US20100201070A1

US20100201070A1 - Dealer Placed Replay Bet for the Game of Craps

Info

Publication number: US20100201070A1
Application number: US12/705,588
Authority: US
Inventors: Anthony M. Ramsey
Original assignee: Individual
Current assignee: Individual
Priority date: 2009-05-22
Filing date: 2010-02-13
Publication date: 2010-08-12

Abstract

A new proposition bet for the game of craps rewards players for establishing and making multiple occurrences of the same point during a single series of dice rolls. The craps players must place the REPLAY™ bet prior to a shooter's initial come out roll. The REPLAY™ bet pays a bettor for making the same point repeatedly with the payout established by a set table based on probabilities of making each respective point number multiple times.

Description

CROSS REFERENCE TO RELATED APPLICATIONS

This application claims the benefit of priority to United States Provisional Patent Application Ser. No. 61/180,465 filed on May 22, 2009. The prior provisional patent application is incorporated by reference as if set forth fully herein.

FIELD OF INVENTION

The invention relates to a new proposition bet for the game of craps.

BACKGROUND

A brief summary of the game of craps is helpful in understanding the invention. The game has been played for generations, and the rules are consistent in every location. U.S. Pat. No. 6,805,352 (Hunter, 2004) summarizes certain rules of the game. The Hunter '352 patent forms the basis for an overall discussion of the game as set forth below.
The game includes players positioned around the craps table. One player is the shooter who rolls the dice on which all players may wager. The first roll of the dice is referred to as a “come out” roll. After the come out roll, the game continues with points being established and made along with wagers being placed and paid out as follows.
The player may choose to set up a “pass-line-bet” before the come out roll. The pass-line-bet pays when the come out roll is either a 7 or 11. Rolling a 2, 3 or 12 means that the player with a pass line bet loses. A player establishes a point by rolling a number other than 2, 3, 7, 11, or 12 (i.e., a come out roll of 4, 5, 6, 8, 9 or 10 “establishes” a point). Keeping in mind that rolling a 7 ends the series (referred to as “sevening out”), a shooter will continuously roll the dice on the table until either the established point is rolled again (called “making” the point) or the shooter “sevens out.” When the established point is rolled and “made,” the pass line bettor wins the pass-line-bet. A shooter sevening out before “making” an established point means that the pass line bettor loses. When the player places the pass-line-bet and the point is established, the player may place a true odds bet that the point will be made before sevening out. The true odds bet pays according to a standard true odds table. If the player wins the pass line bet, then the true odds bet also pays.
The inverse of the pass line bet is the “don't-pass-line-bet” placed prior to the come out roll. The same numbers establish points as set forth above for the pass-line-bet (4, 5, 6, 8, 9, 10); however, a second roll resulting in these numbers on the dice (i.e., making the established point) means that the bettor with a don't-pass-line-bet loses. Again, the number 7 has a special role because when the shooter rolls a 7 on come out, then the don't-pass-line-bets lose. When the shooter rolls a 7 after the come out roll, then the don't-pass-line-bet wins! The don't-pass-line-bet also pays when the shooter's come out roll is a 2 or a 3, and the don't-pass-line-bet loses when the come out roll is 11. A 12 is neutral overall, and hitting 12 on come out means a don't-pass-line bettor gets his bet back, but wins nothing.
Bettors who place their bets after the come out roll establishes a point may choose a “come bet” that pays out depending upon the next roll. A next roll of 7 or 11 wins on the come bet. A 2, 3, or 12 loses, and if the come out roll established a 4, 5, 6, 8, 9, or 10, and that established point is hit again, then the come bet pays. Seven ends the series, and come bets lose if an established point has not been made.
Similar to the pass/don't pass pair, the come bet has an inverse in the “don't-come-bet.” As one might expect, after the come out roll, the next roll of 2, 3, 7, 11, or 12 loses the don't-come-bet. If the come out roll established a 4, 5, 6, 8, 9, or 10, and that established point is hit again, then the don't-come-bet loses. Seven after come out ends the series, but don't-come-bets win on that 7.
The Hunter '352 patent goes on to describe place bets (a bet that a particular number will be rolled before sevening out); lay bets (a bet that a shooter sevens out before rolling a particular number); field bets (betting on specified numbers with particular payouts); hard way bets (dependent upon identical dice faces that add up to the number being bet); and one roll bets (betting that a certain number results from an upcoming roll).
With the Hunter '352 patent summary as a backdrop regarding the available bets, improvements to the game of craps have been previously established. For purposes herein, one of the most significant changes to the game is set forth in two companion patents—U.S. Pat. No. 6,655,689 (Stasi et al., 2003) and U.S. Pat. No. 7,100,919 (Stasi 2006).
As noted in the Abstract of each Stasi patent, these two patents are both directed to a proposition bet for Craps referred to as a FIRE BET™. The proposition bet set forth in the Stasi patents includes a predetermined schedule on a pay-out table; players place FIRE BET™ wagers at player betting areas prior to a shooter's initial come out. A shooter accumulates points responsive to outcomes of the shooter's dice throws and “makes points” when a number 4, 5, 6, 8, 9, or 10 is twice rolled before sevening out. One key feature set forth in the FIRE BET™ patents is that any point that has been “made,” by shooting it twice, is ignored for future rolls before sevening out. In other words, the FIRE BET™ requires a shooter to “make” from 3 to 6 different points before “sevening out”. In the FIRE BET™, the shooter gets no credit for “making” the same point twice.
With the above noted limitation to the FIRE BET™ in making the same point twice, a need exists in the game of craps for a new proposition bet that increases a shooter's chances of accumulating made points. This new method of playing craps will have odds that are entirely different from the odds of previously known bets described above.

