Math Help - Craps Average Bet Problem

Dear Wizard and All the Other Math Experts on this Site:

I have the following math related problem for you. I want to find out what my actual average craps bet is for comp purposes, not counting any of the odds bet.

Over this past weekend, I bet the following way in craps in Las Vegas:

The tables all had 3x, 4x, 5x odds. I would take full odds for every single bet (but again, the odds do not matter as they do not get factored in for any comps).

1. Pass line of $10.
2. Once point has been set, place the 6 and 8 for $60 each ($120 total). If the point is either 6 or 8, I would only place the opposite number for $60.
3. Come bet of $10 (continuous).
4. If a come bet moves to the 6 or 8, the place bet come down. Full odds taken on the new come bet.
5. Next come bet of $10 (continuous until the final 7 out).
6. ABSOLUTELY NO OTHER BETS MADE. Tips were handed in at various times.

If the point has been made, and the shooter rolls a 7 during the new come out roll, I would not place a new 6 and 8 (if they were now come bets).

I hope the above makes sense. The reason why I am so interested is that over this weekend I played at 5 MGM casinos (Mandalay Bay, Luxor, Excalibur, New York, New York, and MGM), with this exact same betting pattern. My average bet for the weekend was $140 (odds never factored in) over a period of 15 hours. Somehow, this number seems rather high for me, as the place bets are not working during any of the come out rolls, and 5/12 of the time, the point is either a 6 or 8, making me place only one number for $60. Finally, when the shooter rolls a 6 or 8, my come bet travels there, making the $60 place bet a $10 come bet.

I absolutely love comps. I fully understand that most casinos only comp players 25% to 30% of their expected theoretical loss on table games. If I am able to have a higher perceived average bet then my actual average bet, this may increase my comps to 40% or 50% of my expected theoretical loss.

Thanks for your help in advance. If someone could run a simulation of this in WinCraps for me, and share the results, that would be awesome too.

Quote: gambler

Dear Wizard and All the Other Math Experts on this Site:

I have the following math related problem for you. I want to find out what my actual average craps bet is for comp purposes, not counting any of the odds bet.

Over this past weekend, I bet the following way in craps in Las Vegas:

The tables all had 3x, 4x, 5x odds. I would take full odds for every single bet (but again, the odds do not matter as they do not get factored in for any comps).

1. Pass line of $10.
2. Once point has been set, place the 6 and 8 for $60 each ($120 total). If the point is either 6 or 8, I would only place the opposite number for $60.
3. Come bet of $10 (continuous).
4. If a come bet moves to the 6 or 8, the place bet come down. Full odds taken on the new come bet.
5. Next come bet of $10 (continuous until the final 7 out).
6. ABSOLUTELY NO OTHER BETS MADE. Tips were handed in at various times.

If the point has been made, and the shooter rolls a 7 during the new come out roll, I would not place a new 6 and 8 (if they were now come bets).

I hope the above makes sense. The reason why I am so interested is that over this weekend I played at 5 MGM casinos (Mandalay Bay, Luxor, Excalibur, New York, New York, and MGM), with this exact same betting pattern. My average bet for the weekend was $140 (odds never factored in) over a period of 15 hours. Somehow, this number seems rather high for me, as the place bets are not working during any of the come out rolls, and 5/12 of the time, the point is either a 6 or 8, making me place only one number for $60. Finally, when the shooter rolls a 6 or 8, my come bet travels there, making the $60 place bet a $10 come bet.

I absolutely love comps. I fully understand that most casinos only comp players 25% to 30% of their expected theoretical loss on table games. If I am able to have a higher perceived average bet then my actual average bet, this may increase my comps to 40% or 50% of my expected theoretical loss.

Thanks for your help in advance. If someone could run a simulation of this in WinCraps for me, and share the results, that would be awesome too.

Many times while at the casino, just ask the supervisor at the table for your average bet.

Example:
I start with $1/fire, $12/6 for every shooter, drop $4 after 1st win to make $30/6, after another win, I take $1 change and ask dealer to place all the numbers for $64 across and call same bet and collect winnings. I do this for every shooter and just play $5/fire when i'm shooting.

