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Home » Forums » Questions and Answers » Math » Calculating Return for "Lock & Roll" 5X Pay Quarter Machine
Calculating Return for "Lock & Roll" 5X Pay Quarter Machine
| November 29th, 2009 at 5:03:15 PM permalink | |||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
| craigGA Member since: Nov 29, 2009 Threads: 2 Posts: 10 | "Lock & roll" slot machines are found in certain gaming jurisdictions which require an element of skill. The help screen on these machines show how often each symbol occurs on each of the 3 virtual reels. The skill comes in after the first spin, during which time the player has the option to "lock" any combination of the three reels, and then re-spin. The symbols on the payline after this two spin process map to a pay table like all other slot machines. Given the following reel and pay table information for a 25cent machine, what is the process for determining the optimal strategy and rate of return? Also, how much does the progressive change the rate of return? After spending a large portion of my Sunday trying to do this myself, I humbly concede...I was able to calculate the return after the first spin. I just couldn't figure out how to factor in the lock and re-spin aspect of the game. Thanks! Reel Weights
Pay Table
Pay Table Notes
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| November 30th, 2009 at 4:53:26 PM permalink | |
| dk Member since: Nov 2, 2009 Threads: 19 Posts: 138 | I think I can solve this, but I'm pretty unfamiliar with slots, so I have a couple questions: 1) Does the 7 Bar count towards the "Any Bar" payout? 2) Does the 5x Pay act as a Wild (e.g., Red 7, Red 7, 5x => 60*5 = 300 and Red 7, 5x, 5x => 60*25 = 1500)? I assume both are true. The ratio of people to cake is too big. |
| November 30th, 2009 at 4:59:57 PM permalink | |
| dwheatley Member since: Nov 16, 2009 Threads: 10 Posts: 550 | They are both true Wisdom is the quality that keeps you out of situations where you would otherwise need it |
| November 30th, 2009 at 5:26:35 PM permalink | |
| marksolberg Member since: Nov 14, 2009 Threads: 24 Posts: 197 |
Just to be clear, it also counts towards an any 7 payout. |
| November 30th, 2009 at 5:33:11 PM permalink | |
| dk Member since: Nov 2, 2009 Threads: 19 Posts: 138 | Removed. The ratio of people to cake is too big. |
| November 30th, 2009 at 8:43:19 PM permalink | |||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
| craigGA Member since: Nov 29, 2009 Threads: 2 Posts: 10 | DK - You and I are pretty close! I calculated the probability of winning something after one spin = 0.032257557. Just cant seem to get past the second spin aspect...I think the first step is deriving the EV of each possible combination after 1 spin, and then building a strategy based on that...and then calculating the probability of winning after each optimal strategy situation...and that adds up to A LOT of scenarios. Here is the table I have so far:
Note that the returns are based on a 1 coin bet. Also note that this is my first attempt at anything like this...so all of the above may be totally wrong. :) I calculated the second spin probability of the jackpot by assuming that the player would only go after the jackpot after any first spin combination of 5Xs and blanks. However, without having the full optimal strategy, I am not sure if that is even correct. | ||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
| December 1st, 2009 at 8:40:39 AM permalink | |
| dk Member since: Nov 2, 2009 Threads: 19 Posts: 138 | We differ on 8 of the "P After 1 Spin" numbers. "Any Three 7s", it looks like you made the same error I made the first time. I think you counted "Three Red7" and "Three 7bar" as "Any Three 7s", but these are already accounted for. If you subtract these out, your "Any Three 7s" "P After 1 Spin" should be 5.00679E-05. The other 7 we differed on were the "One 5x + ..." numbers except for "One 5x + Two Any 7s". Here is how I calculated the "One 5x + Two Red7": 5x on Reel1 = 1*3*3/1283 = 9/2,097,152 5x on Reel2 = 1*1*3/1283 = 3/2,097,152 5x on Reel3 = 1*1*3/1283 = 3/2,097,152 Summing these 3 numbers, we get 15/2,097,152 ~ 7.15256E-06 I used the same process for the other "One 5x + ..." numbers. Here are the numbers I got: + Two 7bar 1.95503E-05 + Two 3bar 0.000105381 + Two 2bar 0.000187397 + Two 1bar 0.000171185 + Two Cherry 4.95911E-05 + Two Any Bar 0.001396656 (Note: Be sure to subtract out any possibilities already counted elsewhere). I'm still working on the second spin... The ratio of people to cake is too big. |
| December 1st, 2009 at 9:56:34 AM permalink | |
| dk Member since: Nov 2, 2009 Threads: 19 Posts: 138 | Another question...Is 5x, Cherry, Blank worth 0 or 10? If 0, I get a first spin payback of 17.086%. The ratio of people to cake is too big. |
| December 1st, 2009 at 12:41:53 PM permalink | |
| dk Member since: Nov 2, 2009 Threads: 19 Posts: 138 | I finished my analysis. It's not pretty. I get an overall payback of 75.5363% with optimal play (without the progressive). Is that even possible/legal? The ratio of people to cake is too big. |
| December 1st, 2009 at 4:21:29 PM permalink | |||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
| JB Administrator Member since: Oct 14, 2009 Threads: 309 Posts: 906 | Note: Figures revised 12/2/2009 4:07 PM The total return based on the initial spin (the "deal") is 467428/(128^3) = 22.2887% The total return after the final spin (the "draw") is 3960964784580/(128^6) = 90.0619% when the jackpot is at its minimum (reset) value. With a jackpot of $8,668 the return was 90.5295%. The break-even jackpot amount is 42,746 times the bet = 213,730 coins = $53,432.50. Here is the strategy for when the jackpot is at its lowest:
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