BRIEF SUMMARY OF THE INVENTION

The game of craps described herein includes a new proposition bet that may be placed by the dealer upon a player's request. The bet is set forth in a method and associated craps table in which a series of dice rolls and winning payout rates are based on the respective probabilities of accumulating specified numbers of occurrences of particular pairs of dice roll combinations having identical total point values. The method of betting includes identifying an established point by rolling dice having a total point value selected from the group consisting of 4, 5, 6, 8, 9, and 10, wherein the established point is equal to the total point value of the dice. Next, the player converts an established point into a made point by rolling dice within a single series of dice rolls such that the dice have the same total point value as the established point. One goal is for the player to accumulate multiple occurrences of any made point to a specified number of occurrences within a single series of dice rolls, wherein each roll in the series has a point value other than 7 and wherein the specified number of occurrences of a single made point determines a payout for bettors.
An associated game table includes options for placing the new bet.

DESCRIPTION OF THE FIGURES

FIG. 1 is a drawing of a craps table with the appropriate indicia of a REPLAY™ bet located proximate the dealer on each end of the table.

FIG. 2 is a drawing of a craps table with the indicia of a REPLAY™ bet located below the proposition bet area.

FIG. 3A is a drawing of the REPLAY™ puck used with the proposition bet of this game.

FIGS. 3B-3F are drawings of REPLAY™ chips used with the proposition bet of this game.

