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JB
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JB
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February 13th, 2010 at 10:44:19 AM permalink
Quote: tuttigym

I want to know the chances, the odds, the probabilities of exactly having 244 wins against 251 losses in 495 PL outcomes.


3.5848%, or approximately one "chunk" of 495 Pass Line resolutions out of 28 "chunks" of 495 Pass Line resolutions.

The exact formula is: 495!/(244! 251!) (244/495)244 (251/495)251


To address the notion that the house advantage is a hoax, consider a coin toss. The chance of it landing on heads is 50%, and the chance of it landing on tails is the other 50%. But the probability of exactly 250 heads and 250 tails in 500 coin tosses is 3.5665%, also roughly 1 in 28. Does this mean that the probability of heads being 50% and tails being 50% is a hoax? Of course not. In the short term, anything can happen. But over time, the results will approach expectations (50% heads, 50% tails). It's no different with the Pass Line bet in craps. In the short term, anything can happen, but over time you will win 49.2929% of the time and lose 50.7071% of the time. Just because every sequence of 495 rolls doesn't produce exactly 244 wins and 251 losses does not make it a hoax.
Mosca
Mosca
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February 13th, 2010 at 12:29:45 PM permalink
Quote: tuttigym

Mosca: The "math": After the point is established, fully 65% or more of craps betting and play, the HA becomes huge. The player's chances of winning diminish those PL/FO, if bet, by up to 67% depending on the point according to the Wizard. Feb. 2000.

tuttigym



Your math is faulty. Review the entire analysis and see why; it is not my job to show you why it is wrong. It's not like you've found something the professionals have missed over the last 300 years.

But, believe as you will.
NO KILL I
seattledice
seattledice
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February 13th, 2010 at 12:39:00 PM permalink
Quote: tuttigym

Mosca: Look at page 3 on this thread. The second post shows part of the monstrous equation and number configurations.

No business can survive on a 1.41% gross profit which is what some are eluding to that might represent the HA. Businesses have operating expenses which far exceed the portions of gross profits posted by a business. The resultant amount becomes the net profit. That 1.41% might buy tiolet tissue for a casino for a week.

You need to define "long term" and "short term." Obama says the "stimulus" will create jobs in the "long term." What is that?

tuttigym



I have read that if the only bets anyone made at the craps table were the line bets (pass, don't pass, come, and don't come -- all with HA <= 1.41%) then the craps tables would be shut down because they wouldn't make enough money to cover the cost of running the game. I don't know if that's true, but it seems reasonable. Many bets are made on the higher HA place bets (1.52-6.67% HA) and the center "sucker" bets (up to 16.67% HA).

All bets except the free odds are losing propositions for the player. The line bets are simply the best bets you can make.

The "hold" at a craps table is much higher than 1.41% - I don't have a source handy, but I think this is more like 15% of chips bought by players are won back by the casino. This is due to the higher HA bets and the way most people gamble -- I'm certain that most of us will play until a bet has lost. Even if we are ahead, we don't leave until the win streak ends, which means our last bet lost. If you only walked up to the table and made some fixed number of pass line bets and then left regardless of whether you were up or down, I think that after thousands of sessions you would see the 1.41% HA reflected in your bankroll.
goatcabin
goatcabin
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February 13th, 2010 at 9:26:06 PM permalink
Two people have supplied the correct answer, .0358 or so.

Suppose that a couple of million people all play 495 passline decisions. Their win-loss records will be distributed in the familiar bell-shaped curve, with 244 wins as the mean, or very, very close to it. Although coming out 244-251 is not very likely (odds of 27-1 against it), it is MORE likely than any other SINGLE W-L record. It's sort of like horse-racing odds: the favorite may go off at 3-1, but the other horses have longer odds. It's fairly rare for a horse to be an "odds-on" favorite, favored over the entire field. (Of course, horse-racing odds are not actually probabilities, or even the bookies' estimate of probabilities.)

The 1.4% is not a hoax. It is simply the difference between the probability of winning a passline bet and the probability of losing it.

.49293 - .50707 = -.01414

It's like you have a 495-sided die (remember Dungeon Dice?): 244 of the surfaces have a 'W', and the other 251 have an 'L'.

