Casino Backgammon

I made a trip to O'Sheas this weekend specifically to see this Casino Backgammon game. Has anybody run an analysis on it, as far as what the house advantage is? I took one look at the layout of the game, the payouts of the game, and knew instantly that I did not want to play this game.

They had a nice looking woman there trying to get people to play the game, and, quite frankly, she was not very successful at getting people to put their money down. After I won some money playing craps, I went back over there. She was talking to a few guys trying to get them to bet. I decided to help her out. I made a bet, and yelled out, "This is the best game in the house! Can't possibly lose!" I proceeded to win my two bets. I made another bet, on the next point, and once again said, "Can't even lose at this game!", and won again. I think made another two bets, and lost. At which point, looking at my money, I said "$13 dollar win in 3 minutes. Can't lose here!" The woman was grinning while I was doing all this, and even though I walked away, the other guys were pulling money out of their wallets to try the game.

Anyway, the game seems very skewed in the house's favor, and I really can't think of any reason why you would want to play this game. While I haven't worked out the math myself, the odds seem horrible. If anybody wants my other impressions of this game, or why I don't think it will last, I'm happy to post my thoughts here.

Quote: konceptum

The game seems very skewed in the house's favor, and I really can't think of any reason why you would want to play this game.

Then why did YOU play it? Oh, wait. I think I know...

Quote: konceptum

They had a nice looking woman there....

:)




So what are the bets and rules?

Quote: DJTeddyBear

So what are the bets and rules?

I looked it up online, assuming it's the same game, and the simulated bet the site shows requires the dice to come up with a 3-3 minimum in order to win. The bet consists in whether the backgammon checkers will "jump" the bar or not. Since they are two spaces removed from the bar, and each dice moves one checker, you need to move each at least 3 spaces.

This si where it gets complicated, as the requirement for each die is 3 or more. A 5-2 shot loses, for example, so it's not ike you have to shoot a total of six or more. Each die should be looked at as independent from the other die.

I don't ahve a link, but look up casino backgammon in Google.

Link
Unless me and/or the calculater that comes with Windows is not working correctly the house edge is horrible.

I played it just to mess with the lady. I tried explaining to her that if she got some shills to stand around playing the game, it would entice others to play real money on the game. I don't know if she worked for the casino or for whoever is marketing the game.

Anyway, the game is supposed to resemble backgammon. The table layout looks like half of a backgammon table, with 6 points on each side of a Jump Bar. When starting, there are 2 pucks placed on Point 1, which is 2 spaces from the Jump Bar.

You have to make 2 equal bets, a Jump Bet, and an Out Bet. The Jump Bet is that you can get the 2 pucks over the Jump Bar with one roll of the dice. The Out Bet is that you can get the 2 pucks off the board within 2 rolls of the dice, with the caveat that if either of those 2 rolls are doubles (1-1,2-2,3-3,4-4,5-5,6-6), you can roll a third time.

Unlike what someone else wrote above, you don't need a minimum of 3-3, but rather a minimum of 2-2. The Jump Bar itself is not counted in the movement of the pucks.

If you win (either the Jump Bet or the Out Bet), then you have the option of playing on the next higher point. Each successive point is one point farther away from the Jump Bar, and thus harder to make, with successfully higher payouts.

The payout structure was, for the Jump Bets:
Point 1 --- 3 to 5
Point 2 --- 2 to 1
Point 3 --- 3 to 1
Point 4 --- 10 to 1
Point 5 --- 40 to 1

For the Out Bets:
Point 1 --- 1 to 1
Point 2 --- 1 to 1
Point 3 --- 4 to 1
Point 4 --- 5 to 1
Point 5 --- 9 to 1

There was also an optional Doubles Side Wager, which had to be made prior to the first dice roll of any point in play:
2 Non Equal Doubles --- 3 to 1
2 Equal Doubles --- 20 to 1
3 Doubles --- 100 to 1

If the shooter loses both the Out Bet and the Jump Bet or the shooter no longer wants to roll the dice, then the dice gets passed to the next shooter, who has to start over from Point 1.

Again, Point 1 would require a minimum first roll of 2-2 to win. Point 2 would need 3-3. Point 3 would need 4-4. Point 4 would need 5-5. and Point 5 would need 6-6.

When I initially looked at the payouts of the game, my thoughts were negative because, on the first Point, assuming you won both the Jump and the Out Bets, you would be risking $10 ($5 on each bet) to win $8 (3 to 5 on the Jump, and 1 to 1 on the Out). Other than the Don't Odds in Craps, Casino War, and Sports Betting, I couldn't initially come up with any other bets in the casino where you risk an amount to win less.

Last night, when running numbers in my head regarding Casino Backgammon, it does appear that the Jump Bet might have a positive player expectation. Thus, it must be the Out Bet that wins the game for the casinos. After all, if you risk $10, and only win $3, the casino is going to be happy. Players have the illusion that they won something, when in reality they are getting nailed.

