Craps - True Odds vs Payout

In a game with two dice, there are 3 possible ways to throw a 4. So the probability of throwing a 4 is 3/36 = 1/12 = 8.33%. We can express this as odds of 11 to 1.
Thus it seems like the true odds of throwing a 4 would be 11:1. However, in craps you always see the true odds of throwing a 4 or 10 stated as "2 to 1". (This is also the payout for pass line/come bet odds.)


How do you get from 11:1 to 2:1 odds?


I know I'm overlooking something really simple here, so thanks in advance for any help you can give in explaining this to me.

Quote: Pocketsidewalk

In a game with two dice, there are 3 possible ways to throw a 4. So the probability of throwing a 4 is 3/36 = 1/12 = 8.33%. We can express this as odds of 11 to 1.
Thus it seems like the true odds of throwing a 4 would be 11:1. However, in craps you always see the true odds of throwing a 4 or 10 stated as "2 to 1". (This is also the payout for pass line/come bet odds.)


How do you get from 11:1 to 2:1 odds?


I know I'm overlooking something really simple here, so thanks in advance for any help you can give in explaining this to me.

The odds against rolling a 4 on the next throw is 33:3 = 11:1.

The odds of rolling a 7 before a 4 is 6:3 = 2:1. (Therefore, the free odds bet on 4 pays 2:1.)

11/1 = odds for getting a 4 on any one throw

5/1 = odds for getting a 7 on any one throw

11/1 = 12 and 5/1 = 6

12/6 = 2/1

Therefore, the odds are fair at 2/1 when trying to roll "a 4 against a 7".

----
The math in the link below may be easier to read/understand:

https://wizardofodds.com/games/craps/basics/#toc-DefiningtheHouseEdge

scroll down to the table "Multi-Roll Bets in Craps" (about 70% down the page) >>>> look at the row that says "Taking Odds 4 and 10" in the bet column >>> to the right there should be three figures ("PROB. WIN", "PROB. PUSH" and "PROB. LOSS") >>> you can then use those figures for working the "fair odds".

Quote: Pocketsidewalk

In a game with two dice, there are 3 possible ways to throw a 4. So the probability of throwing a 4 is 3/36 = 1/12 = 8.33%. We can express this as odds of 11 to 1.
Thus it seems like the true odds of throwing a 4 would be 11:1. However, in craps you always see the true odds of throwing a 4 or 10 stated as "2 to 1". (This is also the payout for pass line/come bet odds.)


How do you get from 11:1 to 2:1 odds?


I know I'm overlooking something really simple here, so thanks in advance for any help you can give in explaining this to me.

As stated above, Odds bets and Place bets are live until a seven rolls. They are not wagers on the next roll only. That one roll bet is the Hop, and pays accordingly (with some vig deducted).

Quote: Pocketsidewalk

In a game with two dice,

two fair 6-sided dice (2d6)

Quote: Pocketsidewalk

there are 3 possible ways to throw a 4.

when the dice are the same color and size if would be hard to tell the difference of a 4 rolled
D1.1,D2.3 or
D1.3,D2.1

D1.2,D2.2 is very easy to figure out

Quote: Pocketsidewalk

So the probability of throwing a 4 is 3/36 = 1/12 = 8.33%. We can express this as odds of 11 to 1.
Thus it seems like the true odds of throwing a 4 would be 11:1.

This is not an answer to your question (others answered your question) but many still struggle to this day on the house edge deal

In Craps, when allowed, one can bet the very next roll will be an easy 4 - 1,3 (not a hard 4 (2,2) as that is a different Hop bet)
So the probability of throwing an easy 4 is 2/36 = 1/18 = 5.56%.
We can express this as odds of 17 to 1 AGAINST or 1 chance in 18.
Thus it seems like the true odds of throwing an easy 4 would be 17:1
These hop bets pay ONLY 15 to 1 on a win (some pay lower in the US, 14 to 1, and some pay a bit higher outside the US)
Right there is the short pay (some call that the house edge)
17 chip winner and gets paid only 15

Quote: ksdjdj

11/1 = odds for getting a 4 on any one throw

5/1 = odds for getting a 7 on any one throw

11/1 = 12 and 5/1 = 6

12/6 = 2/1

Therefore, the odds are fair at 2/1 when trying to roll "a 4 against a 7".

----
The math in the link below may be easier to read/understand:

/games/craps/basics/#toc-DefiningtheHouseEdge

scroll down to the table "Multi-Roll Bets in Craps" (about 70% down the page) >>>> look at the row that says "Taking Odds 4 and 10" in the bet column >>> to the right there should be three figures ("PROB. WIN", "PROB. PUSH" and "PROB. LOSS") >>> you can then use those figures for working the "fair odds".

Thanks, this helps a lot. I also found the p/(p+q) formula at WizardofOdds, craps, Appendix 1 "How the House Edge for Each Bet is Derived" to be very helpful.