Odds for craps
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Why spend 2-3 hours standing around a table? It only takes a minute and $2 to buy a PowerBall ticket. What about those odds? Do you really think there will be the exact number of winners in each drawing as calculated by the statisticians? It's all about luck and the right numbers showing up to get you $123 Million next week. It's all good if you are winning the lottery jackpot; the odds are just "crap".
Hey, if the OP has something better, lay it all out.
Quote: champ724well 180 rolls in an hour is extreme in the first place thats a roll every 20 seconds the record is 150 4 or 157 rolls that took 4 hours and 18 minutes
With 4 players at a table, I don't think 1 roll every 20 seconds is extreme. If something out of the ordinary happens, like a 1 hour roll, or super heavy action the dealers can't handle or weird action, then 180/hour isn't going to happen.
The monster 4 hour roll probably got jammed up like a mother f***er. Just making a wild stab in the dark here, but I'm guessing 8 people on both sides, perhaps more. Really big action all around the table, come bets, place bets, line bets, and of course the prop box. Not to mention the dealers probably had a good amount of action on the table, as well. And of course, plenty of whooping and hollering, which slows the game down, because people don't pick up their bets quickly.
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Quote: Gman711All these odd about craps --to me is just crap. Odds are over a duration - whatever that is. If four players are at a table for a hour it is estimated that there will be about 180 rolls of the dice. Do you really think there will be 30-7's, 25 each of the 6 & 8, 20 each of the 5 & 9, 15 of the 4 & 10, 10 of the 3 & 11, and the 2 & 12 rolled 5 times? That is what the odds are for 180 rolls. I am there for only a short time 2-3 hours and not a duration. How many times have you seen the same number repeat 3-4 times or more in a row. What about those odds? It's all about luck and the "7" not showing up! All the best are good if you are winning.
Gman711, I agree with you. In fact, I believe the Wizard himself must also agree with you that odds and his own advice about playing full odds are crap because he never does it. The point is, there is theory and then there is reality. Even the theoretical rolls per hour are far from reality on any given table depending on the given circumstances.
If you would have been down at the Golden Nugget in downtown Las Vegas this past weekend and charted the tables for over 14 hours, you would have seen more 7s than statistically possible with balanced dice. Theoretical odds are based upon balanced dice. The Golden Nugget was not paying true odds based upon the dice they were using. (Can't wait for those smart-ass answers to say play the Don'ts -- That's not the point. Tell Tom Brady it doesn't matter if he plays with properly specified balls or not.)
Quote: BohemianGman711, I agree with you. In fact, I believe the Wizard himself must also agree with you that odds and his own advice about playing full odds are crap because he never does it. The point is, there is theory and then there is reality. Even the theoretical rolls per hour are far from reality on any given table depending on the given circumstances.
If you would have been down at the Golden Nugget in downtown Las Vegas this past weekend and charted the tables for over 14 hours, you would have seen more 7s than statistically possible with balanced dice. Theoretical odds are based upon balanced dice. The Golden Nugget was not paying true odds based upon the dice they were using. (Can't wait for those smart-ass answers to say play the Don'ts -- That's not the point. Tell Tom Brady it doesn't matter if he plays with properly specified balls or not.)
Did you chart the numbers for 14 hours? Can you provide the data so that your claim that it was statistically impossible to roll that many 7's with balanced dice?
The edge the house has is based upon not paying the correct odds on most bets, not on unfair dice. They have an advantage over every player on every roll. If someone hits a bunch of 7's, it can be a good thing or a bad thing for the players based on what their bets are and when in the playing cycle they roll a 7. Lots of 7's on the "right side" bets coming out can be great...lost of 7's on the same side that come quickly after a point roll can be a disaster.
The best thing for the house is to have fair dice. They have an an advantage that no combination of bets can overcome over time. If they used unfair dice, how would they be assured that the 7 would show up enough to help their side? What if a 6 or 8 showed up more often than 7? Those could be bet with an advantage.
I was on a table this weekend where more 12's were rolled than would be seen if the dice rolled exactly as expected. I was betting $5 on the 12 on come out rolls. I made some money that session. Thing is, I've seen that same bet lose every time I made it, too. The house collects a huge "tax" or "edge" when I win by not paying the bet at true odds. They don't need biased, unbalanced dice to do so.
...but I've said nothing that is any different than others say. I guess I'd just like some proof that "unbalanced dice" are really a problem. Are they all perfectly balanced? No. Does the imperfection impact play? My thought is that if it did, it would be unpredictable...and the house would not like it any more than the payers.
