Tracksino Crazy Time

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Introduction

Crazy Time could be briefly described as an elaborate form of Big Six. It adds random multipliers and four slices represent independent games the player will play if the initiating spin stops in the slice for that game. The whole thing is played by live dealers about once a minute, 24 hours a day, 7 days a week, by the upbeat and energetic live dealers of Evolution Gaming.

According to Bitcasino.io, the return of the game is 96.08%.

Disclaimer

Evolution, the maker of Crazy Time, is very protective of their game rules and don't disclose many details that one would need to do a proper math analysis of the game. Fortunatley, there is Tracksino, which tracks some statistics of the game. For elements of the game that can't be quantified I used historical data from Tracksino and tweaked it a bit to get the return of all bets close to 96.08%. That said, I do not claim all of the following rules are exact, but they are my best guess.

Base Game Rules

Sit back and pay attention, as the Crazy Time rules are rather involved. If you get confused, maybe watching my video on how to play Crazy Time will help.

The base game is played on a vertical wheel with 54 stops. The player may bet on where the wheel will stop. The table below shows the available bets and the number of stops of each on the wheel.
After betting is closed, the 'Top Slot' will spin. The left of two reels will stop first on one of the eight bets. Then the right wheel will usually stop on a multiplier. If the wheel stops on the same bet chosen by the Top Slot, then the win for that bet shall be multiplied by the multplier on the right reel. If the right reel stops between multipliers, then no prize will be multiplied. For example, the game might pick Pachinko and 5X. This would mean that if the outcome of the spin lands on Pachinko, then the win from the Pachinko game will be multiplied by 5.
All wins are on a 'to one' basis. Bets on 1, 2, 5, and 10 pay those same odds. For example, a winning bet on 5 will pay 5 to 1.
If the wheel stops on Coin Flip, Pachinko, Cash Hunt, or Crazy Time, then that game will be played. Any bets on that slice be eligible to play the game and pay according to its outcome and any Top Slot multiplier earned.
The rules of each bonus game are indicated below.

Following are the basic rules of each bonus. I get into much more detail on them in the analysis sections below.

Cash Hunt: This is a simple bonus with 108 symbols with a win behind each one. The player may pick any symbol. At the end of the bonus the wins behind the symbols are revealed.
Coin Flip: Two wins are randomly assigned to both sides of a coin. One side will have a win from 2 to 5 and the other from 7 to 100. The coin is flipped, determining the player's win.
Pachinko: This is played on a Plinko board with 16 possibles wins or multipliers on the bottom. If the puck lands in a multiplier, then all the fixed wins are doubled and the puck dropped again. Eventually, the puck will land in a fixed win, which is what winning Pachinko bets will pay.
Crazy Time: This is both the name of the game itself as well as a particular bonus round. This bonus round is the most elaborate and takes the most time to play. It is played on a prize wheel with three stoppers, which the player may choose from. Where the prize wheel stops on the chosen stopper will be bonus win. There are also multipliers on the wheel, which will double or triple all fixed wins and the wheel will be re-spun.

Both the Pachinko and Crazy Time bonuses could, in theory, go on indefinitely with doubles and triples, resulting in enormous prizes. Although this rule will probably never have to be enforced, there is a maximum win of 20,000 for both games.

The following table shows the eight available bets on the Base Game wheel and the number of stops on each one.

Base Game Wheel

Crazy Time Tracker

Bet	Number Stops
$1	21
$2	13
$5	7
$10	4
Coin Flip	4
Pachinko	2
Cash Hunt	2
Crazy Time	1
Total	54

Cash Hunt Bonus Analysis

Click on this image to go directly to my explanation of the Cash Hunt Bonus on YouTube.

As mentioned in the rules section, the Cash Hunt bonus is simply picking from one of 108 icons to reveal a win behind it. The table below shows just three prize distributions I have seen. Below are three prize boards I have seen.

Cash Hunt Prize Distribution

Win	Board 1	Board 2	Board 3
5	14	15	15
7	14	18	13
10	24	25	20
15	29	15	15
20	18	19	25
25	0	9	7
50	0	3	7
75	0	3	5
100	9	0	1
500	0	1	0
Total	108	108	108
Average	19.47	19.96	19.36

Board 2, with the 500 win and highest average win, does not seem to happen very often. I would estimate about 10% of the time. To get an overall average win, I took a weighted average consisting of 40% board, 10% board 2, and 50% board 3, for an mean Cash Hunt win of 19.47.

