Can anyone answer a probability question on craps?
October 2nd, 2013 at 10:07:04 PM
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I've noticed on an electronic craps machine (where the dice are "rolled" by bouncing them on a drum that is vibrated) that whenever I look at the statistics showing the number of times a 7 is rolled in the last 100 rolls, I have noticed that it's more often than not 23 thru 27 times out of the last 100 rolls than 7 through 10 times. The average should be 16 or 17 (since the average # of times a 7 is rolled is should be statistically 16.67%).
Since 23 thru 27 times is 7 to 10 times above the expected average, I would expect the board to show an equal amount of occurences of a 7 thru 10 times the 7 has hit in the last 100 rolls (i.e. the same number below the average as I've seen above the average. But I've never seen it that low. The lowest I've seen it is 15 times of the last 100 rolls).
My question is: Is this an acceptable rate for the 7 to be showing (i.e. if different from the norm of 16.67% then it is more likely higher rather than lower)? Or is the fact that the 7 is the most common outcome make it more likely to be higher than the norm than below the norm?
Or, since most bettors are place or pass line bettors, could the machine be purposely skewed (i.e. cheating the players).
Can someone with a statistics background let me know if what I observe (more than likely chance of the % of 7's hitting is above the norm than below the norm or 16.67%) is unusual or acceptable?
I've seen this over a 9 month period at random times in 2 different casinos (Empire City in Yonkers NY and Resort World in Queens NY)
Thanks,
Bob
Since 23 thru 27 times is 7 to 10 times above the expected average, I would expect the board to show an equal amount of occurences of a 7 thru 10 times the 7 has hit in the last 100 rolls (i.e. the same number below the average as I've seen above the average. But I've never seen it that low. The lowest I've seen it is 15 times of the last 100 rolls).
My question is: Is this an acceptable rate for the 7 to be showing (i.e. if different from the norm of 16.67% then it is more likely higher rather than lower)? Or is the fact that the 7 is the most common outcome make it more likely to be higher than the norm than below the norm?
Or, since most bettors are place or pass line bettors, could the machine be purposely skewed (i.e. cheating the players).
Can someone with a statistics background let me know if what I observe (more than likely chance of the % of 7's hitting is above the norm than below the norm or 16.67%) is unusual or acceptable?
I've seen this over a 9 month period at random times in 2 different casinos (Empire City in Yonkers NY and Resort World in Queens NY)
Thanks,
Bob
October 2nd, 2013 at 10:52:19 PM
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looks fine to meQuote: bobgioMy question is:
Is this an acceptable rate for the 7 to be showing
(i.e. if different from the norm of 16.67% then it is more likely higher rather than lower)?
Or is the fact that the 7 is the most common outcome make
it more likely to be higher than the norm than below the norm?
at the 2SD point.
anything is possible,Quote: bobgioOr, since most bettors are place or pass line bettors,
could the machine be purposely skewed (i.e. cheating the players).
but I say not probable
due to any type of honest cheating.
The binomial probability distribution is positively skewed at 0.1789
the data
out of the 101 possible outcomes for the # of 7s in 100 rolls,
23 looks to be the 13th highest.
23 looks to be the 13th highest.