Quote: RonCDid you chart the numbers for 14 hours? Can you provide the data so that your claim that it was statistically impossible to roll that many 7's with balanced dice?
RonC, I saw the charts. They are proprietary information and I do not have the authority to share them here. Don't take my word for it, obtain and test the data yourself.
Quote: RonCThe best thing for the house is to have fair dice. They have an an advantage that no combination of bets can overcome over time. If they used unfair dice, how would they be assured that the 7 would show up enough to help their side? What if a 6 or 8 showed up more often than 7? Those could be bet with an advantage.
RonC, I could not agree with you more! Unbalanced dice will favor several numbers to the detriment of other numbers. In any event, the actual odds are adjusted so that the HA increases overall unless you know exactly what the imbalance is - who knows that except the casino and father time.
Quote: RonCI was on a table this weekend where more 12's were rolled than would be seen if the dice rolled exactly as expected. I was betting $5 on the 12 on come out rolls. I made some money that session. Thing is, I've seen that same bet lose every time I made it, too. The house collects a huge "tax" or "edge" when I win by not paying the bet at true odds. They don't need biased, unbalanced dice to do so.
...but I've said nothing that is any different than others say. I guess I'd just like some proof that "unbalanced dice" are really a problem. Are they all perfectly balanced? No. Does the imperfection impact play? My thought is that if it did, it would be unpredictable...and the house would not like it any more than the players.
RonC, exactly. Consider First that casinos can change the dice imbalance from shift to shift and table to table so that you do not know what to bet to your advantage. 12s are a good bet 1 day and the next day they may include a larger HA by design. It's Marketing 101 to switch and bait for the unsuspecting casual weekend craps player that was getting wins on his 12s Friday night so he loads up on the 12 the next day with different dice only to find out the HA on the 12 has changed and no 12s are to be found.
Consider Second:
Quote: BohemianBiased dice or Unbalanced dice are Percentage Dice that increases the casino house edge in craps.
John Scarne describes Percentage Dice on page 209 of his book Scarne on Dice. Scarne explains that whoever is using percentage diceQuote: John Scarne" doesnt have a sure thing, but he has a percentage in his favor that pays off in cash.
If the dice roll long enough, The victim (player) loses because he is playing against two opponents
the cheat (casino) and that invisible but very dependable and powerful gentleman: Old Time Percentage.
Percentage dice, not on the level "
Quote: RonCThe best thing for the house is to have fair dice. They have an an advantage that no combination of bets can overcome over time. If they used unfair dice, how would they be assured that the 7 would show up enough to help their side? What if a 6 or 8 showed up more often than 7? Those could be bet with an advantage.
Keep in mind that, if it's a question of changing the probability of rolling a 7, then both dice have to be unbalanced. If one die is fair, then the probability of rolling a 7 with a pair of dice will always be 1/6.
Let P1, P2, P3, P4, P5, and P6 be the probabilities of rolling a 1, 2, 3, 4, 5, and 6, respectively, on an unbalanced die, and assume the other die in the pair is fair.
Regardless of how the die is balanced, P1 + P2 + P3 + P4 + P5 + P6 = 1.
There are six ways to roll a 7; these are {1,6}, {2,5}, {3,4}, {4,3}, {5,2}, and {6,1}, where the first number is on the unbalanced die and the second is on the fair die.
The sum of the probabilities is (P1 x 1/6) + (P2 x 1/6) + (P3 x 1/6) + (P4 x 1/6) + (P5 x 1/6) + (P6 x 1/6) = (P1 + P2 + P3 + P4 + P5 + P6) x 1/6 = 1 x 1/6 = 1/6.
Think about it. No matter what number shows up on the unbalanced die, only one number on the fair die (7 minus the unbalanced die's number) will make the total a 7, and there is always a 1/6 chance of rolling that number.
How many "more 7's than statistically possible"? Even a rough guesstimate helps, as it will be a factor in how much bankroll to bring.Quote: BohemianIf you would have been down at the Golden Nugget in downtown Las Vegas this past weekend and charted the tables for over 14 hours, you would have seen more 7s than statistically possible with balanced dice.
Quote: ThatDonGuyKeep in mind that, if it's a question of changing the probability of rolling a 7, then both dice have to be unbalanced. If one die is fair, then the probability of rolling a 7 with a pair of dice will always be 1/6.
Let P1, P2, P3, P4, P5, and P6 be the probabilities of rolling a 1, 2, 3, 4, 5, and 6, respectively, on an unbalanced die, and assume the other die in the pair is fair.
Regardless of how the die is balanced, P1 + P2 + P3 + P4 + P5 + P6 = 1.
