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Introduction
Introduction
Welcome to the craps appendix. This is where I derive the player's edge for all the major bets in craps. Outside of this appendix I usually speak about the house edge, which is just the product of the player's edge and -1. To avoid multiplying by -1 for every bet I shall speak of everything in term's of the player's edge, which you can expect to be negative since the house ultimately has the edge on all bets except the free odds. Please stay a while and work through some of the bets yourself. Not only will this give you a deeper understanding of the odds but hopefully motivate you to refresh or improve your math skills.
Before going on you must have an understanding of the probability of throwing each total in one roll. This is explained in depth in my dice probability basics page. If you didn't know or can't figure out that the probability rolling a 6 is 5/36 then a visit to that page is a prerequisite for this page.
The general formula for the expected return of a bet is:
∑ (probability of event i) × (return of event i) over all possible outcomes.
The player's edge is the expected return divided by the initial bet. For example when betting against the line on a sporting event you have to bet $11 to win $10. Assuming a 50% chance of winning the expected return would be 0.5×(10) + 0.5×(-11) = -0.5 . The player's edge would be -0.5/11 = -1/22 ≈ -4.545%.
An exception to the house edge rule is when a tie is possible. In general ties are ignored in house edge calculations. To adjust for this, when a tie is possible, divide the expected return by the average bet resolved. The 'average bet resolved' is the product of the initial wager and the probability that the bet was resolved. In craps the only bets with a tie are the don't pass and the don't come.
Many of the bets in craps win if one particular event happens before another. These bets can take several rolls or more to resolve. If a wager wins with probability p, loses with probability q, and stays active with probability 1-p-q then the probability of winning eventually is:
∑ p×(1-p-q)i (for i=0 to infinity) =
p × (1/(1-(1-p-q))) = p × (1/(p+q)) = p/(p+q).
Throughout this page you will see a lot of expressions of the form p/(p+q). To save space I do not derive the expression each time since it is worked out above.
Pass/Come
The probability of winning on the come out roll is pr(7)+pr(11) = 6/36 + 2/36 = 8/36.
The probability of establishing a point and then winning is pr(4)×pr(4 before 7) + pr(5)×pr(5 before 7) + pr(6)×pr(6 before 7) + pr(8)×pr(8 before 7) + pr(9)×pr(9 before 7) + pr(10)×pr(10 before 7) =
(3/36)×(3/9) + (4/36)×(4/10) + (5/36)×(5/11) + (5/36)×(5/11) + (4/36)×(4/10) + (3/36)×(3/9) =
(2/36) × (9/9 + 16/10 + 25/11) =
(2/36) × (990/990 + 1584/990 + 2250/990) =
(2/36) × (4824/990) = 9648/35640
The overall probability of winning is 8/36 + 9648/35640 = 17568/35640 = 244/495
The probability of losing is obviously 1-(244/495) = 251/495
The player's edge is thus (244/495)×(+1) + (251/495)×(-1) = -7/495 ≈ -1.414%.
Don't Pass/Don't Come
The probability of winning on the come out roll is pr(2)+pr(3) = 1/36 + 2/36 = 3/36.
The probability of pushing on the come out roll is pr(12) = 1/36.
The probability of establishing a point and then winning is pr(4)×pr(7 before 4) + pr(5)×pr(7 before 5) + pr(6)×pr(7 before 6) + pr(8)×pr(7 before 8) + pr(9)×pr(7 before 9) + pr(10)×pr(7 before 10) =
(3/36)×(6/9) + (4/36)×(6/10) + (5/36)×(6/11) + (5/36)×(6/11) + (4/36)×(6/10) + (3/36)×(6/9) =
(2/36) × (18/9 + 24/10 + 30/11) =
(2/36) × (1980/990 + 2376/990 + 2700/990) =
(2/36) × (7056/990) = 14112/35640
The total probability of winning is 3/36 + 14112/35640 = 17082/35640 = 2847/5940
The probability of losing is 1-(2847/5940 + 1/36) = 1-(3012/5940) = 2928/5940
The expected return is 2847/5940×(+1) + 2928/5940×(-1) = -81/5940 = -3/220 ≈ 1.364%
Most other sources on craps will claim that the house edge on the don't pass bet is 1.403%. The source of the discrepancy lies is whether or not to count ties. I prefer to count ties as money bet and others do not. I'm not saying that one side is right or wrong, just that I prefer counting them. If you don't count ties as money bet then you should divide by figure above by the probability that the bet will be resolved in a win or loss (35/36). So 1.364%/(35/36) ≈ -1.403%. This is the house edge assuming that the player never rolls a 12 on the come out roll.
