An Odds ? for the Mathmatically Gifted

Whoson1st · Dec 12, 2004

A couple of days ago the old craps bug hit me big time and I had to play. My favorite way is to play the #6 and #8 at the same time against the 7. (When either hits they both come down until the 7 shows. They "work" on the come-out.)

My question is: What are the odds of 8 --#7's showing up before eith the 6 or the 8? (Now, understand I'm not talking about 7 shoing up on 8 straight results of the dice. Just 7 showing up 8 times before either the 6 or the 8?

----------------------------------------------------------------------------
May all have a good day.

DarrylParsons · Dec 12, 2004

A) The probability of a 7 occurring on a given roll is 6/36

B) The probability of a 6 or an 8 occurring is 10/36

C) The probability that a 7 occurs GIVEN THAT a 6,7,or 8 occurred is 6/16

The event you're talking about requires event C to occur 8 times in a row and the probability of that is simply (6/16)^8 or 0.000391 or 1 chance in 2557.

kermit16 · Dec 12, 2004

Both the 6 and 8 can come up in 5 different ways each while the 7 came come up 6 different ways. Therefore if you combine both the 6 and 8 you come up with 10 chances to 6 for the 7 or 10/6 The 7 can come up with 6-1,5-2,4-3,3-4,2-5,1-6 for the 6 chances The answer is that buying the 6 & 8 is not a good deal for the player but an excellent deal for the house. A better situation is simply to take the pass or come out line and take odds on the number.

Note the 8 can be made with 6-2.5-3,4-4,3-5,2-6 while the 6 can be made with 5-1,4-2,3-3,2-4,1-5 both adding up to 5 chances/

Whoson1st · Dec 12, 2004

Darryl Parsons said:
A) The probability of a 7 occurring on a given roll is 6/36

B) The probability of a 6 or an 8 occurring is 10/36

C) The probability that a 7 occurs GIVEN THAT a 6,7,or 8 occurred is 6/16

The event you're talking about requires event C to occur 8 times in a row and the probability of that is simply (6/16)^8 or 0.000391 or 1 chance in 2557.

Over 2500 to 1. LOL! (It happened to me yesterday. I need my ass kicked for thinking even for half a second, these on-line games are fair even at the so --called Casino only places.)

Thanks Parsons.

kermit16 · Dec 12, 2004

The house has a 1.5 percent advantage over the player if you simply play nothing but the pass or come bet. You can reduce this advantage even more by taking odds on the number. However buying the 6 or 8 or both increases the house advantage from 1.5 % to a huge 9.1 % advantage for the house. Not too clever a move IMO !

WildBill · Dec 12, 2004

Who buys the 6 or 8??? Placing either one is a 1.52% house edge, almost the same as the line bets. The only advantage for the line bets is you can bet your odds. But say you wanted to bet $24 on the 6 or you were going to bet $25 on the line and whatever in odds, really doesn't matter. Both bets will yield almost the same house edge in theory, either 35 cents for the line bet and 36 cents for the '6'. The house loves it when you talk about how line bets with odds lowers your edge. Odds don't make a bit of difference to them, unless you are betting astronomical amounts where a hot run hurts them. That is why most craps tables have distinct rules limiting amounts they will pay out for odds bets.

kermit16 · Dec 12, 2004

Wild Bill,
I have seen many players buying the Big 6 or 8. Placing the 6 or 8 gives the house the 1.52 percent you mentioned. But I disagree that the house percentage remains the same when you bet the pass or come and take double odds. The return on the extra odds is exactly even while the original bet has a 1.4 house advantage. Playing double odds reduces the house percentage to .60 %. I will take this as if the dice get hot you can win with less than a 1 % house advantage.

