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Gambling/Craps odd and hedging


Can you explain to me lets say odds of 3x-4x-5x and also a good way to hedge bets would it be best with a large dont come to have money on the table for a good shooter?


Thanks for your craps question.  Let me see if I understand each part of your question by taking them one at a time.

Q) Can you explain what is meant by odds, specifically 3x-4x-5x?
A)  The odds bet is the only house bet in the casino with an expected value (EV) equal to zero.  This means that you nor the house have any mathematical advantage on this type of bet.  Remember, all other bets, such as the field, hard ways, and pass line, have a negative EV (-EV), which represents the house advantage.  This makes the odds bet the best bet for the player in the entire casino.  So, what is an odds bet?  The odds bet is the extra bet the casino allow players to make on Pass Line and Come bets (as well as Don't Pass and Don't Come bets).  The "3x-4x-5x" means that for points of 6 and 8 (the easiest points to make) your odds bet can be up to 3x your initial Pass Line bet (or Come bet).  

Example: Your Pass Line bet is $5.  The shooter rolls an 8.  Anytime after the point of 8 is established you may place an odds bet of up to $15.  Odds bets are placed a few inches behind your Pass Line bets or handed to the dealer if you've made a Come bet.  Let's assume that you make an odds bet of $15.  Now let's continue our example.  The shooter eventually rolls his point of 8.  The dealer will pay you $5 on your initial Pass Line bet, but since the "true odds" of making an 8 is 6-to-5, you will get paid $18 on your $15 odds bet.  This is how the odds bet works.  Points of 6 & 8 may wager odds bets of up to 3x the initial Pass Line bet, points of 5 & 9 may wager odds bet of up to 4x, and points of 4 & 10 may wager odds bets of up to 5x.  To give you your full odds payback, and to make payoffs easier for the casino, you'll need to keep these odds betting rules in mind:

Points of 6 & 8 get paid 6-to-5, so odds bets should be made in increments of $5.
Points of 5 & 9 get paid 3-to-2, so odds bets should be made in even dollar amounts.
Points of 4 & 10 get paid 2-to-1, so odds bets of any increment are allowed.

If you don't remember this at the craps table just ask the dealer and they will tell you what the proper odds bet would be for your situation.  Odds bet can be placed anytime after the point is established.  You don't have to place it on the very next roll of the dice.  Also, since this type of bet isn't in the house's favor, you are allowed to remove (or pick-up) your odds bet any time during the shooter's roll.

The odds bets we've discussed thus far were for Pass Line and Come bets.  You can also place odds bets on your Don't Pass and Don't Come bets.  Remember, the odds of NOT MAKING the point are reversed from the table I've shown you above.  So, if you have a $5 Don't Pass bet and the point is an 8, your maximum odds bet would be $18 and would pay for $15.  Notice that the max odds bet and its payout are in reverse from the Pass Line example.

We've said that the odds bet is the best bet in the casino for players, so if you're going to play craps you should ask what the casino's odds bets are and bet the maximum.  Odds bets of 3x-4x-5x are pretty standard, but you'll also see that a tight casino may offer only 2x odds.  In Las Vegas you might find 5x, 10x, or even 100x odds offered by some casinos!

Q)  What is a good way to hedge your bets?
A)  The odds bet is the best way to hedge your bet.  

Hedging your bet means making another bet with a higher expected value so that your overall expected value rises.  Let's look at how placing that odds bet in the previous example hedged your bet.  You made a $5 Pass Line bet.  The odds of winning is 6-to-5, but the house is only going to pay out even money.  This means that you will only win 5/6ths of the time.  Multiply this by your $5 bet and your expected return is 5/6 x $5 = $4.16.  This means that for every point of 8 (or 6 since they carry the same odds) that you will lose 83.33.  That's a loss of 83.33 / $5 = 16.66 for each dollar wagered .

Hedging your bet means making reducing this expected loss of 16.66 per dollar.  Now, let's run the numbers with a $15 odds bet.  The odds of the shooter making his 8 is still 6-to-5.  You are still going to lose that same 83.33 on your $5 Pass Line bet.  Let's factor in your $15 odds bet.  You will also lose the $15 odds bet 5/6ths of the time, but when you win, you will get paid $18.  We've explained in our response to question 1 that this is a neutral wager with no house edge.  Now, for your $5 Pass Line bet you'll lose 83.33 but lose 0 on the $15 odds bet.  Your total bet has grown to $20 ($5 Pass Line + $15 odds bet) but your expected loss has held constant at 83.33.  This reduces your loss to only 83.33 / $20 = 4.16 for each dollar wagered !  This greatly reduces your expected losses and hedges your initial $5 wager.

Is it possible to make some combination of hedge bets to bring your expected losses per dollar to zero, or perhaps turn it into a positive?  The answer, as you've probably expected, is no.  All of the bets offered on the craps table are in the house's favor with the exception of the odds bet, which is neutral.

Q)  What about Don't Come bets?
A)  Mathematically the Don't Pass (or Don't Come) bet is the next best bet at the table next to the odds bet.  While it's not neutral, like the odds bet, it gives the house the smallest edge of any game in the casino (with the exception of card-counting at blackjack).   Because the Don't Pass bet is just ever so slightly better than the Pass Line bet, most players will give up this tiny edge and bet the Pass Line.  Why?  Because it's more fun for the table to root "against" the house and "for" the shooter.

Don't Pass (and Don't Come) bets, once the point is established, is a good bet.  It's so good in fact that the casino will allow you to pick-up these bets anytime while the shooter is trying to make that point.  So there's never a need to hedge a Don't Pass bet since it's already mathematically in your favor.  But what if you think that the shooter is "hot"?  Then just pick up your bet and risk nothing.

Al, I hope I've answered your question.  If you have any additional questions, just let me know.



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Vic G


I can assist you with a number of casino games to include blackjack, craps, roulette, and poker (Texas Hold'em, 7 Card Stud, and Omaha). I have visited hundreds of casinos and may be able to answer specific questions about casinos or poker rooms in your area. Lastly, I have a collection of over 3,700 casino chips, so if you're a collector, or are just curious of what the value of a chip may be, I can assist you.


I grew up in New Jersey during the late 1970's when casinos came to Atlantic City. I played blackjack and craps in Resorts and the Golden Nugget during my high school and college years. I play poker at least once a week in my local card room and make the annual trip to Las Vegas for the World Series of Poker each year.

Ante Up magazine: October 2008

BS from Rutgers in Electrical Engineering. MBA from Wright State in Management Science.

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