

3 Yes 9900 0.00012979 100 0.01297929

4 No 7875 0.00010324 150 0.01548665

4 Yes 225 0.00000295 5000 0.01474919

5 No 35 0.00000046 150000 0.06882957

5 Yes 1 0.00000001 4500000 0.05899677

Total 2473170 0.03242423 0.23860863

Again I was surprised by the total return, this time by how low it was at 0.23860863, for a house edge of 76.14%! In all my years studying gambling this is the worst bet I have ever seen!

 

Annuity or Lump Sum?

Here in Maryland when you buy a lotto 6/49 or big game lottery ticket you must indicate at the time of sale whether you prefer to be paid in a 20 year annuity or a lump sum if you win the jackpot. The lump sum option is half the total of the annuity payments. To help make this decision the following table indicate the value of a $1,000,000 annuity paid out over 20, 25, or 30 years and at various interest rates from 3% to 15%.

As a practical example suppose you are deciding whether to take the annuity or lump sum on a Maryland lottery jackpot. The value of the lump sum is $500,000. Maryland lottery annuities are paid over 20 years. At an interest rate of 8.8% a $1,000,000 annuity has a value of $503,752. At 9.0% the value is $497,506. Using linear Wild Casino Review interpolation we find that at an interest rate of 8.88% the value is very close to $500,000. 8.88% is much more than the interest rate of most safe investments so for this reason I would suggest opting for the annuity. The maximum tax rate of 39.6% will also apply to most of the jackpot if taken in a lump sum, as opposed to more of the payments falling in lower tax brackets if paid as an annuity.

 

Lottery Annuity Values

Interest Rate 20 Year 25 Year 30 Year

3.0% $766190 $717422 $672948

3.2% $753673 $703055 $657153

3.4% $741475 $689134 $641930

3.6% $729585 $675641 $627255

3.8% $717996 $662561 $613105

4.0% $706697 $649879 $599457

4.2% $695680 $637579 $586290

4.4% $684936 $625650 $573583

4.6% $674458 $614076 $561317

4.8% $664237 $602845 $549474

5.0% $654266 $591946 $538036

5.2% $644537 $581365 $526986

5.4% $635043 $571092 $516308

5.6% $625778 $561116 $505986

5.8% $616734 $551427 $496008

6.0% $607906 $542014 $486357

6.2% $599286 $532868 $477022

6.4% $590870 $523980 $467990

6.6% $582650 $515340 $459248

6.8% $574622 $506941 $450784

7.0% $566780 $498773 $442589

7.2% $559118 $490830 $434651

7.4% $551633 $483103 $426961

7.6% $544317 $475586 $419508

7.8% $537168 $468270 $412284

8.0% $530180 $461150 $405280

8.2% $523349 $454219 $398488

8.4% $516670 $447471 $391898

8.6% $510139 $440900 $385505

8.8% $503752 $434499 $379300

9.0% $497506 $428264 $373276

9.2% $491396 $422189 $367427

9.4% $485418 $416269 $361746

9.6% $479570 $410499 $356228

9.8% $473847 $404874 $350865

10.0% $468246 $399390 $345654

10.2% $462764 $394041 $340587

10.4% $457398 $388825 $335660

10.6% $452145 $383736 $330868

10.8% $447001 $378771 $326206

11.0% $441965 $373925 $321670

11.2% $437032 $369196 $317255

11.4% $432201 $364580 $312958

11.6% $427468 $360073 $308773

11.8% $422832 $355671 $304697

12.0% $418289 $351373 $300727

12.2% $413837 $347174 $296858

12.4% $409475 $343071 $293088

12.6% $405199 $339062 $289413

12.8% $401007 $335145 $285830

13.0% $396898 $331315 $282336

13.2% $392870 $327572 $278928

13.4% $388919 $323911 $275603

13.6% $385045 $320332 $272359

13.8% $381246 $316830 $269192

14.0% $377518 $313405 $266101

14.2% $373862 $310055 $263083

14.4% $370275 $306776 $260136

14.6% $366755 $303567 $257257

14.8% $363301 $300426 $254444

15.0% $359912 $297351 $251696

 

My method of analysis was entirely mathematical. The probability of x marks on the card given y calls is easily calculated as combin(24,x)*combin(51,y-x)/combin(75,y). The probability that x marks will form a bingo (five in a row) is more compicated and necessitated a computer program to run through all possible combinations and tabulate the results.

 

Another good source on bingo probabilities is Durango Bill’s Bingo Probabilities. He has the same probabilities I do but goes into more depth on how they were calculated.