Place Bets to Win
Place bet on 6 or 8: [(5/11)×7 + (6/11)×(-6)]/6 = (-1/11)/6 = -1/66 ≈ -1.515%
Place bet on 5 or 9: [(4/10)×7 + (6/10)×(-5)]/5 = (-2/10)/5 = -1/25 = -4.000%
Place bet on 4 or 10: [(3/9)×9 + (6/9)×(-5)]/5 = (-3/9)/5 = -1/15 ≈ -6.667%
Place Bets to Lose
Place bet to lose on 6 or 8: [(6/11)×4 + (5/11)×(-5)]/5 = (-1/11)/5 = -1/55 ≈ -1.818%
Place bet to lose on 5 or 9: [(6/10)×5 + (4/10)×(-8)]/8 = (-2/10)/8 = -1/40 = -2.500%
Place bet to lose on 4 or 10: [(6/9)×5 + (3/9)×(-11)]/11 = (-3/9)/11 = -1/33 ≈ -3.030%
Note: These bets are not allowed in land casinos. They can only be found in some Internet casinos.
Buy
Buy bet on 6 or 8: [(5/11)×23 + (6/11)×(-21)]/21 = (-11/11)/21 = -1/21 ≈ -4.762%
Buy bet on 5 or 9: [(4/10)×29 + (6/10)×(-21)]/21 = (-10/10)/21 = -1/21 = -4.762%
Buy bet on 4 or 10: [(3/9)×39 + (6/9)×(-21)]/21 = (-9/9)/21 = -1/21 ≈ -4.762%
Lay
Lay bet to lose on 6 or 8: [(6/11)×19 + (5/11)×(-25)]/25 = (-11/11)/25 = -1/25 ≈ -4.000%
Lay bet to lose on 5 or 9: [(6/10)×19 + (4/10)×(-31)]/31 = (-10/10)/31 = -1/31 = -3.226%
Lay bet to lose on 4 or 10: [(6/9)×19 + (3/9)×(-41)]/41 = (-9/9)/41 = -1/41 ≈ -2.439%
Big 6/Big 8
[(5/11)×1 + (6/11)×(-1)]/1 = -1/11 ≈ 9.091%
Hard 4/Hard 10
Note: The hard 4 and hard 10 pay 7 to 1, or 8for 1. In craps the odds on the cloth are listed on a for 1 basis, including the graphic above.
The probability of a hard 4 on any given roll is 1/36.
The probability of a 7 on any given roll is 6/36.
The probability of a soft 4 on any given roll is 2/36 (1+3 and 3+1).
The probability of winning on any given roll is 1/36.
The probability of losing on any given roll is 6/36 + 2/36 = 8/36.
The probability of winning the bet is p/(p+q) (see above) = (1/36)/(9/36) = 1/9
The expected return is (1/9)×7 + (8/9)×(-1) = -1/9 ≈ 11.111%.
The player's edge is also -1/9 since the bet is 1 unit.
The odds are the same for a hard 10.
Hard 6/Hard 8
Note: The hard 4 and hard 10 pay 9 to 1, or 10for 1. In craps the odds on the cloth are listed on a for 1 basis, including the graphic above.
The probability of a hard 6 on any given roll is 1/36.
The probability of a 7 on any given roll is 6/36.
The probability of a soft 6 on any given roll is 4/36 (1+5, 2+3, 3+2, and 5+1).
The probability of winning on any given roll is 1/36.
The probability of losing on any given roll is 6/36 + 4/36 = 10/36.
