Tri-State Megabucks Probability Calculations
Tri-State Megabucks Probability Calculations
Tri-State Megabucks Probability Calculations
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There are 13 possible tier conditions (5,4,3,2,1,0 primary matches and 2 conditions on the bonus (match, no<br />
match), or the condition of matching all six primary numbers matching; that is 6x2+1=13. Of the 13<br />
conditions 8 are winning tiers and 5 are no prize tiers.<br />
The combination formula for counting the number of ways to match the tiers is:<br />
Ways {h hits and a bonus} = COMBIN(6,h)*COMBIN(1,a)*COMBIN(42-6-1,6-h-a)<br />
Where:<br />
h is the player matching the number of primary numbers (6,5,4,3,2,1,0)<br />
a is the player matching the number of bonus number (1,0)<br />
if h=6, then a=0<br />
The Reciprocal <strong>Probability</strong> or 1/<strong>Probability</strong> for each tier is:<br />
1/<strong>Probability</strong>{ w and a} = Total Ways/ Ways{ w and a }<br />
The following table describes the formulas and count of all the ways to win and lose and their<br />
corresponding reciprocal probability<br />
<strong>Megabucks</strong> Game Probabilities<br />
Winning Prize Tiers<br />
Tier Match Formula Ways 1/<strong>Probability</strong><br />
1 6 Numbers (COMBIN(6,6) * COMBIN(1,0)) * (COMBIN(42-6-1,6-6-0) 1 5,245,786.000<br />
2 5 Numbers + Bonus (COMBIN(6,5) * COMBIN(1,1)) * (COMBIN(42-6-1,6-5-1) 6 874,297.667<br />
3 5 Numbers (COMBIN(6,5) * COMBIN(1,0)) * (COMBIN(42-6-1,6-5-0) 210 24,979.933<br />
4 4 Numbers + Bonus (COMBIN(6,4) * COMBIN(1,1)) * (COMBIN(42-6-1,6-4-1) 525 9,991.973<br />
5 4 Numbers (COMBIN(6,4) * COMBIN(1,0)) * (COMBIN(42-6-1,6-4-0) 8,925 587.763<br />
6 3 Numbers + Bonus (COMBIN(6,3) * COMBIN(1,1)) * (COMBIN(42-6-1,6-3-1) 11,900 440.822<br />
7 2 Numbers + Bonus (COMBIN(6,2) * COMBIN(1,1)) * (COMBIN(42-6-1,6-2-1) 98,175 53.433<br />
8 3 Numbers (COMBIN(6,3) * COMBIN(1,0)) * (COMBIN(42-6-1,6-3-0) 130,900 40.075<br />
Total Ways and Overall Ways to Win: 250,642 20.929<br />
No Prize Tiers<br />
Tier Match Formula Ways 1/<strong>Probability</strong><br />
9 2 Numbers (COMBIN(6,2) * COMBIN(1,0)) * (COMBIN(42-6-1,6-2-0) 785,400 6.679<br />
10 1 Numbers + Bonus (COMBIN(6,1) * COMBIN(1,1)) * (COMBIN(42-6-1,6-1-1) 314,160 16.698<br />
11 1 Numbers (COMBIN(6,1) * COMBIN(1,0)) * (COMBIN(42-6-1,6-1-0) 1,947,792 2.693<br />
12 0 Numbers + Bonus (COMBIN(6,0) * COMBIN(1,1)) * (COMBIN(42-6-1,6-0-1) 324,632 16.159<br />
13 No Matches (COMBIN(6,0) * COMBIN(1,0)) * (COMBIN(42-6-1,6-0-0) 1,623,160 3.232<br />
Total Ways to Lose: 4,995,144 1.050<br />
Total Ways: 5,245,786 1.000<br />
Richard Mishelof<br />
Games Design Consultants<br />
Scientific Games International Corporation<br />
Alpharetta, GA<br />
March 31, 2004
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