# ugly night a the tables

Discussion in 'General Craps Discussion' started by scott22, Feb 5, 2012.

1. slorch, Mar 10, 2012

### slorch Member

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My intuition was fine. I asked a question about the data contained in the chart. You clarified.

Don't act as if we're all falcons here...

#121
2. 7Craps, Mar 10, 2012

### 7Craps Member

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Not to mix things up but any good prob/stat book will show that there are a few Laws of Large Numbers:
Strong Law of Large Numbers
Weak Law of Large Numbers
Empirical Law of Large numbers.
And some even call the Strong Law the Theoretical Law of Large Numbers.

Here is the Law in words
"If a certain chance experiment is repeated an unlimited number of times
under exactly the same conditions, and if the repetitions are independent of
each other, then the fraction of times that a given event A occurs will converge
with probability 1 to a number that is equal to the probability that A occurs in
a single repetition of the experiment."

Both the Strong and Weak Laws can be proved with math and both have their formulas.
http://en.wikipedia.org/wiki/Law_of_large_numbers

Since The Law of Averages is an informal fallacy, that will imply that there can be a formal fallacy.

Gotta love math, especially probability theory math.
It leaves no stone unturned.

#122
3. falcon, Mar 10, 2012

### falcon Member

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Your answers to some of my questions did provide clarifications. It should be meaningful to all here who have piled on to my basic assertions that the "perfect 1980" or 1.41% does not happen and should not be considered truly important in a random, short term exploration of craps. The key is above - "that any number could show up at any time" and "over time." The first phrase is definitive and accurate; the second is undefinable and beyond unreliable.

The exercise and simple conclusions above offer the craps "establishment" nothing to justify their zealous embracing of the "perfect 1980" or the "1.41% HA of PL outcomes." While the exercise provided some bundling or packaging of numbers to effect gross results, the fact that the dice were the same color did not allow for the differentiation of points, i.e., 4-2 or 2-4. If those determinations were made, I believe, the final results would have been well beyond the "predictions" quoted in the "perfect 1980" etc.

I commend 777 for his exercise and the lessons hopefully embraced by his students. The one question still remains: What are the odds of producing the "perfect 1980"?

falcon

#123
4. falcon, Mar 10, 2012

### falcon Member

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[q=guido]: I like facts that are 100% accurate.
Not 92.67834% accurate like Enron accounting or US Fed Government Labor statistics.
or 18.435% accurate fact statements by Falcon.(margin of error: +/- 5.555%)[/quote]

WOW 81.565% inaccurate? Where did I go wrong?

How far is Tunica from home for you?

falcon

#124
5. kaysirtap, Mar 10, 2012

### kaysirtap Member

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Maybe you should explain to us what you believe the 1.41% means? In your mind, what does the 1.41% represent?

#125
6. 7Craps, Mar 11, 2012

### 7Craps Member

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Slam the message and not the messenger.
The perfect 1980 or 244/495 is NOT about the individual dice numbers. The game of Craps is about the SUM of the two dice.

Falcon's statement is a 100% LIE. UNTRUTH.
He may just not know it. I wonder where he got his info from?
Alan!!!!!!!!!!!!!!!!!!!

Hey, Falcon, I have 6,835 in a US saving account.
All the money is yours as soon as you PROVE to the world the perfect 1980 is about points being rolled as 4,2 and 2,4 instead of just any 6.
"the fact that the dice were the same color did not allow for the differentiation of points, i.e., 4-2 or 2-4."

whoever is the big cheese at this forum can hold the money in escrow.

You have money to back up your message of LIES!!!???

Lets do it!
Then you are the Highest Craps God.

And that's no crap

added: Don Catlin, a long time math guru shows his proof here:
http://catlin.casinocitytimes.com/article/the-pass-line-6503

Lets see if Falcon can prove him wrong!
Falcon = Einstein
Wait and see!

#126
7. guido1, Mar 11, 2012

### guido1 Member

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WOW 81.565% inaccurate? Where did I go wrong?

How far is Tunica from home for you?

falcon[/quote]Hey Bro'
You did not go wrong.
see the margin of error?
Just like that 1.41% with a SD of 2%
or is it 3%.
Im tired

#127
8. guido1, Mar 11, 2012

### guido1 Member

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Technically the perfect 36 is based off of the 36 equal individual dice rolls as they are different colors.
But since the game is played with the same color dice, we do not know if the 6 winner that rolled was a 1,5 or 5,1. So the 1980 in actual play does not care. I think Don Catlin points that out in his article.

