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Thread: Harley Davidson Slot - Spin Bank

  1. #1
    Hi. I assume everyone is familiar with the new Harley Davidson slot machines. Every time a mini, minor, or Maxi symbol appears in the last reel but doesn't trigger a bonus game, an extra spin is banked for when the bonus triggers. I've been watching a Twitter argument discussing this game. The argument is about when the number of banked spins becomes advantageous to the player. One of the guys claims he "did the math" to calculate the break even point. How would you approach the math on a game that banks free spins? Thanks

  2. #2
    Originally Posted by Prozema View Post
    Hi. I assume everyone is familiar with the new Harley Davidson slot machines. Every time a mini, minor, or Maxi symbol appears in the last reel but doesn't trigger a bonus game, an extra spin is banked for when the bonus triggers. I've been watching a Twitter argument discussing this game. The argument is about when the number of banked spins becomes advantageous to the player. One of the guys claims he "did the math" to calculate the break even point. How would you approach the math on a game that banks free spins? Thanks
    How about a link to the twitter discussion.
    "More importantly, mickey thought 8-4 was two games over .500. Argued about it. C'mon, man. Nothing can top that for math expertise. If GWAE ever has you on again, you can be sure I'll be calling in with that gem.'Nuff said." REDIETZ

  3. #3
    Well, it was there yesterday but it's gone now. I took a screenshot of the beginning. Here is the screenshot. I redacted the names because I'm sure they deleted this for a reason.

    https://imgur.com/a/eBYBy

  4. #4
    Originally Posted by Prozema View Post
    Hi. I assume everyone is familiar with the new Harley Davidson slot machines. Every time a mini, minor, or Maxi symbol appears in the last reel but doesn't trigger a bonus game, an extra spin is banked for when the bonus triggers. I've been watching a Twitter argument discussing this game. The argument is about when the number of banked spins becomes advantageous to the player. One of the guys claims he "did the math" to calculate the break even point. How would you approach the math on a game that banks free spins? Thanks
    The first thing is in reference to the picture you posted, depending on how they did it, there's really not necessarily a huge difference between 43 and 44. Although, if two people actually did the work and came up with results just one off from each other, then that's actually a pretty encouraging sign.

    Anyway, let's get some caveats out of the way first:

    1.) Different slot titles come with different variations as well as different return settings, so what is true for a slot machine in one casino in one state may not be true for another casino in another state. Hell, what's true for one slot machine of a certain title isn't even necessarily true of the slot machine right next to it.

    2.) Anyway, your sample size would have to be ridiculous to be absolutely sure, especially with all of the different variables. However, I can explain how you would go about making an educated guess:

    How To Go About It

    In this case, I see a few serious variables:

    A.) What percentage return is on the base reels? (Not counting Free Games or the Wheel spin)

    B.) What is the average return for each individual spin in each set of free games?

    C.) What is the probability of each type of free games hitting?

    D.) What is the Wheel spin worth?

    E.) What is the overall percentage return of the different types of Free Games, combined?

    Items B, C and E are absolutely necessary to know.

    Items A and D can actually be combined into one thing, and you would just do that by looking at actual returns (not including the Free Games) as opposed to tracking each thing separately. Honestly, I seriously doubt if the Wheel corresponds to its own mechanism in terms of probability, (actually, it can't, or the top jackpot would hit multiple times per day) so you would have to see way too many wheel spins to even make an educated guess as to the average return of the Wheel spin.

    Procedure

    The first thing that we are going to do is combine Items A & D into one thing, simply because it's not feasible to see enough spins to make an absolute determination as to the wheel. Besides that, the jackpot spot is probably slightly more likely the greater the amount bet since any bet amount can win it.

    ITEMS A & D: This is the simple part. If you're playing it yourself, (which I don't recommend unless you have some inkling that it's in a good spot) then you know how much money you put in there. Since you're probably watching someone play it instead, just look at how many credits they have before they make the first spin that you watch, then just count the spins and how many credits they have either:

    A.) When they hit Free Games.

    or

    B.) When they get up or you stop watching them.

    For example, if someone has $88.20 on the machine and that person is at the $0.80 bet level and does not deviate from that bet level, the person takes 350 spins and hits the Free Games, and they have $22.40 in credits before the start of the Free Games, you need to write that information down or text it to yourself. After that, here's what you can figure out:

    350 * .8 = $280 (Coin-In)

    $88.20-$22.40 = $65.80 (Amount lost on reels)

    (280-65.80)/280 = .765 (Percentage Return on Reels)

    1 - .765 = .235 or 23.5% (Percentage Lost on Reels)

    Of course, the percentage return on the reels probably isn't actually that high on a game like that. Needless to say, 350 is a very small sample size, I would probably want to see at least 10,000 spins before hazarding a guess. Even then, that's $8,000 coin-in on a bet of $0.80, which seems like a large sample, until you consider that $80 in return throws it an entire percentage point. It only takes a handful extra of good spins (or wheel results) for that to happen.