Actually, if you want to cover all the "bases" in integers, you need 1980 decisions, which I call the "perfect 1980):

440 comeout win
220 comeout loss
125 win on 6
150 lose on 6
125 win on 8
150 lose on 8
88 win on 5
132 lose on 5
88 win on 9
132 lose on 9
55 win on 4
110 lose on 4
55 win on 10
110 lose on 10
----
1980, of which 976 are winners, 1004 losers, 784 are seven-outs, so the probability of sevening out on any given bet is 784/1980 = .396

One can learn a lot by studying the "perfect 1980".
Cheers,
Alan Shank
Cheers, Alan Shank "How's that for a squabble, Pugh?" Peter Boyle as Mister Moon in "Yellowbeard"
goatcabin
goatcabin
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February 13th, 2010 at 9:34:59 PM permalink
Quote: goatcabin



440 comeout win
220 comeout loss
125 win on 6
150 lose on 6
125 win on 8
150 lose on 8
88 win on 5
132 lose on 5
88 win on 9
132 lose on 9
55 win on 4
110 lose on 4
55 win on 10
110 lose on 10
----
1980, of which 976 are winners, 1004 losers, 784 are seven-outs, so the probability of sevening out on any given bet is 784/1980 = .396



About the HA after a point is established. You can easily derive the correct numbers. Note that if you add up all the "win on n" and "lose on n" they sum to 1320. 1320 / 1980 = .667, so two thirds of the time a point is established, on average. Of those, there are 536 winners and 784 losers, so the weighted probability of winning a point (on the "right" side, of course) is 536 / 1980 = .406, the specific probabilities being .4545 on the 6/8, .4 on the 5/9 and .333 on the 4/10. However, on the comeout the pass/come has a 2:1 advantage, 440 to 220 (8 ways to win vs. 4 to lose). That is why, once you make a passline bet and a point is established, you cannot take the bet down or reduce it; it's a "contract" bet. It's also why you cannot make a don't pass bet after a point has been established. The casino is not going to let you "cherry pick" the stage of the bet where the player, not the casino, has an advantage.
Cheers,
Alan Shank
Cheers, Alan Shank "How's that for a squabble, Pugh?" Peter Boyle as Mister Moon in "Yellowbeard"
pocketaces
pocketaces
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February 14th, 2010 at 4:33:39 AM permalink
Quote: tuttigym

pocketaces: Yes, I want to know the chances, the odds, the probabilities of exactly having 244 wins against 251 losses in 495 PL outcomes.

You stated that it is "uncommon" but "it happens." That statement lacks specificity.
You stated that in a "million trials" "some" sets of 495 PL outcomes will show as 244/251. Those generalizations, "uncommon" and "some," are meaningless when players have their money at risk. The 1.41% HA is a finite number which many rely upon to be accurate. If the 244/251 is truly "uncommon," then that HA is going to increase often. So define "uncommon" and "some" in the context of your response. Gross generalizations can be costly. Kinda like Obama saying that the "stimulus" will work in the "long term." What is that?

tuttigym



OK, per above, 1 in 28. I was trying to speak in laymans terms since you seemed quite opposed to mathematical concepts.

Quote: tuttigm

No business can survive on a 1.41% gross profit which is what some are eluding to that might represent the HA. Businesses have operating expenses which far exceed the portions of gross profits posted by a business. The resultant amount becomes the net profit. That 1.41% might buy tiolet tissue for a casino for a week.



Except that each person will make many bets at that 1.41 percent rate, and the effect becomes cumulative. Again, you are applying one concept and trying to connect it to another different concept in an incorrect way. If every person who went to vegas made ONE bet at a 1.41 percent HA, vegas would be a bunch of tumbleweeds. But they don't, and the casino bases revenue from gaming from an individual on one main factor:

Your average bet, multiplied by the hands per hour, hours spent playing (can be a decimal below 1) and house advantage of the bet(s).

The 'hold' figure is based off this, and truly represents their potential profit per customer. It is far higher than the house advantage of one single bet.

Of course many bets are far more lucrative to the casino than 1.41 percent, but no table games offer much more than 5 percent on average and some (like blackjack) offer far lower. The constant churning of bets is the main thing that drives revenue on all of these games.
tuttigym
tuttigym
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February 14th, 2010 at 6:27:29 AM permalink
odiousgambit: The PL bet for the vast majority of players is used as a bridge to the FO bet. The PL bet in general is the smallest wager posted, i.e, $10 table with 10X odds - player bets $10 PL rather than any other higher wager to get to the 10X odds or less. (I know, there are those who bet higher and those who bet the Horn or Hard #'s) It has already been affirmed that at least 65% of the table action occurs after the point is established, and that is where the house exacts its "revenge" on the players who, in the beginning, had a one roll (Come Out) 2 to 1 advantage over the house. Do we have any disagreements to this point?

We all know that the 7 can be rolled more time than any other number, so once the point is established, PL/FO players chances of winning those bets diminish dractically. That so called 1.41% HA now becomes, depending on the point, up to a 67% HA which renews with every new point.

Based on the 244/251 1.41% HA, only about 22% of those PL bets are natural winners ( 7 or 11).
Why place yourself and your money at such a disadvantage with a contract bet? I know the FO bets are not contract, but they are never taken down once placed.