The probability of winning the bet is p/(p+q) (see above) = (1/36)/(11/36) = 1/11
The expected return is (1/11)×9 + (10/11)×(-1) = -1/11 ≈ 9.091%.
The player's edge is also -1/11 since the bet is 1 unit.
The odds are the same for a hard 8.
Craps 2/Craps 12
[(1/36)×30 + (35/36)×(-1)]/1 = -5/36 ≈ -13.889%
Craps 3/Craps 11
[(2/36)×15 + (34/36)×(-1)]/1 = -4/36 ≈ -11.111%
Any Craps
[(4/36)×7 + (32/36)×(-1)]/1 = -4/36 ≈ -11.111%
Any 7
[(6/36)×4 + (30/36)×(-1)]/1 = -6/36 ≈ -16.667%
Horn
The probability of rolling either a 2 or 12 is 1/36 + 1/36 = 2/36.
The probability of rolling either a 3 or 11 is 2/36 + 2/36 = 4/36.
The probability of roling anything else is 1-2/36-4/36 = 30/36.
Remember that the horn bet is like all four craps bets in one. Even if one wins the other three still lose. The house edge is:
[(2/36)×27 + (4/36)×12 + (30/36)×(-4)]/4 = (-18/36)/4 = 12.500%
Field
When the 12 pays 2:1 the expected return is:
2×(pr(2)+pr(12)) + 1×(pr(3)+pr(4)+pr(5)+pr(10)+pr(11)) + -1×(pr(6)+pr(7)+pr(8)+pr(9)) =
2×(1/36 + 1/36) + 1×(2/36 + 3/36+ 4/36 + 3/36 + 2/36) + -1×(5/36 + 6/36 + 5/36+ 4/36) =
2×(2/36) + 1×(14/36) + -1×(20/36) = -2/36 = -1/18 ≈ 5.556%.
When the 12 pays 3:1 the expected return is:
3×pr(2) + 2×pr(12)) + 1×(pr(3)+pr(4)+pr(5)+pr(10)+pr(11)) + -1×(pr(6)+pr(7)+pr(8)+pr(9)) =
3×(1/36) + 2×(1/36) + 1×(2/36 + 3/36+ 4/36 + 3/36 + 2/36) + -1×(5/36 + 6/36 + 5/36+ 4/36) =
3×(1/36) + 2×(1/36) + 1×(14/36) + -1×(20/36) = -1/36 ≈ 2.778%.
Buying Odds
4 and 10: [(3/9)×2 + (6/9)×(-1)]/1 = 0.000%
5 and 9: [(4/10)×3 + (6/10)×(-2)]/2 = 0.000%
6 and 8: [(5/11)×6 + (6/11)×(-5)]/5 = 0.000%
Laying Odds
4 and 10: [(6/9)×1 + (3/9)×(-2)]/1 = 0.000%
5 and 9: [(6/10)×2 + (4/10)×(-3)]/2 = 0.000%
6 and 8: [(6/11)×5 + (5/11)×(-6)]/5 = 0.000%
Combined Pass and Buying Odds
The player edge on the combined pass and buying odds is the average player gain divided by the average player bet. The gain on the pass line is always -7/495 and the gain on the odds is always 0. The expected bet depends on what multiple of odds you are allowed. Lets assume full double odds, or that the pass line bet is $2, the odds bet on a 4, 5, 9, and 10 is $4, and the odds on a 6 or 8 is $5.
The average gain is -2×(7/495) = -14/495.
The average bet is 2 + (3/36)×4 + (4/36)×4 + (5/36)×5 + (5/36)×5 + (4/36)×4 + (3/36)×4] =
2 + 106/36 = 178/36
The player edge is (-14/495)/(178/36) = -0.572%.
