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Mega Ball by Evolution
Introduction
Mega Ball is a live dealer game by Evolution Gaming, a provider of live dealer games for Internet casinos. The game itself is an automated form of bingo featuring a random multiplier if the last ball drawn contributes to a bingo.
Rules
- The game uses a hopper with balls numbered from 1 to 51.
- The player may buy 1 to 200 bingo cards.
- The bingo cards are the 5x5 American kind, with a free square in the middle.
- 20 bingo balls are drawn without replacement and the bingo cards automatically daubed.
- A multiplier wheel is spun, with possible multipliers of 5x, 10x, 12x, 15x, 20x, 25x, 50x, and 100x. An estimated probability of each multiplier appears in the table below.
- A 21st bingo ball, known as the Mega Ball, is drawn from among the 31 balls left in the hopper.
- If the Mega Ball is the last number needed to complete a line, then the win for that card shall be multiplied by the multiplier.
- Sometimes, the multiplier wheel is spun a second time and a second Mega Ball is drawn from the then 30 balls left in the hopper. It is my understanding that if there are two Mega Balls, then if either or both help to complete a line, then the win for that card shall be multiplied by the greater of the two multipliers.
Analysis
Our friends at Tracksino (Online Casino Tracker) track lots of information about Mega Ball. This includes information I need to do this analysis, names the chances of each possible multiplier and how often the game draws two Mega Balls.
For the probability of each multiplier, I looked at 28,172 games for the month ending September 23, 2020. The following table shows those statistics.
Multiplier Statistics
| Mutliplier | Count | Probability |
|---|---|---|
| 5 | 8,623 | 0.306084 |
| 10 | 8,781 | 0.311692 |
| 12 | 3,809 | 0.135205 |
| 15 | 2,928 | 0.103933 |
| 20 | 2,327 | 0.082600 |
| 25 | 1,220 | 0.043305 |
| 50 | 319 | 0.011323 |
| 100 | 165 | 0.005857 |
| Total | 28,172 | 1.000000 |
Taking a weighted average of this data, the mean value for the multiplier is 11.715285.
Assuming the game draws two Mega Balls, the mean value for the greater of two multipliers is 15.417975.
The next table shows the results of a simulation of almost 13 billion games played with one Mega Ball. The lower right cell shows a return of 94.87%.
One Mega Ball Simulation
| Lines | Mega Ball Helpful |
Probability | Base Win |
Average Multiplier |
Return |
|---|---|---|---|---|---|
| 0 | No | 0.846594 | 0 | 1.000000 | 0.000000 |
| 1 | No | 0.112397 | 1 | 1.000000 | 0.112397 |
| 2 | No | 0.006469 | 5 | 1.000000 | 0.032347 |
| 3 | No | 0.000227 | 50 | 1.000000 | 0.011360 |
| 4 | No | 0.000006 | 250 | 1.000000 | 0.001434 |
| 5 | No | 0.000000 | 1,000 | 1.000000 | 0.000117 |
| 6+ | No | 0.000000 | 10,000 | 1.000000 | 0.000029 |
| 0 | Yes | 0.000000 | - | 11.715285 | 0.000000 |
| 1 | Yes | 0.029854 | 1 | 11.715285 | 0.349754 |
| 2 | Yes | 0.004170 | 5 | 11.715285 | 0.244271 |
| 3 | Yes | 0.000270 | 50 | 11.715285 | 0.157933 |
| 4 | Yes | 0.000011 | 250 | 11.715285 | 0.033075 |
| 5 | Yes | 0.000000 | 1,000 | 11.715285 | 0.004461 |
| 6+ | Yes | 0.000000 | 10,000 | 11.715285 | 0.001492 |
| Total | 1.000000 | - | 0.000000 | 0.948669 |
The next table shows the results of a simulation of almost 10 billion games played with two Mega Balls. The lower right cell shows a return of 268.60%.
Two Mega Ball Simulation
| Lines | Mega Ball Helpful |
Probability | Base Win |
Average Multiplier |
Return |
|---|---|---|---|---|---|
| 0 | No | 0.811701 | - | 1.000000 | 0.000000 |
| 1 | No | 0.107935 | 1 | 1.000000 | 0.107935 |
| 2 | No | 0.006212 | 5 | 1.000000 | 0.031061 |
| 3 | No | 0.000218 | 50 | 1.000000 | 0.010890 |
| 4 | No | 0.000005 | 250 | 1.000000 | 0.001374 |
| 5 | No | 0.000000 | 1,000 | 1.000000 | 0.000111 |
| 6+ | No | 0.000000 | 10,000 | 1.000000 | 0.000028 |
| 0 | Yes | 0.000000 | - | 15.417975 | 0.000000 |
| 1 | Yes | 0.062989 | 1 | 15.417975 | 0.971157 |
| 2 | Yes | 0.010126 | 5 | 15.417975 | 0.780635 |
| 3 | Yes | 0.000772 | 50 | 15.417975 | 0.595395 |
| 4 | Yes | 0.000039 | 250 | 15.417975 | 0.152178 |
| 5 | Yes | 0.000002 | 1,000 | 15.417975 | 0.025281 |
| 6+ | Yes | 0.000000 | 10,000 | 15.417975 | 0.009963 |
| Total | 1.000000 | - | 2.686008 |
The final table shows the combined results between the one and two Mega Ball simulations and breaks down the multipliers. The lower right cell shows a return of 96.26%.