x prob[X=x] prob[X<x] prob[X>=x] prob[X<=x] prob[X>x]
5 0.00029090 0.00009402 0.99990598 0.00038492 0.99961508
6 0.00092119 0.00038492 0.99961508 0.00130612 0.99869388
7 0.00247406 0.00130612 0.99869388 0.00378018 0.99621982
8 0.00575219 0.00378018 0.99621982 0.00953237 0.99046763
9 0.01176004 0.00953237 0.99046763 0.02129241 0.97870759
10 0.02140327 0.02129241 0.97870759 0.04269568 0.95730432
11 0.03502354 0.04269568 0.95730432 0.07771922 0.92228078
12 0.05195158 0.07771922 0.92228078 0.12967080 0.87032920
13 0.07033445 0.12967080 0.87032920 0.20000525 0.79999475
14 0.08741567 0.20000525 0.79999475 0.28742092 0.71257908
15 0.10023663 0.28742092 0.71257908 0.38765755 0.61234245
16 0.10650142 0.38765755 0.61234245 0.49415898 0.50584102
17 0.10524847 0.49415898 0.50584102 0.59940744 0.40059256
18 0.09706247 0.59940744 0.40059256 0.69646992 0.30353008
19 0.08378024 0.69646992 0.30353008 0.78025016 0.21974984
20 0.06786200 0.78025016 0.21974984 0.84811215 0.15188785
21 0.05170438 0.84811215 0.15188785 0.89981653 0.10018347
22 0.03713314 0.89981653 0.10018347 0.93694967 0.06305033
23 0.02518596 0.93694967 0.06305033 0.96213563 0.03786437
24 0.01616099 0.96213563 0.03786437 0.97829662 0.02170338
25 0.00982588 0.97829662 0.02170338 0.98812250 0.01187750
26 0.00566878 0.98812250 0.01187750 0.99379128 0.00620872
27 0.00310733 0.99379128 0.00620872 0.99689861 0.00310139
28 0.00162025 0.99689861 0.00310139 0.99851886 0.00148114
29 0.00080454 0.99851886 0.00148114 0.99932340 0.00067660
30 0.00038081 0.99932340 0.00067660 0.99970422 0.00029578
0.06305033 or about 1 in 16
the chance of 10 or less is (5th column)
0.04269568 or about 1 in 24
of course the machine is showing you a window to the last 100 rolls.
that window moves each roll so you may see
a certain # of 7s stay there for some time until they finally drop out of the last 100 rolls.
Thanks for sharing your observation and questions
hope this helps
winsome johnny (not Win some johnny)
October 2nd, 2013 at 10:54:00 PM
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Quote: bobgio
My question is: Is this an acceptable rate for the 7 to be showing (i.e. if different from the norm of 16.67% then it is more likely higher rather than lower)? Or is the fact that the 7 is the most common outcome make it more likely to be higher than the norm than below the norm?
Or, since most bettors are place or pass line bettors, could the machine be purposely skewed (i.e. cheating the players).
Can someone with a statistics background let me know if what I observe (more than likely chance of the % of 7's hitting is above the norm than below the norm or 16.67%) is unusual or acceptable?
I've seen this over a 9 month period at random times in 2 different casinos (Empire City in Yonkers NY and Resort World in Queens NY)
Thanks,
Bob
How acceptable it is really depends on the number of observations you have taken.
It could be rigged, but I doubt it, especially if it's a unit used in casinos in other states like Nevada.
October 2nd, 2013 at 10:54:47 PM
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Quote: bobgio...The lowest I've seen it is 15 times of the last 100 rolls).
How many sets of 100 rolls did you actually observe?
Quote: bobgio
My question is: Is this an acceptable rate for the 7 to be showing (i.e. if different from the norm of 16.67% then it is more likely higher rather than lower)? Or is the fact that the 7 is the most common outcome make it more likely to be higher than the norm than below the norm?
Again it would depend on how many 100 roll observations you made. And it doesn't matter whether the observations were higher or lower than the norm. You would actually never see exactly the norm. You would always expect to see higher or lower results than the norm.
October 5th, 2013 at 4:02:27 AM
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The stats are always for the last 100 rolls, so you are never seeing good data .... good data would be for the last 100,000 rolls or preferably more. Even 10,000 might show a skew. What you are seeing, even if you are there a lot, is similar to just anecdotal.
But if you are convinced, go to the Darkside, sir.
But if you are convinced, go to the Darkside, sir.
the next time Dame Fortune toys with your heart, your soul and your wallet, raise your glass and praise her thus: “Thanks for nothing, you cold-hearted, evil, damnable, nefarious, low-life, malicious monster from Hell!” She is, after all, stone deaf. ... Arnold Snyder
October 5th, 2013 at 6:46:23 AM
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Quote: bobgioI've noticed on an electronic craps machine (where the dice are "rolled" by bouncing them on a drum that is vibrated) that whenever I look at the statistics showing the number of times a 7 is rolled in the last 100 rolls, I have noticed that it's more often than not 23 thru 27 times out of the last 100 rolls than 7 through 10 times. The average should be 16 or 17 (since the average # of times a 7 is rolled is should be statistically 16.67%).