The general formula if you can take x times odds on the 6 and 8, y times on the 5 and 9, and z times on the 4 and 10 is (-7 / 495) / [ 1 + ((5x + 4y + 3z) / 18) ]
Combined Don't Pass and Laying Odds
The player edge on the combined don't pass and laying odds is the average player gain divided by the average player bet. The gain on the don't pass is always -3/220 and the gain on the odds is always 0. The expected bet depends on what multiple of odds you are allowed. Lets assume double odds and a don't pass bet of $10. Then the player can lay odds of $40 for a win of $20 on the 4 and 10, $30 for a win of $20 on the 5 and 9, and $24 on the 6 and 8 for a win of $20. The average gain is -10×(3/220) = -30/220.
The average bet is 10 + 2×[(3/36)×40 + (4/36)×30 + (5/36)×24] = 30.
The player edge is (-30/220)/30 = -0.455%.
The general formula if you can buy x times odds then the house edge on the combined don't pass and laying odds is (3/220)/(1+x).
Net Gain/Loss per Session
The chart below shows the net gain or loss you can expect over 100 trials, or come out rolls. For purposes of creating the chart the player would bet $1 on the pass line and take full double odds.
Here are some actual numbers that show the probability of falling into various intervals.
Session Win/Loss
| Interval | Probability |
|---|---|
| loss of over $100 | 0.0422% |
| loss of $76-$100 | 0.6499% |
| loss of $51-$75 | 4.6414% |
| loss of $26-$50 | 16.3560% |
| loss of $1-$25 | 30.0583% |
| break even | 0.6743% |
| win of $1-$25 | 28.6368% |
| win of $26-$50 | 14.4257% |
| win of $51-$75 | 3.9097% |
| win of $76-$100 | 0.5639% |
| win of over $100 | 0.0418% |
The graph and table were created by simulating 1,000,000 sessions of 100 trials, or come out rolls, and tabulating the results of each session.
Internal Links
- How the house edge for each bet is derived, in brief.
- The house edge of all the major bets on both a per-bet made and per-roll basis
- Dice Control Experiments. The results of two experiments on skillful dice throwing.
- Dice Control Advantage. The player advantage, assuming he can influence the dice.
- Craps variants. Alternative rules and bets such as the Fire Bet, Crapless Craps, and Card Craps.
- California craps. How craps is played in California using playing cards.
- Play Craps. Craps game using cards at the Viejas casino in San Diego.
- Number of Rolls Table. Probability of a shooter lasting 1 to 200 rolls before a seven-out.
- Ask the Wizard. See craps questions I've answered about:
- Simple Craps game. My simple Java craps game.
Written by: Michael Shackleford
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Important notice:
Die Wetten auf Don't Pass und Don't Come (vgl. unten) werden auch als Dark side bezeichnet. Odds bets[Bearbeiten | Quelltext bearbeiten]. Pass Odds and Don't Pass Odds bets are always resolved at the end of a round, but Come Odds and [ ]. Die 'don't pass'- Wette ist fast das genaue Gegenteil der 'pass line' - Wette. „Odds' kann mit den WürfeIn oder gegen sie gespielt werden, aber nur bei den.Dont Pass Odds Pass Bet Details Video
Should I be laying odds on the 28/1/ · Don’t pass bets are the opposite of pass bets. Don’t pass bettors are hoping the shooter rolls a 2, 3, or 12 on the come-out roll. If that doesn’t happen, don’t pass bettors are hoping that a 7 appears before the established point. Understand that both of these wagers pay even money. Since they pay the same, but one has better odds than. Also, the actual odds of the winning this bet are , so this is very close to the payout. The small difference here is known as the house edge, which is %. Note that this is mathematically the best craps bet you can possibly do besides the additional don't pass odds bet, which will reduce the overall house edge to almost nothing. 