    Fortunately, B, C and E are the more important pieces of information, because you can always just assume jurisdictional minimum return on the reels and subtract what the Free Games are worth from the jurisdictional minimum return.

    B.) What is the average return for each individual spin in each set of free games?

    Much like the percentage return of the base spins, this is a tough piece on information to acquire with exactitude.

    The first problem is, not only do the top two types of Free Games have the multiplier, but they could also have totally different reel assignments than the bottom one or each other. Therefore, it's pretty tough to make an assumption that the reel assignments are the same for each type of free games, (unless you have supporting evidence) so you might need to log them separately.

    The second problem is, you're going to want a pretty considerable sample size to even make an educated guess as to how much each spin of each of the three types is worth. To wit, you're going to be watching the game for awhile. (or playing) If I wanted to try to figure out the Mini (by itself) I would still go ahead and keep track of the others, because it's all part of the return. Besides, when you do figure out the Mini (by itself) you can use the times that you hit the others in order to collect more data on those as well as collecting more data on the base game return and the wheel. The more you watch; (or play) the more you know.

    Anyway, when you see a type of Free Games hit, (or when you hit them) the only pieces of information you need are:

    A.) Which type of Free Games was it?
    B.) How many spins were there?
    C.) What was the total return?
    D.) What was the bet amount?

    Imagine you see a Mini hit for 52 spins at an $0.80 bet for a return of $41.80, here's what you have for that sample:

    Amount per spin: 41.80/52 = .80384615384

    Amount per spin relative to bet: .80384615384/.8 = 1.00480769231x bet.

    There you go. That is from actual data by the way, so you can start with that result, if you want to. No charge.

    C.) What is the probability of each type of free games hitting?

    With a sample size of 10,000 spins, the good news is that you can get fairly accurate on this piece of information.

    (DISCLAIMER: I have not done a full analysis of this game--yet--and all numbers from this point forward are strictly for the purposes of example)

    Free Games are hit by hitting the BONUS symbol on the first reel, the BONUS symbol on the third reel and Mini, Maxi or Mega on the fifth reel.

    For this, all you need to do is keep track of how much each of the symbols shows up on the necessary reel. Now, imagine after 10,000 spins, here are your FOR EXAMPLE ONLY results:

    Reel 1 BONUS: 1,895/10,000

    Reel 3 BONUS: 1,952/10,000

    Reel 5 MINI: 685/10,000

    Reel 5 MAXI: 355/10,000

    Reel 5 MEGA: 285/10,000

    Probability MINI: (1895/10000)*(1952/10000)*(685/10000) = 0.0025338424 or 1/0.0025338424 = 1 in 394.657536712

    Probability MAXI: (1895/10000)*(1952/10000)*(355/10000) = 0.0013131592 or 1 in 761.522289148

    Probability MEGA: (1895/10000)*(1952/10000)*(285/10000) = 0.0010542264 or 1 in 948.562851395

    There you go.

    E.) What is the overall percentage return of the different types of Free Games, combined?

    This is a calculation that you might do every time. All it is is the probability of free games hitting multiplied by the number of each type of free games multiplied by the average return for each type of free games.

    However, we can take our example numbers from above and just do it for the MINI, we'll pretend the MINI is at 52 Free Games:

    MINI amount per spin: .80384615384

    Number of Spins: 52

    Probability per Spin on Reels: 0.0025338424

    Okay, so here we go:

    52 * .80384615384 = 41.7999999997 (Free Games Expected Win)

    41.7999999997 * (0.0025338424) = 0.10591461231 (Expected $$$ Value of MINI Free Games result per spin)

    .10591461231/.8 = 0.13239326538 or 13.239326538% (Contribution of MINI Free Games to overall return)

    Okay, so now you can make whatever assumption you want about the base return (or use your data) and if you believe the base return is:

    100 - 13.239326538 = 86.760673462% on everything EXCEPT the Mini Free Games, or more, you have an advantageous play.

    Again, if you have enough data that you think you can also calculate the return of MAXI and MEGA based on where those meters are at, then you can come up with that calculation and add it to whatever you think the base return is on the Reels + the Wheel spin.