WildBill · Dec 12, 2004

Kermit, you fall for the same trap casinos hope you do. Yes the odds theoretically fall, but all the house cares about is how much are you going to bet on the line. The fact that edge drops is meaningless; what matters if how much the house wins. The only way it matters is say you were a die-hard numbers bettor and one day you decided to change to betting the line with odds. The $30 bets on the 6 and 8 now become $10 line bets with $50 odds. Then indeed you are better off, but you could use that logic further and say why not take the $60, leave it in my pocket, and go home. Believe me the house loves it when people talk about how the edge percentage is reduced, it first brings people to the table and then gets them to bet more money than they might have planned.

Whoson1st · Dec 12, 2004

Yes--I was "placing" the 6 and the 8. (without a line bet). $6 on 6 or 8; returns $7. profit for either.$12 on 6 or 8 returns $14. profit, etc.

It's a bad bet---and another lesson learned. 2500 to 1 shot for 8 straight losses. Now that's a little hard to take.

On line Casinos---JUST Say NO. (I need to listen to my own advice)

kermit16 · Dec 12, 2004

Wild Bill,
Once again I have to differ with you on this one. The house is not doing cartwheels when Dice throwers are taking the odds. The house has no advantage on the money that is bet on the extra odds. This is no sucker bet and it does give the thrower a better percentage overall ! Every Mathematician I know will tell you that taking the odds is the correct play and is not a sucker bet !

DarrylParsons · Dec 12, 2004

I remember Binion's Horseshoe offering 100x odds at one time, so you could plop down a $500 bet with a house expectation of $0.07 -- that's right, 7c on $500. Not a bad deal if you ask me. Bet $500 on anything else and you have hosts slobbering all over you offering you show tickets, free rooms etc. Do it using 100x odds and you won't even get a free hot dog after 4 hours of play.

Voodoo · Dec 12, 2004

>>This is no sucker bet and it does give the thrower a better percentage overall !
Every Mathematician I know will tell you that taking the odds is the correct play
and is not a sucker bet ! <<

It's not a sucker bet but it IS a nothing bet. Your expected loss on the pass
line is the same whether you take odds or not. Some people think they are
somehow lowering the house edge but they aren't. If you get rated on the odds
bet than it is worthwhile. Most places don't credit the odds bet so it's a waste
of time. Like flipping a coin.

kermit16 · Dec 13, 2004

Once again, you guys are missing the point so let's try another viewpoint. Let's say that the gambler was putting $ 100 on the line and He intends to put another $ 200 as odds when He receives his point. He is a gambler that is intending to wager $ 300 on his point, right ! However, if He simply puts his $ 300 on the line, when the number is hit, He will receive less than if He takes the point and adds the $ 200 as odds. Simple ! Why does He receive more ? House take is .6 of 1 % instead of 1.4 % It is true that the $ 200 odds bet is even $$ but it lowers his overall negative percentage of house advantage.

WildBill · Dec 13, 2004

Kermit,

Have you ever worked for a casino's strategy staff? Do you really know what the wonks upstairs are thinking. I have given you plenty of clues to the thinking going on. I have been in a number of table games strategy meetings in my past and the odds discussion came up almost every time we talked about craps. Trust me here, the free odds is just a great ploy set up to get people to play and bet higher than they would normally do so. Look at the psychology of everyone talking about "best bet in the casino". That stuff drives action, just like advertising who hit jackpots in your casino. All part of a carefully orchestrated plan.

If you really think the casinos hate to give free odds, well continue believing that if you wish.

kermit16 · Dec 13, 2004

Wild Bill,
Whether or not the Casino you worked at loved the Gamblers that took the odds, the simple fact remains that if a guy bets $ 5 and takes 100/1 odds and bets an extra $ 500 on the odds, the Casino has 0 advantage over this player on the extra $ 500 wager. This is not a winner for them and they are not getting more cash in their pockets. However if the gambler is a $ 500 gambler, He has a far better chance of winning than playing it all at the minus 1.4 percent house advantage. The house only has a 1.4 percent advantage on his measly $5. original wager. If you can't see that, I give up. I really don't care what the Casino Brass were telling you because no matter how you want to cut it, they have 0 advantage on the extra money put on the odds. Bet the line and lose at a - 1.4 rate...It's your choice.

