Ainsworth’s progressives are constructed on a Must Hit By model that is coin-in dependentcoin-in dependent model, therefore the same argument cannot be used to them. 

A Formula for Expected Value in Must-Hit-By Bet-Based Machines 

There is a chance that these are still valid for certain games, however, it has been six years since that article was published, and not every game is the same. As a result of this, a more broad structure may be preferable. This post on Advantage Slots made some more general calculations, but they still capture the core notion. 

The following are the data points: 

  • Your bets allow you to predict how quickly the meter will move based on its present position. 
  • You can rapidly compute the maximum number of wagers required to reach the ultimate top of the “Must Hit By” range. This is conceivable since the game provides the top number, which may be depending on the amount required to increase it by one penny. 
  • You are also aware that you will earn money along the way, allowing you to calculate an approximate total. In a recent post, I chose 85 percent because that is the low-end average for penny slots. Advantage Slots always use the same number in their calculations. 
  • You also understand that the progressive jackpot can be won at any time between now and the top of the leaderboard. As a result, the expected value of that jackpot can be determined by taking the number that falls between those two values. If you want to be extra cautious, choose the worst-case scenario, which is that it strikes at the highest point. 
  • Based on the data inputs that you have supplied, you can assess whether a game has a positive or negative expected value. 

Exemplifications Based Only on Hypotheses 

Consider the following scenario for a real-world application of mathematics: 

By this moment, the progressive must have reached $500. It costs $470, which appears to be an exorbitant amount at first glance. As a result, the progressive’s current worth is assessed to be around $485, which acts as the midway point. Per two dollars and fifty cents, one cent is added to the final amount. This means we get $250 for every dollar we spend. 

That, however, is a coin-in rather than a loss. In a typical case, you should expect to recoup about 85 percent of your investment. Because the progressive jackpot is factored into the machine’s overall return, you’ll need to reduce the payment for the base game. Because the majority of progressives contribute between 2 and 4% to a machine’s overall return, we’ll use 3% as an average and reduce the payout for the base game to 82 percent. 

Add the amount predicted to be won from the jackpot to the amount expected to be won from the 82 percent chance of winning to determine how much money you should receive out of the machine. The coin-in and coin-out totals can then be compared to see where you stand. 

The case near the center: 

  • If the coin-in was $250 per dollar and the midpoint was $15, the total amount would be $3,750. 
  • If you were successful in winning the base game’s normal return of 82 percent with the coin you entered, you would walk away with $3,075 in your pocket. 
  • You would also receive $485 if you struck the progressive jackpot when it was halfway through. 
  • You’d end up with a total of $3,560 in currency. 
  • Under these conditions, you would incur a total loss of $190. 

Worst case scenario: 

  • If the coin-in was $250 per dollar and the top of the meter was $30, the total amount would be $7,500. 
  • The standard return of 82 percent equates to $6,150. 
  • If you hit the progressive jackpot at the top of the game, you’d also earn $500. 
  • You would have a total of $6,650 in coin-out. 
  • In this situation, you would lose an average of $850. 

Because the expected value is always negative in any given instance, a full-time Advantage Player will usually avoid this tactic. A more casual gambler or Advantage Player would take a swing like this and hope for the best because it’s still an above-average scenario compared to a typical penny slot. Even in the worst-case scenario, the projected return is about 90%, compared to the average of 85 percent, which is still greater than the predicted payback of a penny slot. Regardless of how well the base game plays, the player must be persistent and dedicated to winwinning the progressive prize. 

Keep in mind that those losses are average; there is a chance that you will receive a bonus and a handy. There’s a good probability you’ll receive several dead spins. The payoff from the machines varies from spin to spin. However, this is also a concern with Benefit Plays because the gain isn’t as obvious; there is still some risk involved, and it could pay off or fail. The expected value estimates are meant to lower the number of bad plays while highlighting those that are more successful. The concern now is how this could lead to a positive anticipated value. Let us begin by assuming that the meter will be raised to $480: 

The case near the center: 

  • We’re currently at a median price of $490. 
  • Going to the halfway point on the meter will cost an additional $10, bringing the total amount of coin-in to $2,500. 
  • The average payback would be $2050 at an expected return rate of 82 percent. 
  • When you add the $490 progressive wager, you get a total of $2,540. 
  • In this case, you would come out on top by a factor of $40. 

Worst case scenario: 

  • The $5,000 is equivalent to $250 in coin-in per dollar and $20 to the top of the meter. 
  • The standard return of 82 percent equates to $4,100. 
  • If you hit the progressive jackpot at the top of the game, you’d also earn $500. 
  • You would have a total of $4,600 in coin-out. 
  • Under these conditions, you would lose $400 on average. 

The average condition is expected to create a profit! The worst-case scenario, however, is not the case. If you are a more conservative player, you may not be ready to pursue this right now. A risk-taking player, on the other hand, would be willing to give it a go when it gets into this zone, given that the expectation is that it will be a profitable play more than half of the time. Even in the worst-case scenario, which is a little less than $489, the meter in this picture would turn positive EV. The whole sum, $2,750, would be made up of $250 in coin-in per dollar and $11 to the meter’s top. 

  • The standard return of 82 percent equates to $2,255. 
  • If you hit the progressive jackpot at the top of the game, you’d also earn $500. 
  • You’d wind up with a total coin-out of $2,755. 
  • In this situation, you would come out ahead by an average of $5. 

This, of course, assumes that everything happens exactly as planned, which is unlikely to happen while playing slots; but, from this point onward, the play improves as the number approaches the magical $500 mark. 

Why is this even relevant? 

You are currently in the dark about the slot machine’s true payback setting, as well as the projected return of the base game about the progressive. The only reason you should bother with these calculations is to better your decision-making when it comes to firing a progressive. 

When you use Must Hit Bys, you simply receive more information than you would with an open-ended progressive, and you also have more control over the games you play and when you play them. 

If you are a professional Advantage Player, your time is money, and it is never worthwhile to pursue a mediocre opportunity when there is another that is substantially more favorable. If you seek negative expected value (-EV) scenarios, you are more likely to wind yourself in a worse financial position than when you began. 

Looking into progressives simply improves your odds and can help you make your bankroll last for a longer amount of time if you play a machine with a higher probability of paying out a progressive. 

Why am I bringing this up about Ainsworth? Because their Must Hit By machines appears to hit completely at random across the spectrum of possibilities between the lowest and biggest rewards. 

According to the remarks, some players do not believe it is a fair allocation. Michael Shackleford’s assumptions are based on an even distribution, and it appears that the other participants are similarly happy with that assumption. Gambling is a challenging industry to work in since there is a lack of trust (similar to the “Myths vs. Reality” category on this page, which contains information I’ve come across). This could tip the scales in favor of one computation over another. 

AGS machines, on the other hand, are noted for having Must Hit By progressives, which select numbers from the high end of the range the majority of the time. As a result, you are unable to perform math that relies on the midpoint of the current progressive number and the upper end of the range.