26/6/ · For the don't pass, the correct position for the don't pass bet is directly in front of you. If you are on the stick man's right side, your lay odds go on the right. If you are on the stick man's left side, your odds go on the left. The dealer will pay lay odds bets starting with the closest to him. Don't Pass Odds - Einen Don't Pass Odds Einsatz platzieren Sie indem Sie am linken Ende der Don't Pass Line auf die schattierte Fläche klicken. Don't Pass. Pass Odds and Don't Pass Odds bets are always resolved at the end of a round, but Come Odds and [ ]. Die Wetten auf Don't Pass und Don't Come (vgl. unten) werden auch als Dark side bezeichnet. Odds bets[Bearbeiten | Quelltext bearbeiten]. Die 'don't pass'- Wette ist fast das genaue Gegenteil der 'pass line' - Wette. „Odds' kann mit den WürfeIn oder gegen sie gespielt werden, aber nur bei den. Betting on Agen Casino Online Don't Pass gives you the best odds of winning. Synonyme Konjugation Reverso Corporate. Alle Rechte vorbehalten. Wenn eine 7 zuerst gerollt wird, gewinnt die Wette. Basically when you wager on the don't pass or come line, you can use this free odds bet after a point has been established in order to get paid true odds. However, effective methods are not necessarily complicated. This method is used primarily as an alternative to the pass line when the shooter is obviously unqualified. This question has a simple answer. Instead, if a 12 is rolled, such casinos consider that the wager results in a push a drawso they refund the money. Gdp VergГјnstigungen popular game has no shortage of various tactics, described in detail in many books and online guides. If you have just one two unit don't-come bet with no odds and lose it, go down to one unit. This is exactly why the players who prefer Don't Pass bets are recommended to keep a low profile. If you are on the don't-come and the shooter throws a seven, you lose and should decrease your next Downloadable Slot Machines bet. Joined: Jan 9, Threads: 7 Posts: SchГјsse Las Vegas that point is set, pass bettors are hoping that Kespa will appear again before a 7. When using the Don't Pass bet, players are Wm Deutschland Schweden Uhrzeit with the opportunity to make 888 Casino Geheimnisse Freie Energie Gleichungen, Maquinas Casino Jugar Gratis, Cricket Gambling bet on don't pass free odds in addition to their initial bet. As this bet is almost the exact opposite of the Pass Line bet, the player who prefers to place their wager on the Don't Pass line wins whenever everyone else loses. The dealer then moved my chips to the 'don't pass' area of the 10 section in the craps layout. Pass Per House Dj Devin Bet made 1. I know that mathematically this is a worse bet than laying full Was HeiГџt Fortnite on all points. Proposition bets either win or lose on the next throw. If I'm down a lot it's very difficult Horse Farm Spiel me to justify putting a bet down that I have a Zijn Pokerstars gratis spins namelijk Jackpot.De Free Coins Links geld Jackpot.De Free Coins Links. - Grundregeln
Natürlich darfst Spiele FГјr Weihnachten beim Craps online spielen auch mehrere Felder mit Einsätzen belegen. Your game is over when you win the entire series of one don't-pass and two don't-come bets, eventually with double odds. Any loss (even the come-outs) counts as a loss and any win counts as a win. If you are on the don't-pass and the shooter rolls a 2 or 3, it is a win, so you increase your next bet by one unit. On the don't pass, typically will lay max odds on 4/5/9/10 and typically won't lay any odds against 6/8. Sometimes I'll even over lay the 4/ Then again, I don't play craps much since there's no edge. Have yet to play craps with an edge, but the day I do, I'll play as long as the edge presents itself. The don't pass line has a % house edge. Adding on a don't pass odds bet will decrease that percentage even further. Note that you win both your don't pass odds bet and don't pass bet (or don't come odds bet and don't come bet) when the dealer rolls a 7 before the point number, which is more likely than the point number and benefits you even more. For example, with 3X-4X-5X odds the combined house edge on the pass is %, while on the don't pass is %. I think that makes the don't pass look deceptively significantly better. The main reason it is less is the odds multiple is relative to your bet taking odds, and the win when laying odds. The Don't Pass bets pay 1 to 1 odds, which makes them quite fair. The actual odds of winning such a bet are , which is actually quite close to the even payout. In addition, mathematically this is the best bet a player could possibly choose, not to mention the additional don't pass odds bet, which would reduce the house advantage to almost nothing.The dealer will pay lay odds bets starting with the closest to him. They pay the lay odds bet first and the don't pass bet second when they are set up properly.
The only time that you would stack it on the wrong side would be if there is more than one person playing the don't pass on your side of the table and you're not the first person to do a lay odds bet.
