Can someone give me some feedback on the test results obtained below from video analysis that seem at oods with some of the user feedback. I may well have missed something in undestanding along the way !
Firstly, this is my understanding of the basic principle and the method used to make the measurements under V2/E2. Please correct me on any misunderstanding.
We think of the combined ball/wheel movement as one system with its own trajectory and speed/time. The best way to consider the speed/distance/time in such a system is to think about the number of wheel numbers (#) that pass the ball. Then at a given time e.g. 10 secs before the wheel impact point we are always the same # away from the ball.
The best way to then make a final pocket prediction is to measure how far from ‘the end’ (bit vauge here) by using zero crossings as a starting reference and 4.2 secs as a useful sample time (as it simplifies the resulting multiplication required to whole numbers - in this case 3). By extrapolation the final predicted pocket will be this multiple of the observed earlier difference angle and a known offset.
The difference between the initial predicted pocket and actual landing number are due to the basic assuptions e.g. 4.2 secs decay rate etc being simplifications. To counter these effects we measure (over several pre play cycles) an offset to apply to the initail prediction to give a final prediction pocket.
V2 and E2 are identical except the 4.2 sec timing sample is electronically notified in E2 so improving accuracy, prediction method is identical.
The error tables indicate that E2/V2 will be optimised for certain entry time (Tentry) and wheel speed (WS). The ideal theoretical conditions being a WS = 3 rev/s and Tentry = 14 secs (I know in practice we should increase to ensurwe we stay in the linear system region).
The sample time (Ts) of 4.2 secs a derives from this being the typical time it takes the system (ball and wheel) to decay from a system speed X to 2/3 of X. (Alternatively we could use Ts = 6.5 for a decay to 1/3 X - the V1 system). forester correction 1/2 x
Using Ts = 4.2 secs we need to multiply the observed difference angle (or number of wheel numbers (#) by a multiplication factor (MF) of 3 as the system has only traveled one third is initailly predicted total ‘distance’ in # terms.
We can calculate the actual decay for any system using the method of timing 3 ball and wheel intersections (Trev3) and them moving forward approx 4 seconds and searching for the point at which exactly 2 revolutions are performed in the same Trev3 time. This should be near to 4.2 secs.
Alternatively, we can asses the actual multiplication factor (MF) for a given system by measuring the pockets covered by a Trev2 (Start Pocket count (SPC) = 74), then moving forward exactly 4.2 secs and measuring the number of pockets now passed in Trev2 as the Exit Pocket count (EPC). MF = SPC/(EPC - EPC). E.g. if EPC = 47 not the expected 37 then, MF = 2.74. This is due to the system traveling faster so we are less time to the end so MF is lower.
We don’t use the actual MF and decay rates in prcatice because we want to keep the maths simple. The offset is used to counter this simplification along with any others built into our simple system explantion.
I am therefore trying to perform an analysis that verifys my understanding above, the error tables and the predictive system and the potential corrections with actual MF and decay rate.
The questions I am therefore trying to establish by refernece to a practical video test as an agreed reference point for analysis and discussion of V2/E2 are:
What prediction variation effect do different Entry (start) points have ?
Can we observe the 14 sec ideal time to entry in practice ?
Is the offset always simply the differnece between the predicted and final positions for almost any entry point ?
What is the effect of using actual as opposed to simplified decay rates and multiplication factors ?
Is there a way we can start to reduce and/or eliminate some of the system errors ?
Video Reference for Benchmark
I selected a video spin that had been previously analysed by ASD as below and appeared to have NO OFFSET (or very little) - its on the download Forester provided and starts at 1 min 25 secs in.
Here is a test you can perform…
1st zero/ball intersection at (29,3sec) after 4,2 sec (in video 33,5sec) the ball is over 19… thats 3 numbers angle which we multiply by 3 leads us to 34… since the outcome is 34 offset should be zero degrees…
Now same spin but we start later… at 2nd zero/ball intersection (29,9sec) we wait 4,2 sec at (34,1sec) ball is between 30 and 11… if we take 11 thats a 15 numbers angle… 15 X 3 = 45… points to 17
Now lets start on the 3rd zero ball intersection… at (30,5 sec in video) + 4,2 ----> (34,7) so ball is over 22 thats a 9 numbers angle X 3 is 27 which leads us to number 6
My analysis at answering the questions above is preseted below. Please feel free to pick it apart as I have no ownership other than improving my understanding.
