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Must-Hit-By Progressives
Introduction
A must-hit-by jackpot, sometimes called a mystery jackpot, is one that is guaranteed to hit by a certain point. There are two good things about a large jackpot:
- The jackpot itself is larger.
- The probability of winning it is greater.
As with any progressive game, at some point the jackpot becomes large enough to sway the odds in the player's favor. This page will examine these "target points" on some new slots by WMS with mystery jackpots. If you're interested in must-hit-by progressives on Ainsworth slots, please see my separate page on that.
This page assumes that a jackpot is equally likely to trigger anywhere between the starting value and must-hit-by maximum. This seems to be true for all makers except AGS. The reader should be warned that AGS must-hit-by jackpots tend to hit near the must-hit-by-point. For example, on a version of River Dragons, where the large jackpot starts at $4,000 and must hit by $5000, I calculate the average point it does hit is $4,945.49. So, please do not apply the information in this page to AGS machines.
General Rules
Following are generally how must-hit-by progressives work.
- The jackpot starts at a defined minimum amount.
- A point at which the jackpot will hit is randomly chosen on a uniform distribution between the starting value and maximum possible jackpot.
- A certain percentage of money bet, known as the "meter rise," will be directed towards the jackpot.
- When the meter crosses the predestined win point the player will be awarded the jackpot.
The WMS jackpot games are different from the usual Mystery Jackpot games in two ways:
- There are two jackpots.
- The meter rises by the amount won, not the amount bet.
On the WMS games, it is my understanding that the Minor jackpot starts at $25 and must hit by $50. The Major jackpot starts at $200 and must hit by $500. Based on my own play, the rate of meter rise, for each meter, is 0.00582 times money won.
These two images below show two versions of the pertinent rule screen on the WMS games.
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Short-Term Player Analysis
The short-term player might have a limited bankroll or time and will play when a jackpot is already high enough for the first bet to offer a positive expected value. The following is the formula for the minimum jackpot to play for the short-term player.
j = m × (1-f)/(1-f+r)
Where:
- j = Breakeven jackpot size (with 0% house edge)
- f = Value of all fixed wins plus slot club points and incentives.
- m = Maximum jackpot (the must-hit-by point)
- r = Rate of meter rise
How are you going to know the value of fixed wins? I would subtract from the house edge the value of all must-hit-by jackpots. As a rule of thumb, I would triple the meter rise to all must-hit-by jackpots. The reason you triple is for the value of the game reseeding the jackpot. An exact formula for the average value of must-hit-by jackpots is r + 2*r*n/(m-n).
How would you know the house edge? That will be roughly 10%. The table below indicates average for Clark County (where Las Vegas) by denomination. As a rule of thumb, the nicer the casino, the higher the house edge. If the casino has video keno, I would use the house edge from that, which can be quantified, as a close estimate of the house edge of the reeled slots.
Long-Term Player Analysis
The long-term player has a large bankroll and can sit an play a game until a must-hit-by jackpot is hit, regardless how long it takes. He is willing to suffer a slightly negative expected value at first because as he plays the expected value will grow. Using the same variables as above, the following is the formula for the breakeven jackpot size for the player who will play until the jackpot is hit.
j = m × (1-f-r)/(1-f+r)
Clark County Slot Win to 11/1/2017 to 10/31/2018
| Denomination | Casino Win (pct) |
|---|---|
| $0.01 | 9.97% |
| $0.05 | 5.54% |
| $0.25 | 7.11% |
| $1.00 | 6.34% |
| $5.00 | 5.51% |
| $25.00 | 4.99% |
| $100.00 | 6.22% |
| Megabucks | 12.34% |
| Multi-denomination | 5.26% |
| Total | 6.82% |
Source: Nevada Gaming Control Board, Gaming Revenue Report for 12-month period ending October 31, 2018 (PDF, see page 4).
Although the information is a bit dated, you may wish to also consider the returns of random games I sampled in my page on Slot Machine Odds in Las Vegas. All things considered, I think it is safe to assume a house edge of 8% to 12% in Las Vegas. The nicer the casino and closer to the Strip the casino is, the higher the house edge will generally be. Outside of Vegas, you're on your own.
Click any image for larger version.
WMS Target Points for Short-Term Player
The math for the WMS games gets rather complicated because of the two jackpot and that they go up by amount won, not amount bet. So, you'll have to take it on faith that the tables below are correct.
The first table shows the short-term player Target Point for the Major jackpot, according to the house edge on the game and the amount of the Minor jackpot. In most situations, it will need to be about $482.