    Anyway, have fun if you decide you want to do it. It'll take some work, and remember, what's true on one machine isn't necessarily true on all of them. It's not Video Poker where you can just look at a Royal Progressive and look at a base paytable. Hell, some of the Harleys are Progressives with the top jackpot and others aren't, so that already tells me those are different settings.

  5. #5
    Mission, we have an anomaly on the Harley's. It has to do with the frequency of catching the mega free spins. I've collected a lot of stats on the HD's. Here are some of the frequencies I came up with:

    1. Frequency of Bonus/Bonus landing on the 1st and 3rd reels is 13.
    2. Frequency of mini symbol landing on 5th reel is 17
    3. Frequency of maxi symbol landing on 5th reel is 52
    4. Frequency of mega symbol landing on 5th reel is 92

    Using my stats I initially put the frequency of catching the mini freespins at 221, maxi 661, mega 1157. My actual results on the machines were very close on the mini and maxi but not even close on the mega. I was averaging over 2400 spins per mega hit. And everyone else was having the same result. Then someone put up the par sheet numbers on twitter:

    mini = 220
    maxi = 675
    mega = 2553

    So I had come up with accurate numbers for the mini and maxi frequencies but the same methodology didn't work for the mega. It's an anomaly I can't explain.
    "More importantly, mickey thought 8-4 was two games over .500. Argued about it. C'mon, man. Nothing can top that for math expertise. If GWAE ever has you on again, you can be sure I'll be calling in with that gem.'Nuff said." REDIETZ

  6. #6
    Let's not report this anomaly to gaming.

  7. #7
    Originally Posted by Prozema View Post
    Let's not report this anomaly to gaming.
    I agree. In Montana, whenever they install a new game on machine it wipes out the progressive buildup on the other games. I've never even thought about asking gaming about it. I just put up with it. I absolutely will not take the chance that those games will disappear.
    "More importantly, mickey thought 8-4 was two games over .500. Argued about it. C'mon, man. Nothing can top that for math expertise. If GWAE ever has you on again, you can be sure I'll be calling in with that gem.'Nuff said." REDIETZ

  8. #8
    Originally Posted by mickeycrimm View Post
    Originally Posted by Prozema View Post
    Let's not report this anomaly to gaming.
    I agree. In Montana, whenever they install a new game on machine it wipes out the progressive buildup on the other games. I've never even thought about asking gaming about it. I just put up with it. I absolutely will not take the chance that those games will disappear.
    Don't they just transfer that money to other machines? Maybe not right away but within 30 days.

  9. #9
    Originally Posted by MaxPen View Post
    Originally Posted by mickeycrimm View Post
    Originally Posted by Prozema View Post
    Let's not report this anomaly to gaming.
    I agree. In Montana, whenever they install a new game on machine it wipes out the progressive buildup on the other games. I've never even thought about asking gaming about it. I just put up with it. I absolutely will not take the chance that those games will disappear.
    Don't they just transfer that money to other machines? Maybe not right away but within 30 days.
    Nope. The money just goes away.
    "More importantly, mickey thought 8-4 was two games over .500. Argued about it. C'mon, man. Nothing can top that for math expertise. If GWAE ever has you on again, you can be sure I'll be calling in with that gem.'Nuff said." REDIETZ

  10. #10
    In Montana the progressive money doesn't belong to the players?

    In both Nevada and California progressive jackpots that aren't hit must remain or be transferred to other games.

  11. #11
    We know the rules.

  12. #12
    Originally Posted by Alan Mendelson View Post
    In Montana the progressive money doesn't belong to the players?

    In both Nevada and California progressive jackpots that aren't hit must remain or be transferred to other games.
    What is your source on Montana progressive money?
    "More importantly, mickey thought 8-4 was two games over .500. Argued about it. C'mon, man. Nothing can top that for math expertise. If GWAE ever has you on again, you can be sure I'll be calling in with that gem.'Nuff said." REDIETZ

  13. #13
    Originally Posted by mickeycrimm View Post
    Originally Posted by Alan Mendelson View Post
    In Montana the progressive money doesn't belong to the players?

    In both Nevada and California progressive jackpots that aren't hit must remain or be transferred to other games.
    What is your source on Montana progressive money?
    I have no idea, mickeycrimm. I was asking a question. Did you see the question mark?

  14. #14
    Originally Posted by Alan Mendelson View Post
    Originally Posted by mickeycrimm View Post
    Originally Posted by Alan Mendelson View Post
    In Montana the progressive money doesn't belong to the players?

