Three Kings Video Slot Game

This game is a recent arrival in Montana. But from what I'm seeing online it appears the game has been in the major markets for quite some time. I'm just now starting to study and stat the game for potential exploitability. There are about 60 videos of the game on youtube.

Three Kings is an IGT penny denom 100 line video line game. Max bet here in Montana is a penny per line plus 25 cents to qualify for the progressive free games, so $1.25.

The main symbols in the game are the Lions. The purple lions are in the 3rd, 4th, and 5th reels. Catching all 3 purple lions in any position on those reels and you are awarded 12 to 25 free games depending on where the free games meter is. Note, this is not a "must hit by" slot. The meter caps at 25 free games and stays there until the purple lions are hit. The purple lions are wild during the free games.

The red lions are on the 2nd, 3rd, and 4th reels. Catching all 3 red lions in any position on those reels awards 25 to 50 free games. Both the red lions and purple lions are wild during the free games.

The green lions are on the 1st, 2nd, and 3rd reels. Catching all three green lions in any position on those reels awards 50 to 80 free games. The green lions, red lions, and purple lions are all wild during the free games.

The free games meters go up based on action but don't run at a constant speed. The higher the numbers get the more spins it takes to move the meters up another notch.

If there is a short term advantage that develops in this game I'm thinking its when both the green and the red meters are close to maxed out. And the strategy would be to play until you hit one or the other, then take the free games and cash out.

Yesterday, a lady next to me was playing the game. She caught the green lions for 77 free games.

"Congratulations. That ought to be worth $300." I said.
"Not always." she responed.
You must play the game a lot."
"Yes. When I'm in Vegas I play at the Cannery because they have a lot of machines with this game.

I'll finish later. Phone needs a charge.

So the lady said she stayed at the Cannery and played off the Three Kings when she caught high numbers. I knew she wasn't a true AP or I would have seen her playing games I play. But I pumped her for information.

"Are you going to play that one over there when you are through here?"
"Why? Whats it on?
"The purple is on 19, red is on 40, green is on 70."
"Thats a little low."

You are elegible to catch more free games when you are in free games mode.

"Whats the most free games you got at one time?"
"164."
"How'd you do that?"
"I hit the green lions for 77 free games, then hit them again in the free games for another 50. Then I caught the reds for 25 and the purple for another 12."
"How much money did you rack up?"
"$600."

I finished my play and moved on.

Do you guys have this game in your jurisdictions? Is anyone playing this game?

Another question I asked the lady was how much money was unvoled. "Sonetimes it goes early but be preoared to put $300 in the machine. From observation in the casinos and youtube videos catching green lion free games in the high 70's appears to be worth somewhere in the high 200's to $600.

I have a big clue about the overall payback in Montana as state law is no line game above 92%.

I'm slightly embarrassed to say I've never looked at the game, although I've noticed it here in Las Vegas. My impression was that the free spin meters didn't vary a whole lot, therefore the possibility of an advantage seemed unlikely. I don't see anything in your description to change my opinion, but I'm wrong a lot, lol.

I have played a variation of the concept. It's a "4-play" unit with corresponding progressive free spin meters. Each meter starts at 2, and caps at 50. The meter increases when 2 scatter symbols appear, and the free spins are awarded for 3 scatters. I'm not sure it's advisable to mention the name publicly. Fortunately I don't remember :)

My girlfriend has "wonged" this game for years. It is in Vegas at Circus Circus and the Plaza to name a few. It is also at a few SoCal casinos. Her best result was 80 free spins worth $220. I know this because she is always shoving the photo in my face when I doubt the play's value.

Hard Rock in Las Vegas had this game the last time I was there.

I used to put a 10% hold on slots as a general rule nowadays I think that's way overestimating.

They have this game in Vegas. I've seen it at the MGM Grand. I played it a little bit when the number of free games was high.

I can't be sure, of course, but I seriously doubt that the game ever goes to +EV. In fact, I suspect that that's why they cap the number of free games. Although, it might be set to a different payback in Montana than in Vegas.

I don't know, progressives that have a max but are not a "must hit by" have always seemed like a bit of a scam to me.

Quote: AxiomOfChoice

I don't know, progressives that have a max but are not a "must hit by" have always seemed like a bit of a scam to me.

I found a photo of the game I was talking about:



There are a couple of problems here. Because the meters are capped at 50, I won't realize the full value of the meter movement for game 1. (The excess above 50 is kept in memory and added to the next reset.) And I couldn't figure out a way to play game 1 only. The lowest bet option was games 1 & 2.

So I conservatively judged the situation to be unplayable. I would have opted to play with a more balanced distribution between the top two meters. Something like 28 & 27 would have been much more attractive.