I've played those Interblock machines at RW and Empire a number of times. They are not skewed by the Casino. Over time, all the numbers will roll normally, but one or two numbers or sequences seem to get hot before turning very cold. Consequently, the tote board might show the eight rolled fourteen times in 100 rolls, but it does not show that seven of those fourteen hits occurred within a fifteen roll span.
Could the Bubble be too small to adequately shake the three dice (one for Sic-Bo) it contains?
On many occasions I saw one crowded die simply vibrating in place or flopping from side to side between the same two numbers.
I've seen the Seven roll seven times consecutively on two occasions. I've also seen all three dice roll the same 5,2,3 twice in a row, and the Six and Eight roll back to back five times in a row.
I've also seen and the Seven roll only three times in 100 rolls while the Twelve rolled eight times and the Two rolled five times in the same 100 roll period.
All of these events are statistically possible, but I question whether these results were truly random or due to the dice not being adequately shaken in the bubble.
A few Regulars at RW make nothing but Place, Buy, Hardway, Yo and Craps bets based solely upon the tote board results.
One regular sitting next to me once said "Why aren't you Placing the Nine? Look at the board. It's like reading a book. They're telling you what to bet."
It was good advice.
As for me, I stay away from those Robots and prefer to "shake-em" at the real tables.
October 7th, 2013 at 2:54:36 AM
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Quote: TankoOne regular sitting next to me once said "Why aren't you Placing the Nine? Look at the board. It's like reading a book. They're telling you what to bet."
Gee, for some reason having "them" tell you what to bet doesnt seem to work out. Well, of course, I can't really confirm that the old veteran wasn't getting rich by thinking the past predicted the future in craps, but it does fit perfectly into the category of "gambler's fallacy".
If you can truly see that you will have "one crowded die simply vibrating in place" then maybe you have something. Since you'd rather be at a real table, you'll forgive me for thinking it would not seem you could place your bet in time to take advantage of it.
the next time Dame Fortune toys with your heart, your soul and your wallet, raise your glass and praise her thus: “Thanks for nothing, you cold-hearted, evil, damnable, nefarious, low-life, malicious monster from Hell!” She is, after all, stone deaf. ... Arnold Snyder
October 7th, 2013 at 3:15:16 AM
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If a machine were programmed to skew the results in favor of the casino, then the manufacturer of that machine would do everything in their power to hide result histories.
Someday, joor goin' to see the name of Googie Gomez in lights and joor goin' to say to joorself, "Was that her?" and then joor goin' to answer to joorself, "That was her!" But you know somethin' mister? I was always her yuss nobody knows it! - Googie Gomez
October 7th, 2013 at 9:29:40 AM
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Last edited by: Tanko on Mar 10, 2016
October 7th, 2013 at 10:28:49 AM
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I hope you at leastQuote: TankoI recorded these rolls during my last visit:
8,3,4,11,3,8,10,10,3,6,5,6,6,7,6,9,2,5,6,5,7,7,5,9,7,6,10,7,7,11,3,8,11,9,9,8,9,4,6,8,6,8,8,12,11,10,8,6,3,6,9,7,7,8,10,10,8,7,8,8,9,9,8,
5,7,8,5,10,11,10,7,2,6,6,9,8,10,8,4,8,9,4,7,9,8,3,9,10,9,10,6,9,5,6,7,5,7,8,10,6,11,8,2,8,3,11,5,9,12,8,8,8,8,6,7
played the pass with some kind of odds. I think you did.
A right way player should have easily
made good $$$ on these 9 hands.
Just $5 pass and 2X odds shows $197 net profit ($212 was max high)
345X odds shows $365 net profit ($395 was the max high)
never more than $5 plus odds into the starting bankroll
I also noticed on this type of machine, only one in SoCal,
the pass point, when it wins, does it very quickly.
