Are there more wins on a higher-cost machine?
In other words, will you hit more payback on a quarter machine versus a penny machine? I don’t mean the amount you win; I mean the number of times you get paid something.
The statistic you're referring to is hit frequency, what percentage of spins pays back something -- anything, from the lowest-paying combination to the jackpot.
A decade ago, I would have said that there is absolutely no correlation between denomination and hit frequency. Now that video slots, which have high hit frequencies compared to traditional, reel-spinning machines, have taken over the lower denominations, there is a negative correlation between denomination and hit frequency -- that is, the lower the denomination, the higher the hit frequency tends to be.
Taking into account the amount you win per hit gives us long-term payback. For this statistic, there is a positive correlation with denomination. Higher-denomination machines tend to have higher long-term paybacks than lower-denomination machines.
Do Class II slot machines also have a hit frequency? They are controlled by a central bingo drawing.
One method to have the result of a spin determined by a central system (Class II) instead of a Random Number Generator in the machine (Class III) is via a bingo drawing. A central system draws the numbers and the pattern filled in on the virtual bingo card in your machine determines the result of your spin.
We can calculate the probability of filling each pattern, so we can also calculate the probability of getting a hit, i.e., the hit frequency.
Class II machines have hit frequencies too.
Does a machine hit more frequently on a max coin (say, five coin) bet versus a short coin (two or three coin) bet? I know if you bet max coins your return will be higher, but I’m interested in the winning frequency not the amount you win.
Another question: Does the RNG know how much you are betting?
Let's start with your final question. The RNG does not know how much you are betting. Regulations usually say that the Random Number Generator function is to be free of any outside influence, like the number of coins played. You may get a different result betting two instead of five coins, but that's only because you started the spin at a different point in time and the RNG had a different value at that time. The result won't necessarily be better or worse, just different.
The answer to your first question is maybe. Whether the amount you bet affects your hit frequency depends on the type of machine you're playing.
Because you called a five-coin bet a max-coin bet, I assume you're interested in traditional reel-spinning machines. If you're playing a multi-line machine, your hit frequency will increase with the number of lines you play.
Another type of machine on which the number of coins you bet affects the hit frequency is a Buy-a-Pay. There weren't many of this type of machine on the slot floor before the video slot revolution and now there's very few of them out there. In fact, Blazing 7s may be the only one still in use. On a Buy-a-Pay, playing additional coins buys additional winning combinations. On a Blazing 7s machine, you have to play two coins (or three, depending on the paytable) to enable the Sevens combinations. Play fewer coins and you won't get paid anything when the Sevens land on the payline. Enabling additional winning combinations increases your hit frequency.
The last type of reel-spinning slot is a multiplier. The number of coins you play has no effect on hit frequency on a multiplier -- there's only one payline and all winning combinations are active all of the time.
Now let's look at video slots. Most video slots act like multipliers -- all winning combinations are active with a minimum bet. You can increase your hit frequency by betting on more lines, but not by betting more on a line.
Finally, let me address a statement you made about getting a higher return with a max-coin bet. If you don't get a bonus on a combination for playing max coin or you don't buy a combination with a max-coin bet, your long-term payback on the max coin bet will be the same as that of a bet of fewer coins. You don't always have to play max coin to get the highest long-term payback possible on a machine.
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