Quote: mickeycrimm

I have a big clue about the overall payback in Montana as state law is no line game above 92%.

I keep meaning to ask this. Why is it state law in Montana that no game can be ABOVE 92%? I could understand a BELOW restriction, but why do they cap it? Who are they looking out for? If someone wants to offer a game with low variance and 98% payback, say, to bring people into their bar by advertising it, why can't they?

Quote: beachbumbabs

I keep meaning to ask this. Why is it state law in Montana that no game can be ABOVE 92%? I could understand a BELOW restriction, but why do they cap it? Who are they looking out for? If someone wants to offer a game with low variance and 98% payback, say, to bring people into their bar by advertising it, why can't they?

Tax revenue protection, it's 95% (Base Pays) in West Virginia and 100% (or less) in many other States.

Quote: Mission146

Tax revenue protection, it's 95% (Base Pays) in West Virginia and 100% (or less) in many other States.

Ahh. Of course. Thanks.

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Quote: beachbumbabs

I keep meaning to ask this. Why is it state law in Montana that no game can be ABOVE 92%? I could understand a BELOW restriction, but why do they cap it? Who are they looking out for? If someone wants to offer a game with low variance and 98% payback, say, to bring people into their bar by advertising it, why can't they?

Edited. Already answered.

Quote: beachbumbabs

I keep meaning to ask this. Why is it state law in Montana that no game can be ABOVE 92%? I could understand a BELOW restriction, but why do they cap it? Who are they looking out for? If someone wants to offer a game with low variance and 98% payback, say, to bring people into their bar by advertising it, why can't they?

Video poker and vide keno are not restricted to 92%, just the line games. The line games are a recent arrival, installed in January 2012. 15% of the machine win goes to the state with 2/3's of the money going back to the county or municipality the machine is located in. Between the economy crash and the smoking ban tax revenue was down over 20% in 2010, 2011. I imagine the state was looking for a way to get the revenue back up, hence the 92% restriction on line games.

Quote: RogerKint

My girlfriend has "wonged" this game for years. It is in Vegas at Circus Circus and the Plaza to name a few. It is also at a few SoCal casinos. Her best result was 80 free spins worth $220. I know this because she is always shoving the photo in my face when I doubt the play's value.

Some of the youtube videos were filmed in Pennsylvania so the game is there too.

I put down two plays yesterday to collect stats. High numbers in both green and red. Plan was to play until I hit one or the other then cash.

Total spins wad 809. Total wager was $1011. Got dropped in main game for $472. Just a 53.3% return. Hit purple lions 4 times, red lions twice.

Purple Lions

25 free games returned $68.
23 games returned $32.
24 games returned $16.
18 games returned $31.

Red Lions

48 free games returned $107
43 games returned $106

Net loss of $112

I also statted the lions landing in the screen through 587 games.

Purple Lions

3rd reel 4th reel 5th reel
216 129 52

Tentative frequency is 142.4


Red Lions

2nd reel 3rd reel 4th reel
95 80 28

Tentative frequency is 950.48

Green Lions

1st reel 2nd reel 3rd reel
118 42 26

Tentative frequency is 1569.67

Sample space is to small. I fhink I need about 1400 more spins to draw any hard conclusions.

90% of the time I analyze a game like this it comes up tits. Nothing there. But I'm willing to pay the cost because of the 10% of the time I find a gem.

Quote: mickeycrimm

90% of the time I analyze a game like this it comes up tits. Nothing there. But I'm willing to pay the cost because of the 10% of the time I find a gem.

I agree with this 100%, especially when someone else is playing the game and I'm just standing around, sipping coffee and counting spins.

Quote: mickeycrimm

90% of the time I analyze a game like this it comes up tits. Nothing there. But I'm willing to pay the cost because of the 10% of the time I find a gem.

Just thinking about your history is amazing...you have journeyed from a boxcar-riding hobo credit hustler to an advanced slot AP who knows all the math. Incredible.

This is one of the most easily wongable slots around. When the available free spins are in the upper portion of their range, there's a fire graphic behind the number. Just look for one with fire in all 3 spin boxes & go for it. It's much more variable than collecting slots like Golden Monkey or must-hit-by slots, but it's a very easy play to identify. Usually, you can see from across the room whether the values are in the right place.

That's true, but a number of the must-hit by slots I have been noticing recently are coin-in based rather than win-and-increase based, so I really like those because you can put an upper bound on your coin-in. You can also assume whatever you wish in terms of base return without the meter increase and determine an expected loss based on that assumption and assuming you don't hit the must-hit until you, you know, must.