So Falcon is half correct.

But, as long as there are 5 winners from a point of 6, the perfect 1980 is correct.
So, there Falcon is half wrong.

Looks to be a wash!
Falcon, I am as far west as the Pacific Ocean, but I visit Tunica each year.

#128
9. 7Craps, Mar 11, 2012

### 7Craps Member

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Falcon is not even close to 50% correct on his Falconology 101.

It is true that if a point 6 is established as the point and if happened D1,1 and D2,5 the point does not have to now be rolled 1,5 to win. Any of the 5 ways for a 6 is a point winner.
Falcon claims that it must roll 1,5 to be a perfect 1980.
He now mixes Roulette with Craps.
That would make a totally different dice game.

My bet still stands.
Some enjoy being a troll and a flea.

#129
10. DeMango, Mar 12, 2012

### DeMango Member

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We need the bozos to contribute to the casino bottom line, no doubt tutty-fruity obliges. Probably the offspring from two Walmartians we see forwarded in emails all the time.

#130
11. falcon, Mar 12, 2012

### falcon Member

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First, It looks like retirement is not in your near future. With guido declaring me at 50% correct, I will defer the \$3,417.50 and would allow that you place those funds in your children's college fund (or grandchildren, if you have them).

Second, the above article's third paragraph reads:

It seems that the two colored dice are actually needed to differentiate between the points converted, points with a 7 out, each and every 7/11 winner among the point winners/losers, and each and every craps loser among the winners and losers. If that were not true, why would he even mention "each die as being a different color"?

Another important basic factor is that "facts" placed before any group must be proved, not the reverse. The "perfect 1980" does exist, but there is no proof it has ever happened. Therefore, the proof lies in your court, and my assertion will stand unless and until there is actual documentation otherwise, and someone can actually produce the odds of its occurrance.

falcon

#131
12. guido1, Mar 13, 2012

### guido1 Member

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Falcon Bro,
you are getting your perfect 1980 mixed up with the HA of 1.4141% or to quote you "The Rule of 495 REQUIRES the "perfect" math as shown in the formula of 244 wins vs 251 losses in 495 PL outcomes"

You must have done this for a great laugh!!!
The perfect 1980 is just the 36 permutations of the 2 craps dice.
Don Catlin still calculated the HA to be 1.41%. Remember the Hoax?

You are not correct if the point is established with a 1,5 it must roll as a 1,5 to satisfy the Rule of 495.
A 3,3 wins the point of a 6 that was established with a 1,5. Easy.