There are six ways to roll a 7; these are {1,6}, {2,5}, {3,4}, {4,3}, {5,2}, and {6,1}, where the first number is on the unbalanced die and the second is on the fair die.
The sum of the probabilities is (P1 x 1/6) + (P2 x 1/6) + (P3 x 1/6) + (P4 x 1/6) + (P5 x 1/6) + (P6 x 1/6) = (P1 + P2 + P3 + P4 + P5 + P6) x 1/6 = 1 x 1/6 = 1/6.
Think about it. No matter what number shows up on the unbalanced die, only one number on the fair die (7 minus the unbalanced die's number) will make the total a 7, and there is always a 1/6 chance of rolling that number.
ThatDonGuy, I don't believe your post is true except in theory, not reality. 2 fair dice give you 1/6 chance of rolling a 7.
If 1 die is fair, that is 1/6 chance mixed with an unbalanced die that may be skewed to a certain 4 axle of numbers that will result in certain biases.
The combination of 1/6 and say 1/4 (or 25% of the time) does not equal 1/6 of 7s.
If certain numbers keeps occurring more often on the unbalanced die, then a certain bias will show in the results. Nowhere does that equal 1/6 in reality.
Quote: BohemianIf 1 die is fair, that is 1/6 chance mixed with an unbalanced die that may be skewed to a certain 4 axle of numbers that will result in certain biases.
The combination of 1/6 and say 1/4 (or 25% of the time) does not equal 1/6 of 7s.
If certain numbers keeps occurring more often on the unbalanced die, then a certain bias will show in the results. Nowhere does that equal 1/6 in reality.
Don't be silly.
Just for kicks, lets assume an "unbalanced" die that is so far off kilter that the "1" pip shows every single roll. If the other die is completely fair, there is still 1/6 chance that the total will be 7. The same is true if the unbalanced die has a preference for two particular faces, or three or four or even all six. So long as the other die is fair, the probability of the total being 7 is always 1/6.
Oh, I suppose in the extreme you could have an unbalanced die that always lands on an edge or a point so that it is a no roll every time, but if it lands with a single face up and stays on the table in a good-roll area, the probability holds.
Quote: BohemianThatDonGuy, I don't believe your post is true except in theory, not reality. 2 fair dice give you 1/6 chance of rolling a 7.
If 1 die is fair, that is 1/6 chance mixed with an unbalanced die that may be skewed to a certain 4 axle of numbers that will result in certain biases.
The combination of 1/6 and say 1/4 (or 25% of the time) does not equal 1/6 of 7s.
If certain numbers keeps occurring more often on the unbalanced die, then a certain bias will show in the results. Nowhere does that equal 1/6 in reality.
Really? Let's do the math with numbers rather than variables so you can see the quantification. Suppose you can guarantee that on one die, the 1 or 6 faces never show. That die has a face distribution of 2,3,4,5 with 25% chance of each.
How many ways are there to roll a 7? Only four. I'll list them out starting with (fair die, biased die) and then calculate the probabilities of each.
2, 5: Probability is 1/6 * 1/4 = 1/24
3, 4: Probability is 1/6 * 1/4 = 1/24
4, 3: Probability is 1/6 * 1/4 = 1/24
5, 2: Probability is 1/6 * 1/4 = 1/24
Add them up: 4*1/24 = 1/6.
Make sense?
Edit: while I was typing, Doc also replied. I recommend actually noodling with the numbers and try to find a pattern of bias for a single die that would, in combination with a fair die, lead to the probability of 7 being something other than 1/6. You won't be able to find one, but go ahead and try. The key insight is that as long as the number on the biased die is an integer in the range 1..6, it doesn't matter what it is. It's got to be something, and that something plus another number selected with equal likelihood from the fair 1..6 die will total 7 exactly 1/6 of the time. The only way it doesn't work is if the "biased" die has other data on it, like 8 or 20 or the queen of hearts.
Quote: ThatDonGuyKeep in mind that, if it's a question of changing the probability of rolling a 7, then both dice have to be unbalanced. If one die is fair, then the probability of rolling a 7 with a pair of dice will always be 1/6.
Think about it. No matter what number shows up on the unbalanced die, only one number on the fair die (7 minus the unbalanced die's number) will make the total a 7, and there is always a 1/6 chance of rolling that number.
Yep. One unbalanced die, and the game favors either the high or low numbers, but the 7 is still 1/6.
But it makes me wonder... If the Field pays triple on either 2 or 12 but not both, why is it always the 12? Combined with the no field 5, the Field bet becomes a big player advantage when the die are unbalanced towards the high numbers.