This is the website on the brochure I brought home: http://casinobackgammongame.com/site/

EDIT: I hadn't looked at their website until just now. I see that the odds payouts that were actually being made in the casino are different than what is on their website. Further, some of the extra bets were not available. I don't know why there is a difference. I have the handout that was being given at the table, and if people want to see it, I can take some pictures and post them online.

Quote: miplet

Unless me and/or the calculater that comes with Windows is not working correctly the house edge is horrible.

You normally do great work miplet, but you opened yourself up to this one: I don't think you are working properly today!
;)

ways to win 6: 1
ways to win 5: 4
ways to win 4: 9
ways to win 3: 16
ways to win 2: 25

with the new payouts off the table from konceptum, I think there are player advantages on the Jump bets. On the combined bet with OUT, there will naturally be a house advantage. The out bets are harder to figure out, but I bet there is a backgammon page out there that has the probabilities of winning the off bets in 2 rolls.

Quote: konceptum

Unlike what someone else wrote above, you don't need a minimum of 3-3, but rather a minimum of 2-2. The Jump Bar itself is not counted in the movement of the pucks.

I swear I counted three spaces. Two before the bar, then the one past the bar. I may be wrong.

Just finished my own analysis. With the new payouts, there IS a definite player advantage on the Jump payouts. If it was possible to ONLY make Jump bets, we should all be down there cleaning up. With the wager pay table on the Casino Backgammon website, even the Jump Bets have a house advantage.

Analyzing all possible rolls wasn't that difficult, as there are only 15,156 possibilities. The easiest is if you don't roll any doubles. There are only 30 ways to roll non-doubles, so 30*30 = 900. If you roll a double on the first roll, then there are 2 more rolls, for a total of 6*36*36 = 7,776. Finally, not rolling a double on the first roll, followed by a double on the second roll, followed by a third roll: 30*6*36 = 6,480. Total rolls 6,480 + 7,776 + 900 = 15,156. Of course, you have to take into account the fact that the non-double rolls are going to happen more frequently than the double rolls.

OK. Assuming a $5 Jump bet and a $5 Out bet, I came up with the following expected losses for both the pay table as the casino, and the one on the website:

Point = 1
casino PT = -0.42931
website PT = -0.32073

Point = 2
casino PT = -0.63872
website PT = -0.2608

Point = 3
casino PT = -0.477
website PT = -0.727

Point = 4
casino PT = -0.29964
website PT = -0.43656

Point = 5
casino PT = -3.84774
website PT = -0.40584

These numbers are the expected loss. Sometimes I'm confused as to how to turn this into the house edge percentage, but I'm sure someone else can help with that. Also, the website starts with Point 2, and goes to Point 6, but the casino game has Point 1 going to Point 5. It's the same thing though, although the website methodology makes more sense to me.

Further calculations showed that there is a 26.2% chance of losing both bets on Point=1, 48.8% on Point=2, 67.6% on Point=3, 81.9% on Point=4, 91.5% on Point = 5.

Again, I think that the fact that you're going to win SOMETHING around 75% of the time when you're rolling the dice is what is going to attract some people to the game. And, more than likely, that something will be the Jump bet. But again, it's payout is so small, that it's overshadowed by the loss on the Out bet. However, since they push the Jump bet winnings to you at the time you make the Jump, people are going to be overjoyed by having received something, and will not really notice that they are, in fact, losing money over the long run.

For the Jump Bet, assuming a $5 bet on the jump bet, I calculated the expected gains/losses to be
Point=1
casino PT = +0.5556
website PT = -0.1389

Point=2
casino PT = +1.6667
website PT = -0.1111

Point = 3
casino PT = 0
website PT = -0.25

Point=4
casino PT = +1.1111
website PT = -0.2222

Point = 5
casino PT = +0.6944
website PT = -0.2778

Again, someone else turn these into house/player advantage percentages.

Final thoughts: for some reason, the casino or somebody decided that a different payout structured was needed. I can think of 2 reasons. One is that the payout structured as listed on the website seems highly confusing and prone to problems. The second is the concept of the casino accepting a loss on the Jump Bet, in exchange for a higher gain on the Out Bet. The website structure has a house edge for both bets, while the casino structure has a player edge for the Jump and a casino edge for the Out, but since both wagers have to be equal and both wagers have to be made, the combined edge is in favor of the house.

My advice? Find a casino running this game with the better casino payout table rather than the website table. Find someone playing the game, and ask if you can add money to his Jump bets, and collect winnings till the cows come home.

Nareed, the pucks start on the second space before the bar. You can see this on their website under "How To Play". Interestingly, though, if you watch through their Jump Bet examples, they make a mistake on the final play they show. They show the dice rolling 6-1, but they move the pucks 6-5. :)

Quote: konceptum

Nareed, the pucks start on the second space before the bar. You can see this on their website under "How To Play".

I'll take your word for it. Monday night I'm not usually at my best.