The coin toss examples that are illustrated actually increase the validity of my thoughts because while the odds are 50/50 and the probabilities for that exact outcome on a large sample are slim, there are still only two outcomes available at 50/50. The PL/FO outcomes have greater margins for loss and those margins renew with each point at various possible deficits advantages for the player.

The reason the house offers 10X or whatever is exactly because of that HA upward swing, and therefore, the so-called very low published HA wins create a false sense of well being in the player. After the point is established, the house ALWAYS has six ways to win, and the player has that many ways to lose which exceeds his opportunities to win on any given point (PL/FO).

For me, to answer your last question, once that point is established, I have up to 30 ways to win and only 6 ways to lose on any given roll of the dice. My betting starts then and I create betting patterns that will provide me more ways to win than to lose. Can one lose doing that? of course, it is called gambling. The difference for me is discipline.

tuttigym
tuttigym
tuttigym
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February 14th, 2010 at 6:39:20 AM permalink
JB: Okay. Now since we know that 65% of all table action is after the point is established, can you provide the HA for PL/FO bets based solely on winning and losing those bets to either point conversions or 7 outs?

Again, I recognize that the 1.41% HA exists based on the 244/251 PL outcomes, however, removing the Come Out naturals for both winning and losing or about 34% must necessarily skew those results heavily to the house side of the equation which renew with every point, right?

tuttigym
boymimbo
boymimbo
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February 14th, 2010 at 7:47:17 AM permalink
Let's take an total of 990 come out rolls. 220 of those will be the 7 and 11 "Naturals", 110 of those will be the 2,3,and 12 craps, leaving 660 points.

Of those 660 points:
- the point will be 6 or 8 on 10/24 combinations or 275 times. Of those 275 times, on average, the point will be rolled before the seven 125 times and the seven before the point 150 times for a loss of 25 units. With 275 units bet, that is a house advantage of (25/275) 9.0909%, on the points of 6 or 8.
- the point will be 5 or 9 on 8/24 combinations or 220 times. Of those times, on average, the point will be rolled before the seven 88 times and the seven before the point 132 times for a loss of 44 units. With 220 units bet, that is a house advantage of (44/220) 20%, on the points of 5 or 9.
- the point will be a 4 or 10 on 6/24 combinations or 165 times. Of those times, on average, the point will be rolled before the seven 55 times and the seven before the point 110 times for a loss of 55 units. With 165 units bet, that is a house advantage of (55/165) 33.333% on the points of 4 or 10.

When you add it all up, on 660 points, the point will come before the seven 268 times and the seven before the point 392 points. With a bet of one unit, you will lose a total of 124 units over 660 points, for a HOUSE advantage on a point being 124/660 or 18.7879%.

Of the other 330 rolls, you will win on average 220 - 110 units = 110 units of a player advantage of 110/330 = 33.3333%

The total house advantage then, for the table, is (110 - 124) / 990 = 14/990 or 1.4141%.

So, to recap, then, the HA on the 4 and 10 is 33.33%, not 50% or 67%, because out of 3 4 and 10 rolls, you will win one and lose 2 for a loss of 1/3. The HA on the 5 and 9 is 20%. The HA on the 6 or 8 is 9.09090%.

The free odds is used to lower the house advantage. Even though the point is working against you, the fact is the odds are paid according to the frequency of the dice. That is, for $1 odds on a 4 or 10, on three points of 4 or 10, you will win $2 once and lose $1 twice for an average loss on the odds alone of ZERO. That's why they are called "Free Odds".
----- You want the truth! You can't handle the truth!
seattledice
seattledice
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February 14th, 2010 at 9:11:30 AM permalink
Quote: tuttigym


For me, to answer your last question, once that point is established, I have up to 30 ways to win and only 6 ways to lose on any given roll of the dice. My betting starts then and I create betting patterns that will provide me more ways to win than to lose. Can one lose doing that? of course, it is called gambling. The difference for me is discipline.

tuttigym



I did not see where you explained your strategy which gives you 30 chances to win and 6 to lose. One way would be to bet across and on the horn after the point is established and take all place bets down after one roll.

This yields a HA = 2.3% which is effective on the larger amount you would be betting - $36 vs $5 for the pass line - so this method will give the house more of your money over the same period of time.

number bet win return # rolls out of 36 weighted return
4 5 9 41 3 123
5 5 7 39 4 156
6 6 7 39 5 195
8 6 7 39 5 195
9 5 7 39 4 156
10 5 9 41 3 123
2 1 30 63 1 63
3 1 15 48 2 96
11 1 15 48 2 96
12 1 30 63 1 63
7 0 0 0 6 0
total return 1266
total bet 1296
loss 30
HA 2.3%


You can make similar calculations for whatever startegy you employ.

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