I mapped the video using a frame by frame approach to create the timing table below. I used a different splitter than recommended as it times to frame level and then also used interprolation (sub frame timing) to improve accuracy further. The recommended tool only shows to 0.1 secs which can occur across upto three frames causing significant distortion. One frame = 0.04 secs (1/25 frame rate which is indicated my my video application as the recording rate used for the spins).
splitter tool is at : http://www.videoredo.com/
Cross No. Secs Frame Time (s) TtoE
1 29 7.00 29.28 16.720
2 29 22.25 29.89 16.110
3 30 13.00 30.52 15.480
4 31 4.75 31.19 14.810
5 31 22.75 31.91 14.090
6 32 17.00 32.68 13.320
7 33 13.00 33.52 12.480
8 34 11.66 34.47 11.534
9 35 14.33 35.57 10.427
10 36 17.66 36.71 9.294
11 37 24.00 37.96 8.040
12 39 9.00 39.36 6.640
13 40 21.50 40.86 5.140
14 42 12.50 42.50 3.500
15 44 8.00 44.32 1.680
Drop Pt 45 12.00 45.48
Impact Pt 46 0.00 46.00
Assumptions and Constraights
a) I measured the impact point as the first hit of a pocket stator, in this case pocket #25.
b) I used the impact point time to work backwards to calc the time to end per crossing. There is a short period of bounce 2 pockets to 34 which is not included in time to end.
c) The initial wheel landing point (impact point) is the most useful measurement benchmark not the end pocket (2 diff) as the bounce is part of any subsequent offset added not embeeded in the ‘initial prediction’ from V2 method, rather it is reflected in the later offset assesment, i.e. the 4.2 second pocket prediction knows nothing about bounce.
d) The wheel speed over the whole period is on average 4.4 secs (table below) which is in the growing error band if we deviate from 14 second rule.
Pos. Cross Secs Frame Time (s) Rot Secs
1 28 16.00 28.64
2 32 22.00 32.88 4.240
3 37 7.00 37.28 4.400
4I 41 23.00 41.92 4.640
5I 46 15.00 46.60 4.680
I measured the difference angle number A# for an exact 4.2 second sample period starting with the first crossing and then each successive crossing for only the first 6 crossings as we are getting well out of the recommended working range after that.
I then applied the V2 theory. The table below maps the A# position (a key below the table) indicated into a pocket count (by counting clockwise e.g. 32 = 1, 15 = 2, etc as this allows a formula to calculate the predictions and offsets for me). The number is converted back to a wheel prediction number at P#. Note I can’t work out how to paste a wide table so its in two parts below - applologies.
Cross No. TtoE Tentry Texit Secs Frame
1 16.720 29.28 33.48 33 12.00
2 16.110 29.89 34.09 34 2.25
3 15.480 30.52 34.72 34 18.00
4 14.810 31.19 35.39 35 9.75
5 14.090 31.91 36.11 36 2.75
6 13.320 32.68 36.88 36 22.00
7 12.480 33.52 37.72 37 18.00
8 11.534 34.47 38.67 38 16.66
9 10.427 35.57 39.77 39 19.33
10 9.294 36.71 40.91 40 22.66
11 8.040 37.96 42.16 42 4.00
4.2 CW Count Positions 32 = 1
Cross No. A# A 3A P Cnt P# ERR.
1 15 2 6 6 2 1
2 11 14 42 5 21 2
3 22 28 84 10 6 -3
4 21 5 15 15 30 -8
5 10 18 54 17 23 -10
6 28 32 96 22 33 -15
A#: The pocket pointed to after 4.2 secs
A: The equivalent clockwise count, e.g. 32=1
3A: The final count after multiplying A by the 3 (the MF)
P Cnt: The clockwise predicted coun’t number e.g. if 3A = 38, P Cnt = 1 (same as angle method only numbers)
P#: The initail predicted number - before any offset is applied
ERR: the difference between the P# predicted pocket and the impact pocket, conversily its the varying offset per sample.
The qualitative overview of the results suggests that the predictions for the first three samples are closest in grouping (lowest and similar offset). After that accuracy quickly falls away until by the six sample we are on te other side of the wheel. The error grows progrrssively awasy from a minimum point.
The overview ASD provided to verify the method was on these first three spins suggesting zero offset and three close predictions. The analysis questions below however appears to raise the prospect that there is potential significamt flaw in the apparent accuracy these first three samples provide that at least needs further discussion.
Returning to the questions to review:
1. What prediction variation effect do different Entry (start) points have ?
The ERR is low starting on the first three crossings. These correspond to TtoE (time to End) in the range 16.7 to 15.5 seconds and all three indicate an answer in the same betting sector with an offset very close to the predicted number. All woukd suggest a small ans imilar offset as ASD found.