christof · Dec 13, 2004

kermit16 said:
Whether or not the Casino you worked at loved the Gamblers that took the odds, the simple fact remains that if a guy bets $ 5 and takes 100/1 odds and bets an extra $ 500 on the odds, the Casino has 0 advantage over this player on the extra $ 500 wager. This is not a winner for them and they are not getting more cash in their pockets. However if the gambler is a $ 500 gambler, He has a far better chance of winning than playing it all at the minus 1.4 percent house advantage. The house only has a 1.4 percent advantage on his measly $5. original wager. If you can't see that, I give up. I really don't care what the Casino Brass were telling you because no matter how you want to cut it, they have 0 advantage on the extra money put on the odds. Bet the line and lose at a - 1.4 rate...It's your choice.

I would think this would be the best bet if a gambler had to bet $505 on something, but it is still not a good bet. Would you bet $500 at even money that a coinflip comes up heads? If so bet all the odds you can. If you can't get comps for this, then I'll just stick to plus EV bets (poker, sports).

Along the lines of what WildBill said, the casinos bankroll is practically infinite, while a bettor's is not. Over the long run, a casino will get the money, even on a neutral EV bet.

WildBill · Dec 13, 2004

If only those players existed Kermit. You would be hard pressed to find them and when you do you will find guys who are accomplished advantage bettors in most cases. This is literally the only "gambling" they do.

As Darryl pointed out they got free drinks from the cocktail girl and nothing else. People that are willing to put $500 on a hand either don't care about the money on the table, or care about it too much to make a bad bet. The first group bets on everything, the second group rarely bets on anything. The big odds often are what it takes to get these two segments to the craps table.

kermit16 · Dec 13, 2004

Wild Bill,
We know that the craps is a huge money maker for the Casinos as there is no bet on the board that is a Mathematical winner. There are a number of games in Video Poker like Full Pay Deuces Wild etc that the advantage lies with a skilled player as is also the case with Blackjack if an expert knows the correct play etc.
Why is Craps such a winner ? Easy answer. The game is very fast placed with players betting hard ways, Box Cars, Snake eyes, place across the board etc. Yes, there are those tourists that even buy the very convenient placed 6 and 8's, field bets. All of these wagers are sucker bets with house advantage ranging from 5% to as high as 16 %. I can give you the ugly percentages on every wager if you want but I can assure you that there is not a single bet where the house is at a disadvantage. You can always hear the stick man yelling..... Your hard ways are down... bet em hard !
However, I will give you a reason why the Casino bosses might want the player to take odds and it has nothing to do with the Casino having any mathematical advantage. It is more to get the player to dig into his wallet and trade all those $ 100. bills for chips. Once a player has chips, He is likely to remain until his chips are gone. Give even an experienced player enough drinks and you might see him throwing $$ down for a hard way bet for the boys etc. Smart business for sure.

Whoson1st · Dec 13, 2004

One thing I notice about comps at the craps table. Take a guy like me, who will buy chips and play on and on and grinding. Up down slowly up slowly down. No Major BIG bets but steady and "in-action" with most all of the rolls--I got comped three nights room at Harrah's yeras ago (NJ).

Now--I would see a big player come to the craps table buy maybe $1500. worth of chips and be broke (or appear to be in 30 minutes or less). Another guy say would buy in with the same amount and in 30 minutes or so---make a nice score and walk away. Neither of these type players appeared (to me) to get any comps!

Of course that was years ago. My point is that the casinos--prefer the player who is a "grinder" rather than a shot taker. At least as for as comps go. I could be totally wrong. Just my observation.

tuleythetout · Dec 14, 2004

Even if offering true odds lowers the house edge, etc., it must be in the house's advantage. How do I know this? Because the house offers it.

If the casinos felt they were losing money (either in short or long term), you can be damn well sure that they wouldn't continue to offer it. They'd make players lay 11-10 or something, so I side with WildBill's "carefully orchestrated plan" theory.

But enough of math questions, Whoson1st, what I want to know is . . . who's on first???