    In both Nevada and California progressive jackpots that aren't hit must remain or be transferred to other games.
    What is your source on Montana progressive money?
    I have no idea, mickeycrimm. I was asking a question. Did you see the question mark?
    I couldn't find anything in the regs and I'm not about to call gaming and ask them. I don't want to see those games disappear on some technicality. So I just put up with the money disappearing.
    "More importantly, mickey thought 8-4 was two games over .500. Argued about it. C'mon, man. Nothing can top that for math expertise. If GWAE ever has you on again, you can be sure I'll be calling in with that gem.'Nuff said." REDIETZ

  15. #15
    Originally Posted by mickeycrimm View Post
    Originally Posted by Alan Mendelson View Post
    Originally Posted by mickeycrimm View Post

    What is your source on Montana progressive money?
    I have no idea, mickeycrimm. I was asking a question. Did you see the question mark?
    I couldn't find anything in the regs and I'm not about to call gaming and ask them. I don't want to see those games disappear on some technicality. So I just put up with the money disappearing.
    Is it maybe being moved to some other machine in the casino?

  16. #16
    Originally Posted by pkspins View Post
    Originally Posted by mickeycrimm View Post
    Originally Posted by Alan Mendelson View Post

    I have no idea, mickeycrimm. I was asking a question. Did you see the question mark?
    I couldn't find anything in the regs and I'm not about to call gaming and ask them. I don't want to see those games disappear on some technicality. So I just put up with the money disappearing.
    Is it maybe being moved to some other machine in the casino?
    No. These are very small casinos. No more than 20 machines. There are only so many progressives. It's easy to look for the money. It completely disappears and never comes back.
    "More importantly, mickey thought 8-4 was two games over .500. Argued about it. C'mon, man. Nothing can top that for math expertise. If GWAE ever has you on again, you can be sure I'll be calling in with that gem.'Nuff said." REDIETZ

  17. #17
    Originally Posted by mickeycrimm View Post
    Mission, we have an anomaly on the Harley's. It has to do with the frequency of catching the mega free spins. I've collected a lot of stats on the HD's. Here are some of the frequencies I came up with:

    1. Frequency of Bonus/Bonus landing on the 1st and 3rd reels is 13.
    2. Frequency of mini symbol landing on 5th reel is 17
    3. Frequency of maxi symbol landing on 5th reel is 52
    4. Frequency of mega symbol landing on 5th reel is 92

    Using my stats I initially put the frequency of catching the mini freespins at 221, maxi 661, mega 1157. My actual results on the machines were very close on the mini and maxi but not even close on the mega. I was averaging over 2400 spins per mega hit. And everyone else was having the same result. Then someone put up the par sheet numbers on twitter:

    mini = 220
    maxi = 675
    mega = 2553

    So I had come up with accurate numbers for the mini and maxi frequencies but the same methodology didn't work for the mega. It's an anomaly I can't explain.
    A Binomial Distribution would be sufficient to determine the probability of your results v. what was on the PAR sheets. How many spins did you sample? You can get into some Variance with a frequency of 1 in 92, especially if it's actually supposed to be less likely than that. Looks like it should be about 1 in 13 and 1 in 196 for Mega based on the PAR sheets, so we can start there.

    Let's say that your sample size is 20,000 spins, we can then use a BInomial Distribution calculator:

    http://vassarstats.net/binomialX.html

    Okay, so we say 20,000 spins. You got it at a quip of 1 in 92, so we want to see 217 total in 20,000 spins. The actual probability is supposed to be 1 in 196 to see that on the fifth reel.

    <0.000001

    Yup, so you definitely shouldn't have seen that many. WAY outside the third standard deviation.

    Conclusion

    I can only reach three possible conclusions to solve the anomaly. First, I would be interested if the PAR Sheets contain the frequency of what the Mega landing on the fifth reel is supposed to be.

    1.) Your sample size was less than 20,000, in which case, the Mega results could be skewed. If your sample size was MUCH smaller than 20,000, then something like that could reasonably be that skewed.

    2.) Somehow, the Mega symbol is MORE likely to hit if the two Bonus symbols don't hit.

    -Notice that the Mega symbol was showing up more frequently, but the probability of hitting the Mega Free Games came out pretty close.

    3.) You just had a sample WAY outside the third standard deviation.

  18. #18
    I found a Mickey tweet showing 8 megas in 19,566 spins. I recorded 10,296 spins and caught 1 mega. Makes the 1 in 2553 seem reasonable...