After 6hrs of play my average bet shows $35.00 and I also qualify for $20 food comp from the players club.

Just curious, after playing 15 hours at 140 with no odds factored in, do you know how many player points you earned? Did you check?

Quote: CrapsGenious

Many times while at the casino, just ask the supervisor at the table for your average bet.

Example:
I start with $1/fire, $12/6 for every shooter, drop $4 after 1st win to make $30/6, after another win, I take $1 change and ask dealer to place all the numbers for $64 across and call same bet and collect winnings. I do this for every shooter and just play $5/fire when i'm shooting.

After 6hrs of play my average bet shows $35.00 and I also qualify for $20 food comp from the players club.

Oh, I do ask the supervisors for what they believe my average bet is. They stated their opinion (on average) that my bet is $140. However, that is not my question. I want to find out what my actual average bet is. And that is where I need math help.

removed
silly

I love comps too but would trade them all for just another Royal Flush on $1 VP
Sally

I know almost nothing about average bet on craps calculations. The first thing that's variable is some bets ride, some bets are 1 roll propositions, and some bets are added after the come-out roll, odds added later, variable rolls until establishing a come point. The hand itself can go 0, 5. 20, whatever rolls before point resolution. So, mathematically, I don't know how you could calculate an average bet, even with firm bet parameters, beyond an estimation of probability.

One can imagine the poor Boxman and Floorman who have other tasks to perform and only keep track of a player's betting when able to.

The one thing that interests a casino is the amount of his action. What does he take from his wallet and actually put down on the table.

140 seems a pretty good estimate. Each of those come bets would add to the money but a P-SO or a very short roll would take away from the total.

I think they just consider he has 140 at risk ... and if sometimes its a long roll and sometimes its a short roll... its the way the game goes.

His Action is PASS LINE, PLACE BETS, COME BET ... which is 140.

NOT a particularly good way since it ignores the ODDS money, the multiple Come Bets, etc. but most places calculate it that way.

Quote: FleaStiff

One can imagine the poor Boxman and Floorman who have other tasks to perform and only keep track of a player's betting when able to.

The one thing that interests a casino is the amount of his action. What does he take from his wallet and actually put down on the table.

140 seems a pretty good estimate. Each of those come bets would add to the money but a P-SO or a very short roll would take away from the total.

I think they just consider he has 140 at risk ... and if sometimes its a long roll and sometimes its a short roll... its the way the game goes.

His Action is PASS LINE, PLACE BETS, COME BET ... which is 140.

NOT a particularly good way since it ignores the ODDS money, the multiple Come Bets, etc. but most places calculate it that way.

In my opinion, flea is spot on. They will take your original P/L wager, your original place bets and your original come bet, make an estimate and stick it in your rating. What can happen (and quite often does) is the floor person only hawks your first bet of your session and then comes back and watched a later bet, perhaps 10, 15, 20 minutes after your start. This may be at the end or middle of your session. On order to get a more accurate average bet, these bets should be stuck into the computer once every 5 to 10 minutes or so. This isn't always practically possible because the floors are busy or lazy (not all of them obviously).

I think $140 seems fair and it is very close to your actual average bet if yous action remains the same for every roll you are in the game.

As Tom says, they are going to watch your first bets that you make. So if the first point was not a 6 or 8, they will see $10 P/L, $120 Place bets, and $10 CB. At the places I play, they come around every 15 minutes and glance at the felt, but they rarely change the bet amount, unless they notice it is consistently lower than what they have. And if the floor is busy, you might get a break on the fact they don't remember that you were low the last two times they looked.

In reality the 6 and 8 are going to be points fairly often, and each one means a $50 reduction in your bets.

Your worst avg bet case is the point of 6, and your first CB is an 8. That would give you $20 on the table.
Your highest avg bet case is PL and CB on 4,5,9, and 10, with $120 on 6/8, for a max of $160.