The 244/495 has been proven.
So, no matter what language you say it in you are still 100% wrong on your statement that it never has been proven. Two colored dice do not require it.
In the Zumma Dice Rolls the perfect 244/495 happened exactly 360 times.
The first time started with shooter #18 with his first pass-7
and ended with shooter #217 on his pass-9
you can count them if you wish
Code:
```S#  result
18    Pass-7
18    Pass-8
18    Pass-11
18    Miss-10
19    Pass-11
19    Miss-5
20    Pass-11
20    Miss-10
21    Miss-2
21    Miss-5
22    Miss-9
23    Pass-7
23    Pass-9
23    Miss-9
24    Pass-7
24    Pass-10
24    Pass-5
24    Miss-8
25    Pass-7
25    Miss-5
26    Pass-11
26    Miss-3
26    Pass-6
26    Miss-3
26    Miss-4
27    Miss-6
28    Pass-6
28    Pass-9
28    Pass-7
28    Miss-6
29    Miss-12
29    Miss-2
29    Miss-3
29    Pass-7
29    Pass-7
29    Miss-5
30    Pass-7
30    Miss-4
31    Miss-2
31    Pass-7
31    Miss-8
32    Miss-4
33    Pass-11
33    Pass-7
33    Miss-8
34    Miss-8
35    Pass-8
35    Pass-6
35    Pass-8
35    Miss-6
36    Pass-8
36    Miss-8
37    Pass-7
37    Pass-10
37    Miss-4
38    Miss-6
39    Pass-8
39    Miss-6
40    Pass-7
40    Miss-9
41    Pass-9
41    Pass-6
41    Miss-6
42    Miss-6
43    Miss-5
44    Miss-6
45    Miss-10
46    Miss-3
46    Miss-6
47    Miss-12
47    Miss-5
48    Pass-5
48    Pass-5
48    Miss-10
49    Pass-5
49    Pass-6
49    Pass-7
49    Miss-5
50    Pass-7
50    Miss-12
50    Pass-6
50    Miss-9
51    Miss-10
52    Miss-10
53    Pass-8
53    Pass-7
53    Pass-7
53    Miss-8
54    Miss-9
55    Miss-6
56    Pass-9
56    Pass-6
56    Miss-9
57    Pass-6
57    Miss-6
58    Pass-6
58    Miss-8
59    Pass-6
59    Miss-10
60    Pass-7
60    Pass-5
60    Miss-10
61    Miss-4
62    Pass-5
62    Miss-8
63    Miss-4
64    Pass-8
64    Miss-3
64    Miss-12
64    Pass-8
64    Pass-7
64    Miss-8
65    Pass-5
65    Miss-9
66    Miss-10
67    Pass-11
67    Miss-8
68    Miss-3
68    Miss-8
69    Pass-6
69    Miss-3
69    Pass-11
69    Pass-7
69    Miss-2
69    Miss-2
69    Pass-11
69    Pass-11
69    Miss-5
70    Pass-7
70    Miss-6
71    Miss-4
72    Pass-4
72    Pass-9
72    Miss-2
72    Pass-7
72    Pass-8
72    Miss-6
73    Pass-8
73    Miss-10
74    Miss-2
74    Miss-4
75    Pass-8
75    Pass-7
75    Miss-5
76    Pass-7
76    Miss-6
77    Pass-5
77    Pass-4
77    Miss-8
78    Pass-5
78    Pass-7
78    Pass-8
78    Pass-10
78    Pass-11
78    Miss-3
78    Pass-8
78    Miss-4
79    Pass-4
79    Miss-6
80    Pass-6
80    Miss-6
81    Miss-5
82    Pass-7
82    Miss-10
83    Miss-8
84    Miss-10
85    Miss-5
86    Pass-7
86    Pass-11
86    Miss-3
86    Pass-7
86    Miss-5
87    Pass-9
87    Miss-4
88    Pass-11
88    Miss-9
89    Miss-12
89    Pass-7
89    Pass-7
89    Pass-5
89    Miss-3
89    Miss-3
89    Pass-8
89    Miss-9
90    Pass-8
90    Pass-8
90    Miss-6
91    Pass-6
91    Miss-9
92    Miss-10
93    Miss-6
94    Pass-4
94    Pass-4
94    Miss-12
94    Pass-8
94    Pass-4
94    Miss-5
95    Pass-9
95    Miss-8
96    Miss-5
97    Pass-6
97    Pass-4
97    Miss-3
97    Miss-10
98    Pass-7
98    Pass-7
98    Pass-5
98    Pass-7
98    Miss-5
99    Pass-7
99    Miss-2
99    Miss-12
99    Pass-7
99    Miss-9
100    Miss-10
101    Miss-3
101    Miss-10
102    Miss-10
103    Miss-9
104    Pass-6
104    Pass-6
104    Pass-11
104    Pass-6
104    Pass-8
104    Miss-6
105    Miss-9
106    Pass-11
106    Miss-12
106    Pass-7
106    Miss-9
107    Miss-8
108    Miss-8
109    Miss-3
109    Miss-2
109    Miss-10
110    Miss-5
111    Miss-8
112    Miss-2
112    Pass-8
112    Miss-4
113    Pass-9
113    Pass-6
113    Pass-7
113    Pass-9