  19. #19
    Originally Posted by Mission146 View Post
    Originally Posted by mickeycrimm View Post
    Mission, we have an anomaly on the Harley's. It has to do with the frequency of catching the mega free spins. I've collected a lot of stats on the HD's. Here are some of the frequencies I came up with:

    1. Frequency of Bonus/Bonus landing on the 1st and 3rd reels is 13.
    2. Frequency of mini symbol landing on 5th reel is 17
    3. Frequency of maxi symbol landing on 5th reel is 52
    4. Frequency of mega symbol landing on 5th reel is 92

    Using my stats I initially put the frequency of catching the mini freespins at 221, maxi 661, mega 1157. My actual results on the machines were very close on the mini and maxi but not even close on the mega. I was averaging over 2400 spins per mega hit. And everyone else was having the same result. Then someone put up the par sheet numbers on twitter:

    mini = 220
    maxi = 675
    mega = 2553

    So I had come up with accurate numbers for the mini and maxi frequencies but the same methodology didn't work for the mega. It's an anomaly I can't explain.
    A Binomial Distribution would be sufficient to determine the probability of your results v. what was on the PAR sheets. How many spins did you sample? You can get into some Variance with a frequency of 1 in 92, especially if it's actually supposed to be less likely than that. Looks like it should be about 1 in 13 and 1 in 196 for Mega based on the PAR sheets, so we can start there.

    Let's say that your sample size is 20,000 spins, we can then use a BInomial Distribution calculator:

    http://vassarstats.net/binomialX.html

    Okay, so we say 20,000 spins. You got it at a quip of 1 in 92, so we want to see 217 total in 20,000 spins. The actual probability is supposed to be 1 in 196 to see that on the fifth reel.

    <0.000001

    Yup, so you definitely shouldn't have seen that many. WAY outside the third standard deviation.

    Conclusion

    I can only reach three possible conclusions to solve the anomaly. First, I would be interested if the PAR Sheets contain the frequency of what the Mega landing on the fifth reel is supposed to be.

    1.) Your sample size was less than 20,000, in which case, the Mega results could be skewed. If your sample size was MUCH smaller than 20,000, then something like that could reasonably be that skewed.

    2.) Somehow, the Mega symbol is MORE likely to hit if the two Bonus symbols don't hit.

    -Notice that the Mega symbol was showing up more frequently, but the probability of hitting the Mega Free Games came out pretty close.

    3.) You just had a sample WAY outside the third standard deviation.
    Mision, Prozema and I are networked with other harley players. We all have similar results. I think we are pretty much in agreement that Bonus/Bonus lands every 13 spins and mega lands about every 90 spins. And we all have similar results on hitting the mega freespins. It's close to the 2553 frequency on the par sheet. There is another clue on the frequencies of mini, maxi and mega as you can see in the screenshot. The harleys flame like Three Kings.

    The mini meter starts at 7 games and starts flaming at 15. The mini symbol land every 17 spins so it would be an average of 136 games that it starts flaming....and the frequency is 220.

    The maxi starts at 8 games and starts flaming at 16 games. The maxi symbol lands every 52 games so it would be an average of 416 games it starts flaming and the frequency is 675.

    The mega starts at 10 games and starts flaming at 32. Thats an average of 2024 games and the par sheet frequency is 2553.

    So we are still stuck on why is the mega symbol showing up about every 90 spins but the frequency of catching the mega freespins is 2553.
    Attached Images Attached Images  
    "More importantly, mickey thought 8-4 was two games over .500. Argued about it. C'mon, man. Nothing can top that for math expertise. If GWAE ever has you on again, you can be sure I'll be calling in with that gem.'Nuff said." REDIETZ

  20. #20
    Mickey,

    I understand that. If we can eliminate sample sizing as a potential cause, then the only conclusion that we can draw is that the Mega symbol hits more frequently than it should, or the Mega bonus less frequently. (Six of one, half dozen of the other)

    I think that the answer might be in assuming that the probability of hitting the MEGA free games is the same as the frequency of the symbol multiplied by hitting BONUS on Reels 1 & 3, which I'm getting would be about 1 in 1,170 if that were working out correctly.

    My conclusion is that the MEGA symbol on the fifth reel is somehow MORE likely to hit if the result is NOT Free Games. The machine knows the result of the game before it displays it to the player, so maybe when the machine knows that Reels 1 & 3 are not BONUS-BONUS, it adds more MEGA symbols to the fifth reel. I've not really known a machine to operate that way, but there's no reason it wouldn't be possible.

    In other words:

    BONUS + BONUS + (Keep MEGA symbols the same probability)

    BONUS + NO BONUS (Add MEGA symbols)

    NO BONUS + BONUS (Add MEGA symbols)

    NO BONUS + NO BONUS (Add MEGA symbols)

    That's the best theory I can think of. Otherwise, based on the rate you guys are seeing the MEGA symbol, MEGA free spins should be more than twice as frequent.

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