(hands 3,4 and 6 had no point winners)
the first # 8 as first come out roll
shooter (Hand) #1
cor 8,3,4,11,3,8,win (6,#)
cor 10,10,win (2,#)
cor 3,crap out (1,#)
cor 6,5,6,win (3,#)
cor 6,7,out (2,#)
shooter (Hand) #1 14 roll hand
5 # COR
3 # Point Wins
3 # Fire Bets
3,2 shooter (Hand) score: pass,miss
2 # Place Hits
shooter (Hand) #2
cor 6,9,2,5,6,win (5,#)
cor 5,7,out (2,#)
shooter (Hand) #2 7 roll hand
2 # COR
1 # Point Wins
1 # Fire Bets
1,1 shooter (Hand) score: pass,miss
2 # Place Hits
shooter (Hand) #3
cor 7,win (1,#)
cor 5,9,7,out (3,#)
shooter (Hand) #3 4 roll hand
2 # COR
0 # Point Wins
0 # Fire Bets
1,1 shooter (Hand) score: pass,miss
1 # Place Hits
shooter (Hand) #4
cor 6,10,7,out (3,#)
shooter (Hand) #4 3 roll hand
1 # COR
0 # Point Wins
0 # Fire Bets
0,1 shooter (Hand) score: pass,miss
1 # Place Hits
shooter (Hand) #5
cor 7,win (1,#)
cor 11,win (1,#)
cor 3,crap out (1,#)
cor 8,11,9,9,8,win (5,#)
cor 9,4,6,8,6,8,8,12,11,10,8,6,3,6,9,win (15,#)
cor 7,win (1,#)
cor 7,win (1,#)
cor 8,10,10,8,win (4,#)
cor 7,win (1,#)
cor 8,8,win (2,#)
cor 9,9,win (2,#)
cor 8,5,7,out (3,#)
shooter (Hand) #5 37 roll hand
12 # COR
5 # Point Wins
2 # Fire Bets
10,2 shooter (Hand) score: pass,miss
15 # Place Hits
shooter (Hand) #6
cor 8,5,10,11,10,7,out (6,#)
shooter (Hand) #6 6 roll hand
1 # COR
0 # Point Wins
0 # Fire Bets
0,1 shooter (Hand) score: pass,miss
3 # Place Hits
shooter (Hand) #7
cor 2,crap out (1,#)
cor 6,6,win (2,#)
cor 9,8,10,8,4,8,9,win (7,#)
cor 4,7,out (2,#)
shooter (Hand) #7 12 roll hand
4 # COR
2 # Point Wins
2 # Fire Bets
2,2 shooter (Hand) score: pass,miss
5 # Place Hits
shooter (Hand) #8
cor 9,8,3,9,win (4,#)
cor 10,9,10,win (3,#)
cor 6,9,5,6,win (4,#)
cor 7,win (1,#)
cor 5,7,out (2,#)
shooter (Hand) #8 14 roll hand
5 # COR
3 # Point Wins
3 # Fire Bets
4,1 shooter (Hand) score: pass,miss
4 # Place Hits
shooter (Hand) #9
cor 8,10,6,11,8,win (5,#)
cor 2,crap out (1,#)
cor 8,3,11,5,9,12,8,win (7,#)
cor 8,8,win (2,#)
cor 8,6,7,out (3,#)
shooter (Hand) #9 18 roll hand
5 # COR
3 # Point Wins
1 # Fire Bets
3,2 shooter (Hand) score: pass,miss
5 # Place Hits
shooter (Hand) #10
cor
waiting...
winsome johnny (not Win some johnny)
October 7th, 2013 at 1:02:30 PM
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Quote: TankoWho said taking their advice doesn't work out?
Sorry, I guess I did realize my comment was a little insulting, which is not my style really. So I was going on my own observations, which simply amounts to noting that the machines in Maryland have not been removed even though all this posting of 'the last 100 rolls' data has been going on from the get-go. I am 100% confident that every single player who has stuck with it at all there has looked for patterns and every conceivable wrinkle has been explored.