Coin Flip Bonus Rules

The following video starts at the beginning of my narration of a Coin Flip bonus. You can stop at 5:47.

As mentioned in the rules above, the game picks two wins, a smaller and a larger one, assigns a win to each side of a coin and flips it.

The following table shows my best estimate of the probability of each win for the lower win. The lower right cell shows an average win of 3.265625.

Coin Flip -- Lower Win

Win	Weight	Probability	Return
2	37	0.289063	0.578125
3	43	0.335938	1.007813
4	25	0.195313	0.781250
5	23	0.179688	0.898438
Total	128	1.000000	3.265625

The following table shows my best estimate of the probability of each win for the higher win. The lower right cell shows an average win of 15.296875.

Coin Flip -- Higher Win

Win	Weight	Probability	Return
7	16	0.125000	0.875000
8	17	0.132813	1.062500
9	14	0.109375	0.984375
10	15	0.117188	1.171875
12	17	0.132813	1.593750
15	18	0.140625	2.109375
20	13	0.101563	2.031250
25	10	0.078125	1.953125
50	7	0.054688	2.734375
100	1	0.007813	0.781250
Total	128	1.000000	15.296875

The overall average win of the Coin Flip bonus is simple the average of the two average, of (3.265625+15.296875)/2 = 9.281250.

Pachinko Bonus Rules

Click on this image to go directly to my explanation of the Pachinko Bonus on YouTube.

Following are more detailed rules for the Pachinko Bonus.

The game is played on a pegged pachinko/plinko board with 16 slots at the bottom.
Each slot at the bottom shall be associated with multiplier or a 'Double.'
A disk is dropped from the top at a random position.
If the disk lands in a fixed prize, then that shall be what the player wins.
Wins are on a 'to one' basis.
If the disk lands in Double, then all fixed win prizes will be doubled and the disk re-dropped.
The game may re-double an unlimited number of times.
The maximum win is capped at 20,000 to 1.

The way I believe this game works is each of the 16 wins is independently drawn. That means that some games can have a much higher average win than others, once the board is drawn. The table below shows my best estimate of the weighting and probability of each of the 16 wins.

Pachinko Weighting Table

Win	Weight	Probability
2	6	2.34%
3	8	3.13%
5	16	6.25%
7	56	21.88%
10	60	23.44%
15	36	14.06%
20	23	8.98%
25	10	3.91%
35	9	3.52%
40	5	1.95%
50	7	2.73%
100	4	1.56%
200	2	0.78%
Double	14	5.47%
Total	256	100.00%

After a lot of math, before considering the doubles, I find the average win to be 16.62. After the effect of the doubles, I find it to be 17.64.

Crazy Times Bonus Analysis

Click on this image to go directly to my explanation of the Crazy Time Bonus on YouTube.

Following are my detailed rules for the bonus.

The Crazy Time Bonus features a 64-stop prize wheel.
There are at least three different prize wheels the game may randomly choose from.
The player picks from three stoppers on the wheel -- green, blue, and yellow.
The player shall win whatever prize is at the color of his stopper when the wheel stops.
If the wheel lands in 'double' or 'triple' at any stopper then the wheel shall be repsun with all prizes doubled or tripled for that color only. For example, if the blue stopper only lands in 'double' then players picking green or yellow shall be paid according to where those stoppers landed, then prizes will be doubled, and the wheel re-spun to resolve the blue win only.
Re-spins can trigger more re-spin, infinitely.
The maximum win is 20,000.

The following table shows three wheels I have seen used in the Crazy Times Bonus. I believe there are many more. The concept is simple, the dealer spins the wheel and wherever it lands determines what the player wins. If the wheel lands in Double or Triple, then all fixed wins are doubled or tripled and the wheel re-spun. Re-spins can trigger more re-spins. The maximum win is 20,000.

The following table shows the possible prizes in the Crazy Times Bonus and how many appear on the three wheels I observed.

Crazy Time Bonus

Win	Wheel 1	Wheel 2	Wheel 3
10	12	0	9
15	13	11	8
20	7	10	8
25	8	18	17
50	6	17	15
100	2	4	4
200	0	0	1
Double	16	4	1
Triple	0	0	1
Total	64	64	64

The next table shows my analysis of the Crazy Time bonus using Wheel 1 above. The left column shows the final win, the middle the probability, and the right the contribution to the return. The lower right cell shows an average win of 36.066539.