I still would like to know whether there is some sort of, "Behind the scenes," RNG type spin that goes on every time to determine if the progressive will win, or if the machine simply randomly determines a set $$$-value or spin number at reset. If it is the latter, then the probability of hitting the Progressive a coin-in basis is simply 1/(However many spins remain until it must be hit) based on the meter increase. If that could be known, then an expected value (in percentage terms) could be determined for just the Progressive and you could assume whatever you want for the rest.

For an example of what I mean, let's say you had a Minor at $48.09/$50.00 and the meter movement for the Minor is $0.01 per $2.00 bet. I tend to want to minimize Variance if at an advantage (have to determine that first) so I am going to bet the minimum of $0.40 and it takes five bets to move the Minor $0.01, then you have 191*5 = 955 bets to hit the must-hit point.

If we could assume that the remaining amount to the must-hit is simultaneously reflective of the probability of hitting, then the first spin would be 1/955.

The EV of the Minor, if that could be assumed, would be 1/955 * 48.09 = .050356 or 5.0356 cents.

If we have a bet of $0.40, then 5.0356 cents is .0503556/.4 = .12589 or 12.589% of the bet.

Therefore, if you want to assume a base return of 1-.12589 = 87.411%, or better, completely ignoring the Minor Progressive, as well as its base value, then you would be at an advantage.

The problem with this is that it cannot be assumed, I don't think, because it is possible that there is some separate random mechanism that either rewards or does not reward the jackpot on a per spin basis.

On the Wizard's page regarding this:

https://wizardofodds.com/games/slots/mystery-jackpot/

$48.09 would be the target point for the Minor assuming a 12% base hold if the major were at $380, so I would suggest that Wizard is not making the above assumption. I would not make it, either, because there is really no way to know.

EDIT: Actually, Wizard's analysis was based on amount won, so I wonder if he would agree with this?

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I don't believe Quick Strike is a must-hit, is it?

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Well, I've got a sample space of 2,335 spins on this game. I had to make the spins myself. There were so many diffferent stats to record that I couldn't be at the mercy of someone else controlling the spin button. So I was willing to pay the cost to see if the game is exploitable. This is what I came up with. Keep in mind that Montana lines games are a max 92%.

Spins: 2,335

2,335x1.25 = a total wager of $2,919
The return in the main game was $1,576

1576/2919 = a 53.99% return
_________________________________________________

I caught the Purple Lions 13 times for a total of 246 free spins.

2355/13 = a frequency of 181.15

Catching the Purple Lions pays $5.
13X5 = $65
65/2919 = 2.23%

The 246 free spins averaged to $1.4146 per spin for a total of $348

348/2919 = 11.92%
__________________________________________________
I caught the Red Lions 6 times for a total of 269 free spins

2355/6 = a frequency of 392.5

Catching the Red Lions pays $15
15x6 = $90
90/2919 = 3.08%

The 269 free games averaged to $1.9628 per spin for a total of $528

528/2919 = 18.09%
___________________________________________________
I caught the Green Lions twice for a total of 137 free spins.
2355/2 = a frequency of 1178

Catching the Green Lions pays $44
44X2 = $88
88/2919 = 3.01%

The 137 free games averaged to $2.635 per spin for a total of $361

361/2919 = 12.38%
____________________________________________________-
My total return was 3056 bets or 104.7%. Whooppeeeee! We've got a play, don't we? ........Houston we have a problem. These are not the only stats I recorded. I made a spreadsheet out of a couple of pages in my notebook and recorded stats on the lion symbols as they landed in the screen. I literally stopped after every spin and recorded it.

Here are the results from 2000 spins

Green Lions
1st reel............2nd reel............3rd reel
..387.................112...................100

Red Lions
2nd reel...........3rd reel............4th reel
..330................259.....................119

Purple Lions
3rd reel..... ......4th reel...........5th reel
..687..................365...................138

These stats suggest different frequencies for catching the free games than what my actual results were:

Green Lions.........1846 This is a much longer frequency than my actual stat of 1178
Red Lions..............787 This is a much longer frequency than my actual stat of 392.5
Purple Lions..........231 This is a much longer frequency than my actual stat of 181

It appears I just ran lucky on catching the free games. So I applied the longer frequencies to the return I got in the first set of stats. Then I imagined I was getting the max number of free games every time, i.e., 80 free games with the Green Lions, 50 free games with the Red Lions and 25 free games the Purple Lions.

The return comes to 90.5%.

The returns I averaged in the free spins could be much lower than what the actual is since the sample space is rather small. But I'm debating with myself on whether I should continue stat-ing this game or just write it off.

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Quote: Ibeatyouraces

Advantage play my ass!

I concur.