113    Pass-7
113    Pass-7
113    Pass-7
113    Miss-6
114    Pass-7
114    Pass-6
114    Miss-8
115    Pass-4
115    Pass-6
115    Miss-8
116    Miss-8
117    Miss-5
118    Miss-8
119    Miss-4
120    Miss-5
121    Pass-8
121    Pass-5
121    Miss-6
122    Pass-7
122    Pass-5
122    Miss-9
123    Pass-11
123    Pass-7
123    Miss-4
124    Miss-10
125    Miss-2
125    Pass-5
125    Pass-11
125    Miss-9
126    Miss-4
127    Pass-8
127    Pass-7
127    Miss-5
128    Pass-8
128    Pass-11
128    Pass-11
128    Miss-3
128    Pass-11
128    Miss-9
129    Miss-6
130    Pass-11
130    Miss-4
131    Miss-4
132    Pass-5
132    Miss-9
133    Pass-7
133    Miss-9
134    Miss-5
135    Pass-9
135    Miss-8
136    Miss-8
137    Miss-5
138    Miss-8
139    Pass-11
139    Miss-10
140    Pass-9
140    Miss-4
141    Miss-6
142    Pass-7
142    Pass-8
142    Pass-7
142    Miss-4
143    Miss-9
144    Pass-8
144    Miss-8
145    Miss-3
145    Pass-7
145    Miss-6
146    Miss-3
146    Miss-6
147    Pass-8
147    Miss-6
148    Miss-8
149    Miss-5
150    Pass-7
150    Miss-4
151    Pass-10
151    Miss-4
152    Miss-6
153    Miss-6
154    Pass-8
154    Pass-7
154    Pass-11
154    Miss-2
154    Pass-7
154    Miss-6
155    Pass-5
155    Miss-4
156    Pass-7
156    Pass-11
156    Pass-7
156    Miss-6
157    Miss-5
158    Pass-6
158    Miss-10
159    Miss-9
160    Miss-12
160    Miss-12
160    Pass-6
160    Miss-8
161    Pass-9
161    Miss-2
161    Pass-4
161    Pass-7
161    Pass-6
161    Pass-7
161    Miss-5
162    Pass-8
162    Pass-5
162    Miss-5
163    Miss-5
164    Miss-4
165    Pass-7
165    Miss-4
166    Pass-9
166    Miss-12
166    Miss-12
166    Pass-5
166    Miss-5
167    Pass-7
167    Miss-4
168    Miss-6
169    Miss-9
170    Pass-4
170    Pass-7
170    Pass-7
170    Miss-10
171    Pass-7
171    Pass-7
171    Miss-9
172    Miss-6
173    Pass-9
173    Miss-5
174    Pass-9
174    Miss-5
175    Miss-9
176    Pass-6
176    Miss-3
176    Miss-5
177    Pass-9
177    Miss-5
178    Miss-5
179    Miss-2
179    Pass-6
179    Pass-11
179    Miss-10
180    Miss-4
181    Pass-7
181    Miss-9
182    Pass-9
182    Pass-6
182    Miss-8
183    Miss-6
184    Miss-2
184    Pass-7
184    Miss-8
185    Pass-11
185    Miss-6
186    Pass-5
186    Miss-5
187    Miss-5
188    Miss-12
188    Miss-12
188    Miss-6
189    Pass-8
189    Pass-9
189    Pass-5
189    Pass-10
189    Pass-7
189    Pass-8
189    Pass-10
189    Pass-8
189    Pass-6
189    Miss-3
189    Pass-7
189    Pass-9
189    Miss-2
189    Miss-5
190    Pass-5
190    Miss-8
191    Pass-4
191    Pass-8
191    Miss-5
192    Pass-9
192    Pass-6
192    Pass-6
192    Pass-9
192    Miss-5
193    Pass-7
193    Pass-6
193    Pass-8
193    Pass-7
193    Pass-8
193    Miss-4
194    Miss-5
195    Pass-4
195    Miss-6
196    Miss-9
197    Miss-6
198    Pass-11
198    Miss-9
199    Miss-10
200    Miss-6
201    Miss-8
202    Pass-7
202    Miss-8
203    Miss-6
204    Miss-9
205    Miss-10
206    Pass-7
206    Pass-7
206    Pass-10
206    Pass-9
206    Miss-4
207    Pass-11
207    Pass-9
207    Pass-7
207    Miss-3
207    Miss-4
208    Miss-4
209    Pass-5
209    Pass-9
209    Pass-5
209    Miss-10
210    Pass-5
210    Miss-5
211    Miss-8
212    Pass-5
212    Miss-5
213    Pass-7
213    Pass-11
213    Pass-6
213    Pass-10
213    Miss-6
214    Pass-10
214    Pass-9
214    Miss-12
214    Pass-7
214    Pass-5
214    Miss-9
215    Pass-9
215    Miss-6
216    Pass-6
216    Pass-9
216    Pass-7
216    Miss-2
216    Pass-11
216    Pass-7
216    Miss-8
217    Pass-8
217    Pass-9
```
There it is.
I can email you the actual dice rolls if you wish.
I cant post them because of copy-write laws.