Combined Simulation
| Lines | Base Win | Multiplier | Total Win | Probability | Return |
|---|---|---|---|---|---|
| 0 | 0 | Any | 0 | 0.846315 | 0.000000 |
| 1 | 1 | 5 | 5 | 0.009112 | 0.045560 |
| 1 | 1 | 10 | 10 | 0.009376 | 0.093761 |
| 1 | 1 | 12 | 12 | 0.004098 | 0.049171 |
| 1 | 1 | 15 | 15 | 0.003162 | 0.047435 |
| 1 | 1 | 20 | 20 | 0.002521 | 0.050420 |
| 1 | 1 | 25 | 25 | 0.001324 | 0.033112 |
| 1 | 1 | 50 | 50 | 0.000347 | 0.017331 |
| 1 | 1 | 100 | 100 | 0.000179 | 0.017934 |
| 2 | 5 | 1 | 5 | 0.006467 | 0.032337 |
| 2 | 5 | 5 | 25 | 0.001274 | 0.031845 |
| 2 | 5 | 10 | 50 | 0.001313 | 0.065636 |
| 2 | 5 | 12 | 60 | 0.000574 | 0.034460 |
| 2 | 5 | 15 | 75 | 0.000444 | 0.033263 |
| 2 | 5 | 20 | 100 | 0.000354 | 0.035372 |
| 2 | 5 | 25 | 125 | 0.000186 | 0.023236 |
| 2 | 5 | 50 | 250 | 0.000049 | 0.012164 |
| 2 | 5 | 100 | 500 | 0.000025 | 0.012587 |
| 3 | 50 | 1 | 50 | 0.000227 | 0.011356 |
| 3 | 50 | 5 | 250 | 0.000082 | 0.020611 |
| 3 | 50 | 10 | 500 | 0.000085 | 0.042572 |
| 3 | 50 | 12 | 600 | 0.000037 | 0.022384 |
| 3 | 50 | 15 | 750 | 0.000029 | 0.021624 |
| 3 | 50 | 20 | 1,000 | 0.000023 | 0.023009 |
| 3 | 50 | 25 | 1,250 | 0.000012 | 0.015121 |
| 3 | 50 | 50 | 2,500 | 0.000003 | 0.007917 |
| 3 | 50 | 100 | 5,000 | 0.000002 | 0.008193 |
| 4 | 250 | 1 | 250 | 0.000006 | 0.001434 |
| 4 | 250 | 5 | 1,250 | 0.000003 | 0.004323 |
| 4 | 250 | 10 | 2,500 | 0.000004 | 0.008957 |
| 4 | 250 | 12 | 3,000 | 0.000002 | 0.004720 |
| 4 | 250 | 15 | 3,750 | 0.000001 | 0.004564 |
| 4 | 250 | 20 | 5,000 | 0.000001 | 0.004861 |
| 4 | 250 | 25 | 6,250 | 0.000001 | 0.003196 |
| 4 | 250 | 50 | 12,500 | 0.000000 | 0.001674 |
| 4 | 250 | 100 | 25,000 | 0.000000 | 0.001733 |
| 5 | 1000 | 1 | 1,000 | 0.000000 | 0.000117 |
| 5 | 1000 | 5 | 5,000 | 0.000000 | 0.000584 |
| 5 | 1000 | 10 | 10,000 | 0.000000 | 0.001215 |
| 5 | 1000 | 12 | 12,000 | 0.000000 | 0.000642 |
| 5 | 1000 | 15 | 15,000 | 0.000000 | 0.000622 |
| 5 | 1000 | 20 | 20,000 | 0.000000 | 0.000663 |
| 5 | 1000 | 25 | 25,000 | 0.000000 | 0.000436 |
| 5 | 1000 | 50 | 50,000 | 0.000000 | 0.000229 |
| 5 | 1000 | 100 | 100,000 | 0.000000 | 0.000237 |
| 6+ | 10000 | 1 | 10,000 | 0.000000 | 0.000029 |
| 6+ | 10000 | 5 | 50,000 | 0.000000 | 0.000196 |
| 6+ | 10000 | 10 | 100,000 | 0.000000 | 0.000409 |
| 6+ | 10000 | 12 | 120,000 | 0.000000 | 0.000216 |
| 6+ | 10000 | 15 | 150,000 | 0.000000 | 0.000210 |
| 6+ | 10000 | 20 | 200,000 | 0.000000 | 0.000224 |
| 6+ | 10000 | 25 | 250,000 | 0.000000 | 0.000148 |
| 6+ | 10000 | 50 | 500,000 | 0.000000 | 0.000077 |
| 6+ | 10000 | 100 | 1,000,000 | 0.000000 | 0.000080 |
| Total | 1.000000 | 0.962568 |
After all that analysis, I should report that the Bitcoin.io casino reports the return of Mega Ball is 95.40%. This, I do not dispute. The table above shows my estimated return is 96.26%, which is 0.86% higher. I suspect this is due to the limited sampling of multiplier and number of Mega Ball data at Tracksino.
External Links
- Evolution Gaming press release about Mega Ball by the game maker.
- Video by Neil from Live Casino Comparer of playing Mega Ball.