Major Jackpot Target Points
| Minor Jackpot |
House Edge | ||||
|---|---|---|---|---|---|
| 14% | 12% | 10% | 8% | 6% | |
| $25 | $484.82 | $482.32 | $479.03 | $474.47 | $467.77 |
| $26 | $484.78 | $482.27 | $478.95 | $474.36 | $467.59 |
| $27 | $484.74 | $482.22 | $478.87 | $474.24 | $467.40 |
| $28 | $484.70 | $482.15 | $478.78 | $474.11 | $467.19 |
| $29 | $484.64 | $482.08 | $478.69 | $473.96 | $466.96 |
| $30 | $484.59 | $482.01 | $478.58 | $473.80 | $466.69 |
| $31 | $484.53 | $481.92 | $478.46 | $473.62 | $466.40 |
| $32 | $484.45 | $481.82 | $478.32 | $473.42 | $466.07 |
| $33 | $484.38 | $481.72 | $478.16 | $473.18 | $465.69 |
| $34 | $484.29 | $481.59 | $477.99 | $472.92 | $465.25 |
| $35 | $484.18 | $481.45 | $477.78 | $472.61 | $464.74 |
| $36 | $484.06 | $481.28 | $477.55 | $472.24 | $464.13 |
| $37 | $483.92 | $481.09 | $477.27 | $471.81 | $463.41 |
| $38 | $483.75 | $480.86 | $476.93 | $471.30 | $462.53 |
| $39 | $483.55 | $480.58 | $476.52 | $470.66 | $461.44 |
| $40 | $483.30 | $480.23 | $476.01 | $469.85 | $460.04 |
| $41 | $482.99 | $479.78 | $475.35 | $468.81 | $458.18 |
| $42 | $482.57 | $479.20 | $474.48 | $467.40 | $455.60 |
| $43 | $482.01 | $478.40 | $473.26 | $465.38 | $451.78 |
| $44 | $481.21 | $477.23 | $471.44 | $462.27 | $445.53 |
| $45 | $479.95 | $475.35 | $468.43 | $456.84 | $433.44 |
| $46 | $477.72 | $471.89 | $462.52 | $444.97 | $400.25 |
| $47 | $472.64 | $463.29 | $445.49 | $398.35 | |
The second table shows the short-term player Target Point for the Minor jackpot, according to the house edge on the game and the amount of the Major jackpot. In most situations, it will need to be about $48.
Minor Jackpot Target Points
| Major Jackpot |
House Edge | ||||
|---|---|---|---|---|---|
| 14% | 12% | 10% | 8% | 6% | |
| $200 | $48.50 | $48.25 | $47.93 | $47.49 | $46.84 |
| $210 | $48.49 | $48.25 | $47.93 | $47.48 | $46.83 |
| $220 | $48.49 | $48.25 | $47.92 | $47.47 | $46.82 |
| $230 | $48.49 | $48.24 | $47.92 | $47.47 | $46.81 |
| $240 | $48.49 | $48.24 | $47.91 | $47.46 | $46.79 |
| $250 | $48.48 | $48.23 | $47.90 | $47.45 | $46.78 |
| $260 | $48.48 | $48.23 | $47.90 | $47.44 | $46.76 |
| $270 | $48.47 | $48.22 | $47.89 | $47.42 | $46.74 |
| $280 | $48.47 | $48.22 | $47.88 | $47.41 | $46.72 |
| $290 | $48.46 | $48.21 | $47.87 | $47.40 | $46.70 |
| $300 | $48.46 | $48.20 | $47.86 | $47.38 | $46.67 |
| $310 | $48.45 | $48.19 | $47.85 | $47.36 | $46.64 |
| $320 | $48.45 | $48.18 | $47.83 | $47.34 | $46.61 |
| $330 | $48.44 | $48.17 | $47.82 | $47.32 | $46.57 |
| $340 | $48.43 | $48.16 | $47.80 | $47.29 | $46.52 |
| $350 | $48.42 | $48.15 | $47.78 | $47.26 | $46.47 |
| $360 | $48.41 | $48.13 | $47.75 | $47.22 | $46.41 |
| $370 | $48.39 | $48.11 | $47.73 | $47.18 | $46.34 |
| $380 | $48.38 | $48.09 | $47.69 | $47.13 | $46.25 |
| $390 | $48.36 | $48.06 | $47.65 | $47.07 | $46.14 |
| $400 | $48.33 | $48.02 | $47.60 | $46.99 | $46.00 |
| $410 | $48.30 | $47.98 | $47.54 | $46.88 | $45.82 |
| $420 | $48.26 | $47.92 | $47.45 | $46.74 | $45.56 |
| $430 | $48.20 | $47.84 | $47.33 | $46.54 | $45.18 |
| $440 | $48.12 | $47.72 | $47.14 | $46.23 | $44.55 |
| $450 | $48.00 | $47.54 | $46.84 | $45.68 | $43.34 |
| $460 | $47.77 | $47.19 | $46.25 | $44.50 | $40.02 |
| $470 | $47.26 | $46.33 | $44.55 | $39.84 | |
Example: You suspect the Minor jackpot may be high enough to play. The Major jackpot is at $300 and you assume a house edge of 10%. The table above shows the Target point is $47.86.
AGS Warning
This page assumes that a jackpot is equally likely to trigger anywhere between the starting value and must-hit-by maximum. This seems to be true for all makers, except AGS. The reader should be warned that AGS must-hit-by jackpots almost never hit until they are near the must-hit-by point. For example, the large jackpots are supposed to hit by $5,000, but it is rumored in the advantage player slot community that they rarely hit below $4,990. So, please do not apply the information in this page to AGS machines.
Further Reading
- The Secret World of Video Poker Progressives, by Frank Kneeland
- Million Dollar Slots by Peter Liston
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