Too bad Falcon you will never believe the real truth even when it is put in front of you.
That is OK by me.
Maybe not to the Craps Gods.

#132
13. cmonhard8, Mar 13, 2012

### cmonhard8 Member

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Stats are great, until they don't matter...Tonight a girl rolled 5 consecutive high/lows(three-12's and two-2's) in a row...A point had already been established....One guy was mostly playing the horn wagers anyway(he had quite a bit of money)...He probably made about 5 thousand from those 5 rolls, as he was heavily on all the rolls.

That was a reminder to me, that craps is more 'right place, right time', then being brilliant or genius or having a grand strategy...Had I had even \$5 on each of the high/lows when the streak first started, I may have made a similar amount, as it's much easier to press ect. after winning...Instead, I watched someone else be there at the right moment...I could have gone from \$5 to \$30 to \$100 to \$200 to \$300(if I would have, it would have been around \$17000, for just 5 rolls of the dice)....Granted I'm not sure I would have pressed beyond \$100....The other thing is you would always be thinking about 'probability', yet tonight probability didn't mean squat-----just my 2 cents worth..

#133
14. Sancho Panza, Mar 13, 2012

### Sancho Panza Member

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Definitely. But it also makes sense to improve your chances as much as possible.

#134
15. falcon, Mar 13, 2012

### falcon Member

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I understand that a point winner can be converted by ANY like number. That is not my assertion. The "perfect 1980" or "495" must convert each of the ways the point itself is generated. Therefore, the 2-4 (6) can be converted with any 6 combo, however, each 6 point needs to be converted and conversely each 6 loser must also lose by ANY 7 out. That is inherent is the "perfect 1980" or the perfect "Rule of 495." Therefore, the use of two different colored dice is essential as stated by Catlin.

In California, the game of craps uses two different colored dice because the outcome from each roll is determined by the use of playing cards in various forms. That is state gaming law which, I believe, is unique to California. So, if one really wanted to do the beyond tedious research of PL outcomes (without the cards), California would be the optimum playing field.

That is the "truth." To convert two 4-2's just because the dice are the same color becomes meaningless and is a cop out when discussing the "perfect 1980." Using a red di and a green di would then be number and point specific so that if in the course of events two red 4's and two green 2's are converted the "perfect 1980" would be broken, and one would have to start over again fresh with a"perfect 1980." As long as Zumma ignored the use of two different colored dice, there can be no real accuracy is that accounting; there would be no way of telling if the "perfect 1980" or perfect "495" occurred all there is are lots of conversions and lots of point losers along with 7/11 winners and craps losers jumbled up in a large bunch of play.

falcon

#135
16. 7Craps, Mar 13, 2012

### 7Craps Member

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Nice data Dr G.
495 pass line bets.
244 wins
251 losses

house edge for this sample is exactly 7/495 or 01.4141%
Most shooters sucked!!

I assume you used WC to produce this. shoot1.bet is on the website

#136
17. The Midnight Skulker, Mar 14, 2012

### The Midnight Skulker Member

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So what exactly were you claiming when you wrote the following in your post of 23 Feb (http://www.crapsforum.com/viewreply/16289/)? "Because the house pays only even money on the PL wager, the FO “true odds” payout is diluted, and the house therefore “shorts” the player accordingly. That translates to less payouts on the combination bets PL/FO vs Place bets of equal \$\$ at 3X or less and equal payouts at 4X."

#137
18. falcon, Mar 14, 2012

### falcon Member

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The PL and Place bets are two separate bets usually activated at different times. KST and others asked me which bet is "better." If both are activated at Come out, the PL is a "better" bet because it would win more often than the Place bet for that one roll. After the point is established, both bets might seem to be equal but for a couple of exceptions: (a) If the Place bet is not the point and is rolled, it wins and the PL does nothing; (b) If the Place bet becomes the point and is rolled, the Place bet will pay more than the pure PL wager; (c) If a 7 out happens, both lose equally. But you and most others know that, and it never is placed in the discussions.

By adding the FO of only 3X or less for a possible point conversion vs increasing the Place wager for the same \$\$ amount produces a further inequality or shortfall for the PL/FO combo vs that increased Place bet. That was the basis of my post. It is hardly ever mentioned, and I wanted others out there to be aware of how the numbers can be skewed, and offer a possible alternative to playing the PL wager if one does not hold the dice in hand. It becomes an informed choice which is rarely offered. Now why would anyone have a "problem" with this information?

falcon

#138
19. The Midnight Skulker, Mar 14, 2012

### The Midnight Skulker Member

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Just to make sure I understand your scenario let me construct an example. At comeout: \$30 PL vs. \$30 Place 6 (hereafter called P6), off by default. After a point is established: player must decide between adding odds to PL bet or adding the same amount to P6 bet.
Because of the sleight of hand involved. You are comparing the total amounts at risk during the point cycle as though they were both also at risk on the comeout roll. Such is not the case.