Trust me, if those machines were capable of consistently losing money,
*many players would have figured it out
*those same players would be killing it
*the machines would have been removed by now
*for some reason the machines you know of may live in a different universe, or are new
*just IMO !
Quote: 7crapsI also noticed on this type of machine, only one in SoCal, the pass point, when it wins, does it very quickly.
Are you saying your observations amounted to enough data to be more than anecdotal?
the next time Dame Fortune toys with your heart, your soul and your wallet, raise your glass and praise her thus: “Thanks for nothing, you cold-hearted, evil, damnable, nefarious, low-life, malicious monster from Hell!” She is, after all, stone deaf. ... Arnold Snyder
October 8th, 2013 at 7:15:45 AM
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October 8th, 2013 at 7:58:02 AM
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October 8th, 2013 at 8:08:07 AM
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Quote: TankoI would never play the Don't side against these Interblock machines.
Here is another set for anyone interested:
7,8,3,3,9,9,6,6,9,5,6,9,3,2,8,6,9,5,5,6,7,5,6,4,8,4,5,3,3,5,3,5,7,4,6,4,4,8,8,2,6,3,6,9,6,6,8,3,6,8,5,9,6,6,7,6,3,7,10,6,7,9,4,4,7,7,
11,6,9,10,6,2,9,8,10,9,5,8,7,5,8,4,6,8,11,8,4,5,8,2,8,4,7,10,5,6,7,7,7,9,6,10,4,6,9,10,4,7,4,10,10,10,4,6,11,6,10,4,9,10,2,9,4,
11,3,12,10,3,3,4,4,7,6,8,7
If I analyzed these numbers correctly, there were 20-Wins and 14-Losses playing the pass line.
7C/O-W
8C/O,3,3,9,9,6,6,9,5,6,9,3,2,8-W
6C/O,9,5,5,6-W
7C/O-W
5C/O,6,4,8,4,5-W
3C/O-L
3C/O-L
5C/O,3,5-W
7C/O-W
4C/O,6,4-W
4C/O,8,8,2,6,3,6,9,6,6,8,3,6,8,5,9,6,6,7-L
6C/O,3,7-L
10C/O,6,7-L
9C/O,4,4,7-L
7C/O-W
11C/O-W
6C/O,9,10,6-W
2C/O-L
9C/O,8,10,9-W
5C/O,8,7-L
5C/O,8,4,6,8,11,8,4,5-W
8C/O,2,8-W
4C/O,7-L
10C/O,5,6,7-L
7C/O-W
7C/O-W
9C/O,6,10,4,6,9-W
10C/O,4,7-L
4C/O,10,10,10,4-W
6C/O,11,6-W
10C/O,4,9,10-W
2C/O-L
9C/O,4,11,3,12,10,3,3,4,4,7-L
6C/O,8,7-L
October 8th, 2013 at 12:48:08 PM
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October 9th, 2013 at 5:50:30 AM
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Quote: TankoAre the machines that you are referring to Interblock or Aruze?
perhaps 100X can answer that
there was an opinion floating that it was "Organic" co.
https://wizardofvegas.com/forum/off-topic/other-casinos/9824-marylands-venture/2/#post148747
the next time Dame Fortune toys with your heart, your soul and your wallet, raise your glass and praise her thus: “Thanks for nothing, you cold-hearted, evil, damnable, nefarious, low-life, malicious monster from Hell!” She is, after all, stone deaf. ... Arnold Snyder
October 12th, 2013 at 9:39:49 PM
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Not knowing if the first 7 was a 7winner or a 7outQuote: TankoI would never play the Don't side against these Interblock machines.