Above those first three the at the ERR increases rapidly suggesting either i) that the ideal measurement point belowngs in this later range with bigger offset and the first three are incorrect, or,
ii) we can’t start from 0# crossings this late as the system is outside its error tolerance range so we need to start earlier.
2. Can we observe the 14 sec ideal time to enter in practice ?
If we accept the error table condition that the perfect condition is a start 14 secs from the end then the entry point should be 0# number 5 (14.09 secs). This predicts an offset of 10 is required. As there is only a bounce of 2 we could then be confident that the other errors inherent in the method represent the other 8# offset units required, i.e. the systemic (as oposed to randon scatter) offset should be 8 pockets.
It would also mean that the first three spins are poor predictors, actually misleading as would be supported by the error table which suggest that for a wheel speed of 4.4 secs (as here) we coulkd expect around 8 units of error if we enter at 16 seconds. Could be coincidental.
3. Is the offset always simply the differnece between the predicted and final positions for almost any entry point ?
This sounds like a stupid question right, but the error table tells us only certain entry ponts should be used for calculating the offset.
In fact the anlysis above demonstrtaes that the offset is entry point critical, its either zero or 8 depending on entry above.
Aslo the two suggest very different things about the underlying prediction system accuaracy and what the offset is for. Under one sceario the predictive system (at least on this spin) is spot on. In that case what is special about this spin? Under the other scenario the offset is 8 units and our simplifications e.g. 4.2 secs exactly are adding 8 units.
4. What is the effect of using actual as opposed to simplified decay rates and multiplication factors ?
Using the calc method to assess the decay rate (see understanding section) the actual decay rate for this system is 4.40 not 4.20 secs.
I can’t really find anything on varying the sample time or MF is real situations. However, intuitively if you extend the sample time the system (think ball for now) travels further, in this case an extra 0.2 secs. Thats a lot lets say it represents an EXTRA X numbers compared to what you would have seen for 4.2 secs.
Now, using the MF calc method, starting at the 14 sec TtoE (31.91 sec Entry pont) I calc that the MF = 74 /(74 - 47) = 2.74
Again, by induction, the multiplication is lower so we belive we are a further % through the systems overall start to End trajectory, e.g. getting closer to MF = 2 for 6.5 second sample time.
If we now lutiply our incredaed angle (or numbers) relative to 4.2 by the reduced MF we are effectively countering each measure, one up one down. Do we get the same answer?
4.2 x 3 = 12.6, 4.4 x 2.74 = 12.1. It represents (12.6-12.1) = 0.5/12.6 = 4%. That differnce may well me my measurement error. Another way to think about it is that one # represents 2.7% so 4% represents about 1.5 numbers.
It looks to me that the system automatically compensates for errors in the 4.2 sec assuption to a high degree, there may be ‘second order’ errects and/or ‘working range’ issues not visible with this analysis.
5. Is there a way we can start to reduce and/or eliminate some of the system errors ?
I completed the analysis to get a better feel for where the sensitivities in the system lie as understanding a system allows for optimum use in practice. In know i may be stating the obvoius to some and that I could have taken it as read mut I now have a much better feel for it.
It appears to me that the following conclusions (assuming correct analysis - please hight light the errors) are critical to using the system - at least when using it on the video plovided which is not a 3 rev/s wheel
i) When playing a wheel not traveling at 3 rev/s entering at the correct time (within a second or so the optimum point) is critical, failure to do so creates false offset readings
ii) All that glitters is not gold - a small grouping of predictive matches does not nessesarily indicate correct system use. Testing a few seconds apart is a better test than close together to asses the robust use on a particular spin
ii) Playing on wheels that are well outside 3 rev/s is hard without good pre play system mapping, at which point it appears they may well be. Also suggests seperated mapping and play modes with a systemic calculation of statistical pre play tolerance levels would be ideal
iii) The error profiles appear sysmetrical so lend themselves to direct (mapped) offset with then collection of additional system data - some would be pre play e.g. average wheel rates, ball decay rate, wheel decay rate. and some would be in play e.g. wheel rate (this looks like E3 system already) and some would be both pre and in play, e.g. clocking of impact point to eliminate results from the running offset calculation that are outside the valid entrt time conditions
As this is just one spin anlalysis drawing to many conclusion is inappropriate. Can I have some comments/feedback/abuse whatever on where I may have made any mistakes, what looks correct, where somke of the systemic error sources are for a deeper look.