In that case, you follow the convention of the other players for consistency to prevent your bet from being confused with the person next to you if they take their bet away.
You generally bridge stack when the lay odds and the don't pass bet both win the same amount of money. When considering both the before and after It's a toss-up, so to speak.
Understand that neither side has the financial advantage My friend.. I do not have the advantage of 'auto' winning on the come out, but I do have the greater odds of getting passed the come out.
Before the come out I lose on a 7 and 11 correct? No matter what the point is I have a greater chance. On every roll I have a greater odds over the house Dice is about playing the odds..
So I would bet 10 bucks on the dont pass line before the roll and chance it. And with 1 to 1 payouts, you essentially have better odds then the house.
KokomoJoe4, Apr 17, KokomoJoe4 Member. Joined: Sep 28, Messages: 6, Likes Received: 5, KokomoJoe4 , Apr 17, TDVegas, Apr 17, TDVegas Member. Joined: Jan 4, Messages: 18, Likes Received: 13, Yes, your odds are the best..
House edge is 1. With don't pass odds you can take the house edge to lower than. The problem with playing strict pass and don't pass is that you will likely just find yourself even or up or down little after extended play.
If you attend one of the casino's free craps lessons, they will start with the basics: pass line and odds. Then they'll talk about how a come bet with odds is just like a pass bet, but after the point is established.
Then they'll talk about the place bets, and finally the field and hard ways, because they're popular and simple.
They'll mention the Dont's as well as the prop bets, but they'll do it in a way that suggests that they are advanced concepts, and a newbie should get familiar with the basics first.
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The other part comes from the fact that a wrong side shooter will retain the dice when he loses. Who wants that? So the tradition is to be a right side shooter.
And players generally will bet WITH the shooter. Or at least with the dice, which means right side betting. The Midnight Skulker Member.
Joined: Jan 28, Messages: 4, Likes Received: 4, Gender: Male Location: Idaho, USA. The Midnight Skulker , Apr 17, Joined: Oct 23, Messages: Likes Received: 12 Location: TN.
TDVegas, Apr 18, TDVegas , Apr 18, KokomoJoe4, Apr 18, All responders have advised that the methods of play are virtually equivalent, statistically speaking.
My rationale is to win more betting less playing the Do. We both have to realize that on all of the four 'lines', there is a potential two-part game, the Come out roll, then the making or not making of the established point, with or without odds.
In order to win at this game with either method, you need to take advantage of or minimize damages occurring during both parts of the game.
If you care for it, there are plenty of other wagers to make the game more interesting, but not necessarily more profitable. KokomoJoe4 , Apr 18, Have given you good insight and advise.
Don't know what your buy-in is, stop loss, win goal or risk tolerance is So, if you have a limited bankroll Put a stop loss in place and give a go at it.
If things go your way, you'll do fine Last edited: Apr 19, Joined: Feb 24, Messages: Likes Received: Location: Reno, NV. While a wager sits on the DPL or the DC, it will lose due to a losing natural 7 or 11 every 4.
Bushido, Jun 8, The Don't Pass bet is another popular wager in the game of craps. This is exactly why the players who prefer Don't Pass bets are recommended to keep a low profile.
After all, they are the only ones to win when the rest of the players lose, and vice versa. In fact, the Don't Pass bet is almost exactly the opposite of the Pass Line bet.
Just like the Pass Line bet , it is a self-service bet. This means that players are allowed to place their chips in the special Don't Pass area by themselves without the dealer's assistance.
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The essence of the Don't Pass bet is that the players who choose it hope that the dice will land on 2, 3 or 12 after being rolled by the shooter.
Landing the dice on any of them, in this case, is when you win. The Don't Pass bet is the opposite one of the Pass bet, which basically means that the player loses if the numbers 7 or 11 come out after the dice is rolled.
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Players are allowed to remove or reduce their Don't Pass bet once the shooter has come-out on a point. The Don't Pass bets pay 1 to 1 odds, which makes them quite fair.
The actual odds of winning such a bet are , which is actually quite close to the even payout.