In a previous post I spoke about the WMS G+ Deluxe progressives, and how they increment based on wins. That can make it a bit more difficult to know what your expected value on a play will be and how much you’ll need to invest.
The same can’t be said for Ainsworth’s progressives, which are designed with a Must Hit By model that is based on coin-in.
Michael “Wizard of Odds” Shackleford took a look at the games a few years ago, and shared some data based on his experiences with a series of games. The precise nature of those calculations may be helpful for those who are trying to get past the math and to whether you should look at a machine or not.
An EV Formula for Bet-Based Must Hit By Machines
These may still be accurate for some games, but six years has passed since that article, and there’s always the chance not every game is identical. As such, a more generic format might be advisable. The basic idea was calculated on a more generic level by this post on Advantage Slots.
Here’s the data points:
- You can calculate how quickly the meter moves based on your bets.
- Based on how much it costs to increment it a penny, you can easily calculate the maximum amount of wagers you must make to reach the absolute top of the “Must Hit By” range, since the game lists the top number.
- You also know you’ll win money along the way, so you can calculate a rough estimate. In another recent post, I use 85% as that’s the low-end average on penny slots. Advantage Slots opts for the same number for their calculation.
- You also know that the progressive will hit anywhere between now and the top. So you can use the midpoint of those two numbers as the expected value of that jackpot.
Based on those data inputs, you can determine whether a game has an expected value that’s positive or negative.
To show the math in action, let’s use the following scenario:
- The progressive Must Hit By $500. It currently sits at $470, which seems high on the surface. Therefore the midpoint is $485, the expected value of the progressive as it stands now.
- The progressive increments one cent for every $2.50. That means $250 for every dollar. You must go up $30 to go from $470 to the top Must Hit My amount of $500. So $250 x $30 is $7,500 of wagers.
- Now, that’s coin-in, not actual loss. You would normally expect to make 85% of that back, on average. $7,500 x .85 = $6,375.
- Add $6,375 to the $485 of expected value on the jackpot and you get a total expected value, on $7,500 of wagers, of $6,860.
A full-time Advantage Player would generally avoid this, because the expected value currently sits at about -$640. A more casual gambler or Advantage Player might take a swing as this and hope for the best, since it’s still an above-average scenario compared to any average penny slot – a 91.46% expected return vs. the 85% we estimated on average, which is still better than the average penny slot’s expected payback.
Now, keep in mind that -$640 is an average – you could hit a bonus and handpay. You could get tons of dead spins. The machines don’t pay back each spin evenly. But that’s also a challenge with Advantage Plays where the advantage isn’t as obvious – there’s still an element of risk to it that could pay off or not. The expected value calculations are designed to minimize bad plays while identifying the better ones.
So, where would this turn to a positive expected value? Let’s presume the meter goes up to $485:
- Now it’s a midpoint of $492.50.
- There’s $15 of meter growth to get to $500, so $250 x $15 = $3,750 of coin-in.
- The expected average payback at 85% would be $3,187.50.
- Add on the $492.50 for the progressive, and you get $3,680.
You might be surprised to see that it’s still slightly negative, although only about $70, with half the meter gap of the first example. But the reason for this is you’re betting less through the machine, so your expected payout on the regular spins goes down with the wagers. Meanwhile, the progressive expectation only goes up a few more dollars, so it’s only able to help close some of that gap.
Ultimately, in this example, the meter would turn positive EV just shy of $487.
Why This Even Matters
Now, you don’t know what the actual payback setting of the slot is, or what the base game is supposed to return vs. the progressive. But the purpose of these calculations is just to help you make better decisions if you’re working to pop off a progressive.
With Must Hit Bys, you simply get more knowledge than an open-ended progressive, and can be more selective over the games you play and when.
If you’re a full-time Advantage Player, your time is literally money, and chasing a poor opportunity is never valuable if there’s a much stronger one elsewhere. And chasing -EV scenarios means a higher likelihood of coming out behind where you started, vs. achieving a profit.
For more casual gamblers, examining the progressives just improves your chances and can help you stretch your bankroll longer if you play a machine that is more likely to pay out a progressive.
As far as why I chose to talk about this in relation to Ainsworth, their Must Hit By machines appear to select completely at random throughout the range of possibilities between the low end and the high end. (When a progressive on a Must Hit By machine is won, the next winning value is generally selected right from the get-go.)
On the other hand, AGS’s machines have a reputation for Must Hit By progressives that largely pick values from near the top end of the range, which means you can’t do math that relies on the midpoint of the current progressive number and the top end.
I’ll cover that in a future post, but it’s yet another reason why you need to pay attention to who makes the game, how it works, and ultimately Know Your Slots.