Quote: mickeycrimm

I concur.

I have to say, I respect the work that you put in to analyze it. I really think that keeping your eyes open and analyzing any angle that you can think of is half the game here.

I would pay to walk around for a day with some of you. Some of these things are just amazing.

Quote: GWAE

I would pay to walk around for a day with some of you. Some of these things are just amazing.

I would love to follow Mickey around and watch him do his thing.

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Quote: Ibeatyouraces

$875 in the hole before finally hitting the three red lions for the max 50 free games. It was at 46 when I started...

Seriously??? You know that this is not actually +EV, right?

I am going to bring this up every time you say anything about people who "gamble for fun" :)

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Quote: Ibeatyouraces

Hey, had to test it :-)

I'm not mad about it either ;-)

I do stuff like this all the time. I don't claim to have any self-control though.

I gave up on this game long before -$875 though.

Does the machine say the free spins come from the same reels as the base game?

Many slot games aren't like this. But then the ones that are ones like this game where they give you tons of free spins.

I'm assuming you didn't record all symbols of all your spins, did you mickey? Deconstructing the slot reels would make the line pay numbers more accurate. It's possible you ran bad on that portion, which lowers the overall estimate.

Quote: Ibeatyouraces

$875 in the hole before finally hitting the three red lions for the max 50 free games. It was at 46 when I started...

How'd u do on the 50 free games though?

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Quote: Ibeatyouraces

Made around $80.

I got a little revenge a little while later as someone didn't play after their dealt straight...

That is awesome.

I never find this at the 25c level. Apparently none of the ploppies at my local casino can afford anything more than nickels.

I need a casino with richer ploppies...

Quote: AxiomOfChoice

That is awesome.

I never find this at the 25c level. Apparently none of the ploppies at my local casino can afford anything more than nickels.

I need a casino with richer ploppies...

8X's at quarters, yeah never. Dealt 2X or 3X's sometimes. I thought I did good with my tied personal best $400 hit...d'oh.

Nice tax form!!

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Quote: Ibeatyouraces

The most and highest anyone left was ten, 10x's after a dealt flush on nickle DDB. I ended up with a three card royal draw and made 60 credits or so.

Whenever I find these multipliers I always get dealt 2468T of 4 different suits.

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Quote: Ibeatyouraces

Same here usually.

If there was an "all evens" video poker variant I would win SO MUCH money :)

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Quote: Ibeatyouraces

Getting back to the Three Kings slot, earlier on another machine with the free games all up high, I did well on. At first it was a slow decline before hitting the three purple lions then shortly after I hit the three red ones which brought me slightly ahead. After that, I tanked again, hitting the purple ones twice again without much fanfare. Then as I was down about $125 or so, hit the three red ones again for 38 free games. Not ten spins in I hit them again for another 25 games and shortly after that the purples for 12 more. The bonus win was about $260 or so total. Not once on either machine did I get the three green lions. I have no idea how many spins I played, but it had to be a few thousand total between both machines.

This is probably pretty good cover play. I don't even work for a casino, and, reading this, I want to comp you a buffet.

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Quote: Ibeatyouraces

I did earn about $70 in comps. Small consolation prize :-P

I tried. I'll live.

BTW, I've lost more money in two hand of TCP before. I'll win it back 8-)

Kids today, with their good eyesight...

Quote: tringlomane

Does the machine say the free spins come from the same reels as the base game?. I'm assuming you didn't record all symbols of all your spins, did you mickey? Deconstructing the slot reels would make the line pay numbers more accurate. It's possible you ran bad on that portion, which lowers the overall estimate.

I looked all though the rules screens to see if the free games were a different configuration than the regular games. Nothing was listed. I only tracked the lion symbols landing in the screen.

I received some insider information on the game yesterday. I was given the overall payback of the game, the true frequencies for catching the Green Lions, Red Lions, and Purple Lions, and the average value of the free games (which turned out to be much higher than what I averaged). What I have to do now is figure out the average number of free games per the frequencies given. I could probably do this in one session.

What I do know at this point is the free games meters have a staggered type movement. The Purple Lions free games meter starts at 12 and moves like this:

6th spin moves it to 13
11th spin moves it to 14
21st spin moves it to 15
36th spin moves it to 16
56th spin moves it to 17 (the flame graphic appears a few spins after the meter hits 17)

The higher the meter goes the more spins it takes to move it up one more notch. The Red Lions and Green Lions meters work the same way but there are many more spins involved.

Without further information my take on the game right now is there may be a small edge if I catch every meter maxed out. But the problem is I'm not going to find many plays like that. And even if I were to find a few plays I think I would have to quit after catching the Purple Lions which has the shortest frequency.