So yeah, getting a $140 rating is pretty generous.
My guess is once you factor in how many times the 6 and 8 would be a PL or CB point, I bet your real avg is closer to $100, maybe even slightly lower.

Quote: RaleighCraps

In reality the 6 and 8 are going to be points fairly often, and each one means a $50 reduction in your bets.

Your worst avg bet case is the point of 6, and your first CB is an 8. That would give you $20 on the table.
Your highest avg bet case is PL and CB on 4,5,9, and 10, with $120 on 6/8, for a max of $160.

So yeah, getting a $140 rating is pretty generous.
My guess is once you factor in how many times the 6 and 8 would be a PL or CB point, I bet your real avg is closer to $100, maybe even slightly lower.

Thanks everyone. I figured that the $140 rating was generous. Since I also take full odds, that probably helps to gives the appearance that I have more calculated action then I really have.

I used to be a straight $25 pass line (full odds), $25 always come bettor (full odds) and would receive an average bet of $100. I felt that is rating was extremely accurate by the boxman or the pit staff and there was no potential for an inflated rating. It was simply too easy to calculate. This style of betting required a larger bankroll then my current action of a $10 pass line (full odds) with the 6 and 8 place bet for $60 and $10 coming (with odds) continuously. Yes, I understand that the pass line/come bet had a house advantage of 1.414% while the 6 and 8 place bet has a house advantage of 1.515%, but I also figured that the place bet also has no action on a come out roll, thus negating that difference.

I was hoping that one of the math geniuses on this site would be able to help me calculate what my actual average bet would be. Perhaps this is too hard to do mathematically. I really don't know if it could even be done, but I just figured that if there was a forum to ask, it would be here on the Wizard of Vegas.

While I am fully aware that there is no "system" that can eliminate the house advantage in craps, I am looking for a way to increase my perceived value to the casino in terms of comps. If my average bet is really approximately $100 and they rate me at $140, my comps are better. Essentially, if they comp 30% of my theo, I am essentially greeting a 42% comp on my theo thanks to the inflated rating. For me that is a win in my book.

I think it is relatively easy to do, for the math heads.
I think it will come down to there are 24 ways to set a point.
5 of 24 ways to set a point of 6,
5 of 24 ways to set a point of 8,
4 of 24 ways to set a point of 9,
4 of 24 ways to set a point of 5,
3 of 24 ways to set a point of 4,
3 of 24 ways to set a point of 10.

So 5/24 = ~20% of the time your point is 6
40% of the time your point is 6 and 8
32% of the time your point is 5 and 9
28% of the time your point is 4 and 10

I think this is correct, but how to apply it from here is the tricky part. I will just embarrass myself if I try to do any more of the math. Heck, I wonder if there is a rule against having the most inept math formulas ever posted.

Quote: gambler

I was hoping that one of the math geniuses on this site would be able to help me calculate what my actual average bet would be. Perhaps this is too hard to do mathematically. I really don't know if it could even be done, but I just figured that if there was a forum to ask, it would be here on the Wizard of Vegas.

of course it can be done if some one has the interest and drive to do it.
And one needs to define exactly what an average bet is.
You seem to want total $ bets at risk per roll.

RC started the process.
You have to figure in the average number of come points active (3.375) with odds per roll and the times the place bets are both active and only when one is active and when both are not active and the pass and come bets active. Multiply the probs with the $bet and add them all up.

I start with a sim first so I can see where my math should be headed too.
so I added a few lines of code to WinCraps
my teeth feel so much better today after a night of dancing

I tallied the
1) total $ bet per roll at risk (1500 rolls is what I used) no count of place bets or come odds bets on come out roll
I also tallied the
2) total at risk not counting the odds bets (just because some do not count them for comps - this matters not to me)
and ran it a million times to get a mean and a standard deviation

1) avg $bet at risk: 168.93
mean: 253,393.22 (at risk 1500 rolls)
Std Dev: 6,667.76 (interesting value)

2) avg $bet at risk: 112.25
mean: 168,367.85
Std Dev: 3,294.56 (less interesting value)

an interesting average between both

Sally