Crazy Time Bonus Wheel #1

Win	Probability	Return
10	0.187500	1.875000
15	0.203125	3.046875
20	0.156250	3.125000
25	0.125000	3.125000
30	0.050781	1.523438
40	0.039063	1.562500
50	0.125000	6.250000
60	0.012695	0.761719
80	0.009766	0.781250
100	0.062500	6.250000
120	0.003174	0.380859
160	0.002441	0.390625
200	0.015625	3.125000
240	0.000793	0.190430
320	0.000610	0.195313
400	0.003906	1.562500
480	0.000198	0.095215
640	0.000153	0.097656
800	0.000977	0.781250
960	0.000050	0.047607
1280	0.000038	0.048828
1600	0.000244	0.390625
1920	0.000012	0.023804
2560	0.000010	0.024414
3200	0.000061	0.195313
3840	0.000003	0.011902
5120	0.000002	0.012207
6400	0.000015	0.097656
7680	0.000001	0.005951
10240	0.000001	0.006104
12800	0.000004	0.048828
15360	0.000000	0.002975
20000	0.000002	0.030696
Total	1.000000	36.066539

Crazy Time Stats

The next table shows my analysis of the Crazy Time bonus using Wheel 2 above. The left column shows the final win, the middle the probability, and the right the contribution to the return. The lower right cell shows an average win of 36.874718.

Crazy Time Bonus Wheel #2

Win	Probability	Return
15	0.171875	2.578125
20	0.156250	3.125000
25	0.281250	7.031250
30	0.010742	0.322266
40	0.009766	0.390625
50	0.283203	14.160156
60	0.000671	0.040283
80	0.000610	0.048828
100	0.080200	8.020020
120	0.000042	0.005035
160	0.000038	0.006104
200	0.005013	1.002502
240	0.000003	0.000629
320	0.000002	0.000763
400	0.000313	0.125313
480	0.000000	0.000079
640	0.000000	0.000095
800	0.000020	0.015664
960	0.000000	0.000010
1280	0.000000	0.000012
1600	0.000001	0.001958
1920	0.000000	0.000001
2000	0.000000	0.000000
Total	1.000000	36.874718

Crazy Time Slots

The next table shows my analysis of the Crazy Time bonus using Wheel 3 above. The left column shows the final win, the middle the probability, and the right the contribution to the return. The lower right cell shows an average win of 36.361278.

Crazy Time Bonus Wheel #3

Win	Probability	Return
10	0.140625	1.406250
15	0.125000	1.875000
20	0.127197	2.543945
25	0.265625	6.640625
30	0.004150	0.124512
40	0.001987	0.079498
45	0.001953	0.087891
50	0.238525	11.926270
60	0.002052	0.123138
75	0.004150	0.311279
80	0.000031	0.002484
90	0.000095	0.008583
100	0.066227	6.622696
120	0.000063	0.007575
135	0.000031	0.004120
150	0.003792	0.568771
160	0.000000	0.000078
180	0.000034	0.006040
200	0.016660	3.331959
225	0.000065	0.014591
240	0.000001	0.000351
270	0.000002	0.000531
300	0.001094	0.328213
320	0.000000	0.000000
360	0.000002	0.000544
400	0.000260	0.104117
405	0.000000	0.000193
450	0.000060	0.027117
480	0.000000	0.000015
540	0.000001	0.000282
600	0.000277	0.166442
640	0.000000	0.000000
675	0.000001	0.000684
720	0.000000	0.000034
800	0.000004	0.003243
810	0.000000	0.000007
900	0.000018	0.016232
960	0.000000	0.000001
960	0.000000	0.000001
1080	0.000000	0.000001
1200	0.000008	0.010082
1215	0.000000	0.000009
1280	0.000000	0.000000
1350	0.000001	0.001207
1440	0.000000	0.000002
1600	0.000000	0.000096
1620	0.000000	0.000012
1800	0.000005	0.008309
1920	0.000000	0.000000
2025	0.000000	0.000032
2160	0.000000	0.000000
2400	0.000000	0.000468
2560	0.000000	0.000000
2700	0.000000	0.000644
2880	0.000000	0.000000
3200	0.000000	0.000000
3600	0.000000	0.000732
3840	0.000000	0.000000
4050	0.000000	0.000057
4320	0.000000	0.000000
4800	0.000000	0.000019
5120	0.000000	0.000000
5400	0.000000	0.000322
5760	0.000000	0.000000
6400	0.000000	0.000000
7200	0.000000	0.000045
7680	0.000000	0.000000
8100	0.000000	0.000030
9600	0.000000	0.000001
12800	0.000000	0.000000
14400	0.000000	0.000002
16200	0.000000	0.000015
19200	0.000000	0.000000
20000	0.000000	0.005880
Total	1.000000	36.361278

To summarize, the return of wheel 1 is 36.066539, wheel 2 is 36.361278, and reel 3 is 36.361278. Taking the average of the three wheels, my estimate of the return from the Crazy Times bonus is 36.434179.