For an accurate comparison the P6 bet must be broken into two parts and compared to the equivalent parts of the PL/FO bet. On the comeout the PL bettor has \$30 action and the P6 bettor does not. Therefore the players do not have the same amount at risk on the comeout roll, which is where you agree that the PL bettor has the advantage. Furthermore, I have demonstrated (and you have agreed) that if the P6 bet is working on the comeout, making the amounts at risk equal, it is expected to lose more than the PL bet over the course of the entire decision.

After a point is established you note, and I agree, that while both bets get shorted, the PL bet gets shorted a greater amount. My point here, though, is that that is water under the bridge. We can compare only the additional amounts being contemplated. The amount the PL player adds will be paid at true odds; the amount the P6 player adds will be paid at less than true odds. By comparing the total amounts at risk during the point cycle only you are lumping the initial \$30 wagers into the total at risk as though there had been no comeout roll. IOW you are comparing P6 to a Put bet, not to a PL/FO bet.

#139
20. falcon, Mar 14, 2012

### falcon Member

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[q=MS: Just to make sure I understand your scenario let me construct an example. At comeout: \$30 PL vs. \$30 Place 6 (hereafter called P6), off by default. After a point is established: player must decide between adding odds to PL bet or adding the same amount to P6 bet.[/quote]

My scenario was a bit short, so your interpretation of what I meant is incorrect. That is MY fault not yours, but please note, I did state "that if both bets are activated at come out." Those a,b, & c possible results are correct. However, again, I should have specified two players each with their own wager one player playing the PL and the other playing P6.

If a player wishes to have his Place active during come out, the PL bet is still better because it will win more often. The P6 player is not playing the PL during come out. He has opted out of that bet, so we have equal \$\$ at risk just in different places. Using the come out roll here with both bets active with two different players is what I am suggesting. I should have been more specific about the two players and the two bets, again MY fault. If the come out roll is a 6 and the P6 is active, then of course that bet is superior, but I do not want to "muddy the waters" here.

[q=MS]: Because of the sleight of hand involved. You are comparing the total amounts at risk during the point cycle as though they were both also at risk on the comeout roll. Such is not the case.

For an accurate comparison the P6 bet must be broken into two parts and compared to the equivalent parts of the PL/FO bet. On the comeout the PL bettor has \$30 action and the P6 bettor does not. Therefore the players do not have the same amount at risk on the comeout roll, which is where you agree that the PL bettor has the advantage. Furthermore, I have demonstrated (and you have agreed) that if the P6 bet is working on the comeout, making the amounts at risk equal, it is expected to lose more than the PL bet over the course of the entire decision.[/quote]

I included this quote only because I created the misunderstanding and wanted you to note that your assumptions above relied on an unintended premise.

The intended premise was that the PL and the P6 bets for different players would be equal at \$10 and the P6 would be active at come out. After the point is established, the PL player would add \$30 of FO for a total of \$40 at risk. The P6 player would also add \$30 to his P6 bet for a total at risk of \$40. It would be at this juncture that the P6 bet would be superior assuming that the 6 is the point. If there is another number that is the point such as the 9, and the P6 player Placed the 9 for \$40, his P9 would be superior to the PL/FO 9 bet on its own. An option for the P6 player would to be to take down the \$10 P6 bet to make everything equal dollarwise. I do not see the P6 bet losing more "over the course of the entire decision" unless you mean that a come out winner on the PL leaves the P6 bettor one win down otherwise, "the entire decision" means a point conversion or a 7 out.

I hope that my clarifications above regarding the two players, two separate wagers; and both bets being active at come out does allow that the "water under the bridge" is the PL player's \$\$ floating down the river. The fact that the FO bet when added is paid at true odds does not mitigate the actual short payout vs the P6.

I also realize that the scenario I have described is far far less usual than the reality of PL/FO play.

One small p.s. is that an active P6 at come out winner now puts the PL player at a disadvantage. But I know you know that.

And in the spirit of full disclosure and the most elementary math, it is quite likely that in any given two hour craps session, the PL player vs the P6 player using the stategies described above, would come out ahead overall due to the double jeopardy of the come out 7 winner vs the P6 come out loser.

falcon

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