Many of your questions can be answered by referring to the Wizard of Odds' website and following the "Craps" link under "Advice and Strategy": (http://wizardofodds.com/craps)

Specifically, the house edge on Don't pass is: 1.36%. On each $25 bet, you can expect to lose $0.34.

The house edge on a field bet that pays double on the two and the twelve is: 5.56%. On each $25 bet, you can expect to lose $1.39.

Quote:dihaigTHANK YOU. SO IT IS 5.56+1.36 DIVIDED BY TWO WHICH WOULD EQUAL 3.46% HA?

There's a lot more to evaluating craps strategy than figuring the HA, dihaig. Let's examine this strategy and compare it to just betting $50 on either the DP or the Field.

For 60 bets:

$25 each -- expected loss is about $104, standard deviation about $314, probability of breaking even or better about .37

$50 DP -- expected loss is about $42, standard deviation about $387, probability of breaking even or better about .46

$50 Field -- expected loss is about $167, standard deviation about $418, probability of breaking even or better about .34

By mixing in that Field bet, you not only more than double your expected loss, due to the high HA on Field when they don't pay any triple, but you also reduce your variance, which means you have to be luckier to overcome the expected loss. The only advantage is that you will lose less if you have bad luck to the extent of .85 SD, which you can expect to happen about 20% of the time. So, you have about a .8 probability of coming out ahead using just the $50 DP.

Cheers,

Alan Shank

Woodland, CA

Quote:goatcabinBy mixing in that Field bet, you not only more than double your expected loss, due to the high HA on Field when they don't pay any triple, but you also reduce your variance, which means you have to be luckier to overcome the expected loss. The only advantage is that you will lose less if you have bad luck to the extent of .85 SD, which you can expect to happen about 20% of the time. So, you have about a .8 probability of coming out ahead using just the $50 DP.

Cheers,

Alan Shank

Woodland, CA

I've always found it interesting that variance is the friend of the negative EV player, while it is the enemy of the advantage player. Similarly, variance is the casino's enemy (if Megabucks hits one more time in a year than it "should", the whole system will be deeply in the red), and lack of variance is its friend. This goes to the "best" strategy for the -EV player (aside, of course, from simply staying home), which is to make one massive bet and then walk away, win or lose.

That also points out why blackjack and other low -EV games are such consistent winners for the house. You can never win more than 3:2 on any bet, and usually, only even money. This means that the house endures very low variance. The house edge usually skyrockets as bets carry more and more variance (look at any crap table). Also, slots with bigger top jackpots have a larger hold. (That's why video poker is such a good game to play; the relatively modest 800-1 top jackpot for a royal flush means that the casino can tolerate a low house advantage.)

Quote:mkl654321I've always found it interesting that variance is the friend of the negative EV player, while it is the enemy of the advantage player. Similarly, variance is the casino's enemy (if Megabucks hits one more time in a year than it "should", the whole system will be deeply in the red), and lack of variance is its friend.

Well, that's simply because, if there were such a thing as an "advantage player", he/she would stand in the place of the casino, relative to random players. If you have an edge, you want to minimize variance.

Quote:mkl654321That also points out why blackjack and other low -EV games are such consistent winners for the house. You can never win more than 3:2 on any bet, and usually, only even money. This means that the house endures very low variance. The house edge usually skyrockets as bets carry more and more variance (look at any crap table).

Yes, you have to pay for more variance. I once saw a special about gambling on the History Channel, and a guy from UN, Reno, said exactly that: "You buy variance from the casino via the house advantage".

Of course, in the center of the craps table are some bets with very high vig and not much variance (Any 7), either. The house hates it when you bet 12 and parlay!

Cheers,

Alan Shank

Woodland, CA

Quote:goatcabinWell, that's simply because, if there were such a thing as an "advantage player", he/she would stand in the place of the casino, relative to random players. If you have an edge, you want to minimize variance.

Yes, you have to pay for more variance. I once saw a special about gambling on the History Channel, and a guy from UN, Reno, said exactly that: "You buy variance from the casino via the house advantage".

Of course, in the center of the craps table are some bets with very high vig and not much variance (Any 7), either. The house hates it when you bet 12 and parlay!

Cheers,

Alan Shank

Woodland, CA

This really isn't true however because odds bet have an extremely high variance.

Quote:TriplellThis really isn't true however because odds bet have an extremely high variance.

No, they don't, not compared to the 30-1, 15-1 bets. The standard deviations on the odds bets is pretty close to those on the place bets; compare:

SD place 6/8 1.0788

odds on 6/8 1.0954

SD place 5/9 1.1758

odds on 5/9 1.2247

SD place 4/10 1.3199

odds on 4/10 1.4142

SD on 12 5.0944

SD on 2 3.6650

(All expressed relative to the bet amount)

You can see all these numbers in the Configure/Advantage screen of WinCraps.

Cheers,

Alan Shank

Woodland, CA

Quote:goatcabinNo, they don't, not compared to the 30-1, 15-1 bets. The standard deviations on the odds bets is pretty close to those on the place bets; compare:

SD place 6/8 1.0788

odds on 6/8 1.0954

SD place 5/9 1.1758

odds on 5/9 1.2247

SD place 4/10 1.3199

odds on 4/10 1.4142

SD on 12 5.0944

SD on 2 3.6650

(All expressed relative to the bet amount)

You can see all these numbers in the Configure/Advantage screen of WinCraps.

Cheers,

Alan Shank

Woodland, CA

I don't think he gets what "variance" is. It could perhaps be expressed by the fact that a series of low-variance bets is unlikely to produce drastic positive or negative results; a series of high-variance bets is much more likely to do so.

Guess a number between 1 and 1000. If you win, I pay you 999-1. This is a high-variance bet. Guess whether the number is above or below 500. If you win, I pay you even money. This is a low-variance bet. Go on a date with my ex-wife. This is an extremely high-variance bet, and -EV to boot.