Here is another set for anyone interested:
7,8,3,3,9,9,6,6,9,5,6,9,3,2,8,6,9,5,5,6,7,5,6,4,8,4,5,3,3,5,3,5,7,4,6,4,4,8,8,2,6,3,6,9,6,6,8,3,6,8,5,9,6,6,7,6,3,7,10,6,7,9,4,4,7,7,
11,6,9,10,6,2,9,8,10,9,5,8,7,5,8,4,6,8,11,8,4,5,8,2,8,4,7,10,5,6,7,7,7,9,6,10,4,6,9,10,4,7,4,10,10,10,4,6,11,6,10,4,9,10,2,9,4,
11,3,12,10,3,3,4,4,7,6,8,7
the first hand (shooter) was either 54 or 55 rolls
5 point wins, 4 fire bets and 30 place #s hit
not bad for the right side
hand (shooter) #1
cor 7,win (1,#)
cor 8,3,3,9,9,6,6,9,5,6,9,3,2,8,win (14,#)
cor 6,9,5,5,6,win (5,#)
cor 7,win (1,#)
cor 5,6,4,8,4,5,win (6,#)
cor 3,crap out (1,#)
cor 3,crap out (1,#)
cor 5,3,5,win (3,#)
cor 7,win (1,#)
cor 4,6,4,win (3,#)
cor 4,8,8,2,6,3,6,9,6,6,8,3,6,8,5,9,6,6,7,out (19,#)
hand (shooter) #1 55 roll hand
11 # COR
5 # Point Wins
4 # Fire Bets
8,3 hand (shooter) score: pass,miss
30 # Place Hits
hand (shooter) #2
cor 6,3,7,out (3,#)
hand (shooter) #2 3 roll hand
1 # COR
0 # Point Wins
0 # Fire Bets
0,1 hand (shooter) score: pass,miss
0 # Place Hits
hand (shooter) #3
cor 10,6,7,out (3,#)
hand (shooter) #3 3 roll hand
1 # COR
0 # Point Wins
0 # Fire Bets
0,1 hand (shooter) score: pass,miss
1 # Place Hits
hand (shooter) #4
cor 9,4,4,7,out (4,#)
hand (shooter) #4 4 roll hand
1 # COR
0 # Point Wins
0 # Fire Bets
0,1 hand (shooter) score: pass,miss
2 # Place Hits
hand (shooter) #5
cor 7,win (1,#)
cor 11,win (1,#)
cor 6,9,10,6,win (4,#)
cor 2,crap out (1,#)
cor 9,8,10,9,win (4,#)
cor 5,8,7,out (3,#)
hand (shooter) #5 14 roll hand
6 # COR
2 # Point Wins
2 # Fire Bets
4,2 hand (shooter) score: pass,miss
5 # Place Hits
hand (shooter) #6
cor 5,8,4,6,8,11,8,4,5,win (9,#)
cor 8,2,8,win (3,#)
cor 4,7,out (2,#)
hand (shooter) #6 14 roll hand
3 # COR
2 # Point Wins
2 # Fire Bets
2,1 hand (shooter) score: pass,miss
6 # Place Hits
hand (shooter) #7
cor 10,5,6,7,out (4,#)
hand (shooter) #7 4 roll hand
1 # COR
0 # Point Wins
0 # Fire Bets
0,1 hand (shooter) score: pass,miss
2 # Place Hits
hand (shooter) #8
cor 7,win (1,#)
cor 7,win (1,#)
cor 9,6,10,4,6,9,win (6,#)
cor 10,4,7,out (3,#)
hand (shooter) #8 11 roll hand
4 # COR
1 # Point Wins
1 # Fire Bets
3,1 hand (shooter) score: pass,miss
5 # Place Hits
hand (shooter) #9
cor 4,10,10,10,4,win (5,#)
cor 6,11,6,win (3,#)
cor 10,4,9,10,win (4,#)
cor 2,crap out (1,#)
cor 9,4,11,3,12,10,3,3,4,4,7,out (11,#)
hand (shooter) #9 24 roll hand
5 # COR
3 # Point Wins
3 # Fire Bets
3,2 hand (shooter) score: pass,miss
9 # Place Hits
hand (shooter) #10
cor 6,8,7,out (3,#)
hand (shooter) #10 3 roll hand
1 # COR
0 # Point Wins
0 # Fire Bets
0,1 hand (shooter) score: pass,miss
1 # Place Hits
hand (shooter) #11
cor
waiting...
winsome johnny (not Win some johnny)
