Columnist; Science and Academics
The Tri-State Megabucks is a simple lottery draw game with a roll-over jackpot and fixed prizes in the other tiers. It has no add-ons or options besides the main draw. The draw is structured like the more popular Powerball and Mega Millions, but uses smaller pools of numbers and therefore offers far higher odds of winning than those games.
Category
Tri-State Megabucks is a combinatorial lottery game drawing from two independent pools: five numbers drawn from 1 – 41 (the base draw) and one number drawn from 1– 6 (the Megaball).
Size of the draw: 6, that is, 5 + 1.
Size of a played line: 6, that is, 5 + 1.
Cost of a line: $2
Prizes
There are nine prize tiers, defined as matching 2 to 6 numbers in the draw. They are all fixed prizes, except the top prize (6 numbers matched), which is a roll-over jackpot.
The fixed prizes do not increase uniformly from the lowest to the highest. There is an abrupt jump from the 3rd tier to the 2nd tier ($1,300 to $30,000), also for the corresponding odds of winning.
Odds of winning
The odds of winning a prize range wildly, from a daunting 1 in 4,496,388 for the jackpot to 1 in 13 for the eighth tier, the easiest one to win. The overall odds of winning a prize are about 1 in 6.
Average win and fairness
The table below shows the average win for each prize in the base draw:
| Prize tier | Average win |
|---|---|
|
5 + 1 |
Jackpot ÷ 4,496,388 |
|
5 |
0.03336 |
|
4 + 1 |
0.05204 |
|
4 |
0.03002 |
|
3 + 1 |
0.03501 |
|
3 |
0.04895 |
|
2 + 1 |
0.07937 |
|
2 |
0.15385 |
|
1 + 1 |
0.13333 |
For an average jackpot of $2 millions*, the average win is $0.44.
This is one way to interpret the information in this table: Over the long run, a win in the match 4 tier is distributed as an average win of $0.03 per line played (assuming the prize is won with a relative frequency of about 1 in 4,996 draws).
A screen capture from a Tri-State Megabucks draw. Photograph credit: Tri-State Lottery.
The next table lists the fairness of each prize relative to its probability:
| Prize tier | Fairness |
|---|---|
|
5 + 1 |
- |
|
5 |
1.66% |
|
4 + 1 |
2.59% |
|
4 |
1.48% |
|
3 + 1 |
1.61% |
|
3 |
1.76% |
|
2 + 1 |
2.41% |
|
2 |
0.00000 |
|
1 + 1 |
0.00000 |
For an average jackpot of $2 millions*, its fairness is 22.24%. However, this only applies in the circumstance where such a jackpot is actually won, as rollovers actually mean zero prizes in this tier.
The highest fairness is associated with tiers 4 + 1 and 2 + 1. The last two tiers (offering a $2 prize) have a fairness of zero as they actually refund the cost of a line (net profit is zero).
*Note: The average jackpot was chosen as an average of the jackpots won in this game over the last four years, per available public records.
Expected value and house edge
The exact expected value of the Tri-State Megabucks game cannot be obtained, as the first-tier prize is variable. It is yet relevant to estimate it in three cases, associated with three assumptions: a) The first case is taking the jackpot amount as zero (case justified by a long series of draws when the jackpot is not won). b) The second case is taking an average amount for the jackpot won over a period of time (say, the last four years). c) The third case is taking the jackpot amount as its lower threshold of $1 million.
- In case a), the expected value is –$1.77, or –88.51% as a percentage of the line cost. The house edge of the game is 88.51%.
- In case b), the expected value is –$1.32, or –66.27% as a percentage of the line cost. The house edge of the game is 66.27%.
- In case c), the expected value is –$1.55, or –77.39% as a percentage of the line cost. The house edge of the game is 77.39%.
One way to interpret this is that in case a) you are expected to lose on average $1.77 for every $2 invested, over the long run.
Final remarks
Tri-State Megabucks is not a game suitable for syndicates or group play, as the roll-over jackpot is won relatively frequently (which keeps its level down compared to other popular games in this category), and the second-tier prize is not that big relative to its probability.
Over the long run, since the house edge is not much different from Powerball or Mega Millions, there is no actual advantage for the player choosing the Tri-State Megabucks, despite the higher odds of winning. However, players chasing the jackpot (no matter its value) have a better chance of success with Tri-State Megabucks than with the two biggest multi-state games.
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