Top Slot Analysis

Our friends at Tracksino tracked the outcome of 76,175 Top Slot spins in their page Crazy Time Multipliers Revealed. The following table shows their results of the winning symbol. The second column quotes the Tracksino results exactly, which add up to 100.48%. The right column divides each probability by 1.0048, to get the probabilities to add up to 100%.

Top Slot Winning Symbol

Symbol	Tracksino Odds	Adjusted Odds
$1	13.25%	13.19%
$2	13.34%	13.28%
$5	11.45%	11.40%
$10	8.32%	8.28%
Pachinko	11.70%	11.64%
Coin Flip	14.06%	13.99%
Cash Hunt	12.34%	12.28%
Crazy Time	16.02%	15.94%
Total	100.48%	100.00%

The next table shows the Tracksino results for the multiplier. They refer to the multiplier reel stopping between symbols as a 'miss,' which is mathematically equivalent to a 1x multiplier. These probabilities add to 100%, so no adjustment was needed.

Top Slot Multiplier

Symbol	Tracksino Odds
Miss (1x)	21.52%
2	25.04%
3	21.34%
4	10.23%
5	8.97%
7	5.28%
10	3.44%
15	1.70%
20	1.34%
25	0.82%
50	0.32%
Total	100.00%

The average multiplier, given these probabilities, counting a miss as a 1x muliplier, is 3.8155.

However, based on my own observations, the average multiplier for some symbols was significantly higher than others. This did not surprise me because if every symbol had a 3.8155 average multiplier, then some bets would pay significantly more than others. To be specific, if we assumed there symbol and multiplier were drawn indpendently, according to the probabilities above, the following would be the returns of the flat win bets:

$1 -- 92.22%
$2 -- 90.22%
$5 -- 98.57%
$10 -- 98.75%

Evolution, the company that makes Crazy Time, is too smart for that. To equalize the return of every bet, I had to assume the average multiplier was higher for bets like $2 and lower for bets like $10. Based on tweaking the data from Tracksino, to make sure the overall probabilities still matched for each symbol and multiplier, I created the following table which shows my best estimate for each combination of symbol and multiplier.

Top Slot Reel Pairings

Multiplier	$1	$2	$5	$10	Pachinko	Coin Flip	Cash Hunt	Crazy Time	Total
1	0.024492	0.024972	0.025641	0.018887	0.026148	0.030288	0.028990	0.035783	0.215200
2	0.031284	0.029666	0.029652	0.021852	0.027663	0.037123	0.031896	0.041265	0.250400
3	0.028140	0.028332	0.024318	0.017670	0.024849	0.029861	0.026208	0.034023	0.213400
4	0.013490	0.013582	0.011657	0.008471	0.011912	0.014315	0.012564	0.016310	0.102300
5	0.011828	0.011909	0.010222	0.007427	0.010445	0.012552	0.011016	0.014301	0.089700
7	0.006963	0.007010	0.006017	0.004372	0.006148	0.007388	0.006484	0.008418	0.052800
10	0.006272	0.006769	0.003232	0.002160	0.003570	0.004657	0.003080	0.004659	0.034400
15	0.003544	0.003908	0.001421	0.000892	0.002135	0.001779	0.001229	0.002091	0.017000
20	0.003049	0.003451	0.001011	0.000594	0.001909	0.001083	0.000787	0.001517	0.013400
25	0.001949	0.002190	0.000590	0.000335	0.001109	0.000683	0.000449	0.000894	0.008200
50	0.000856	0.000975	0.000193	0.000143	0.000553	0.000199	0.000107	0.000174	0.003200
Total	0.131867	0.132763	0.113953	0.082803	0.116441	0.139928	0.122811	0.159435	1.000000

Overall Game Analysis

After all that, we are finally ready to calculate the return of each bet. We can definite that return as a * (1 + b * (c * (d-1) + 1)), where:

a = Probability of winning
b = Average base win (before Top Slot)
c = Probability Top Slot multiplier
d = Average Top Slot multiplier