DETAILED DESCRIPTION

The game described herein utilizes the same terminology as in a traditional game of craps unless otherwise noted. As described above, a shooter in a craps game typically continues rolling dice until rolling a dice combination that totals seven, an event described as “sevening out.” For purposes of this detailed description, a single shooter's rolls completed prior to rolling a total point value of seven is referred to as a “series.” In other words, rolling a pair of dice with the total point value (i.e., a face-up value) of 7 completes a series. For purposes of clarity, if a 2, 3, 7, 11, or 12 is rolled on the come-out roll, then the series has only one member in it, and a new series begins because 7 and 11 are natural winners on come-out and 2, 3, and 12 are natural losers on the come-out. By rolling a 4, 5, 6, 8, 9, or 10 on the come-out roll, the shooter “establishes” a “point” just like the original game of craps. As might be expected, on future rolls, when the shooter rolls an established point again, the established point becomes a “made point.” Overall, one purpose of the new proposition bet described herein is to accumulate made points that have an identical total point value. This proposition bet is distinctly different than any other known bet used in craps today.
The proposition bet of this game includes a method of playing the game of craps with a series of dice rolls and with winning payout rates based on the respective probabilities of accumulating specified numbers of occurrences of particular pairs of dice roll combinations having identical total point values. For starters, a shooter takes the dice and rolls the come-out roll. For purposes of the new proposition bet described here, the goal is to roll a total point value of 4, 5, 6, 8, 9, or 10 to establish a respective point equal to the total point value rolled. While the shooter continues to roll, the series continues to grow, until rolling a 7 as noted above. Upon rolling a previously established point again at any point in the same series, the shooter converts the previously established point into a made point. To take advantage of the new bet described herein, referred to generally as a REPLAY™ bet, the shooter accumulates multiple occurrences of any made point (i.e., “establishing and making” the same point again and again is advantageous to a bettor making a REPLAY™ bet).
The REPLAY™ bet has an associated pay-out table that requires the game operator (usually a casino) to pay bettors according to a set standard. The pay-out is based on the probabilities of establishing and making the same point a certain number of times. As an example, there will be a payout for the shooter who establishes and makes the same point for a specified number of occurrences within a single series of dice rolls. In one embodiment, the specified number of occurrences of the single made point leading to a payout for bettors is between 3 and 6.
The craps game with a REPLAY™ bet utilizes methods of noting on the craps table 5 which points have been established, which have been made, and how many times the point has been made. When a point has been established on a come-out roll, the game includes the step of indicating on the craps table 5 the established point in the series with an established point indicator, typically a puck. Likewise, when an established point has been made, the game includes the step of indicating on the craps table the made points in the series of dice rolls. For example, in the traditional game of craps, the step of indicating made points involves moving the puck to a made point location on the craps table. The made point location is usually in a position off the point number itself.
In one embodiment, the established point is marked by placing a traditional craps puck on the appropriate point in the point number area 10 (the area marked with numbers 4, 5, 6, 8, 9, and 10). When the point is made by the shooter rolling the established point again, the dealer replaces the traditional craps puck with a REPLAY™ puck 20. The REPLAY™ puck 20 bears the indicia “1” along with a replay symbol 25 that is new to the proposition bet described herein and shown in FIG. 2. The replay symbol shown in FIG. 3 is for example purposes only and does not limit the scope of the game or the kinds of symbols that may be used in any given embodiment. The replay symbol 25 may be identically shown on the craps table 5 as areas for players to place REPLAY™ bets. The method of the REPLAY™ bet includes moving the REPLAY™ puck 20 off the actual point number in the point number area 10 on the table when the point has been made. In other words, the dealer simply slides the REPLAY™ puck 20 over a bit off the number at issue so that the replay number in the point number area 10 is visible again.
When the shooter establishes the same point again, a traditional craps puck is moved back on to the number in the point number area 10. Upon making the established point a second time, the regular craps puck is removed from the point number area 10, and a REPLAY™ chip 30, shown in FIG. 3, is placed on top of the “1” on the REPLAY™ puck already in position for that point. The process continues for establishing and making the same point number for the maximum number of occurrences of that made point. With the goal of the bet being for the shooter to achieve 3 to 6 occurrences of the same point number, the game includes moving the regular craps puck on and off the point number for occurrences of established points and adding an appropriate REPLAY™ chip 30 every time the point number is made more than once in a single series. In other words, each REPLAY™ chip 30 (FIGS. 3B to 3F) bears an indicia showing how many times the point has been converted from an established point to a made point in a single series of dice rolls.
In one sense, a goal of the invention is to allow craps players to place bets on the accumulation of multiple occurrences of a single made point in a series of dice rolls. In one embodiment, bets placed during the series are dealer-placed bets, as opposed to having betting positions in front of each player for placing the REPLAY™ bets. For example, according to one set up, craps players must ask the dealer to place their REPLAY™ bet prior to a shooter's first come-out roll of any series. When any given series ends by rolling a 7 (sevening out), the game pays the bettor a payout corresponding to the payout rate for the made point having the highest number of accumulated occurrences during that single series of dice rolls. When multiple made points have the same number of accumulated occurrences during a single series of dice rolls, the bettor receives a payout that is the highest payout available.
The proposition bet according to this invention further includes the option of players making an insured bet that pays out when a single point is established and made two times during a single series of dice rolls, and at least one other point has been made at least once. Again, the bettor on an insured bet receives the highest payout available for any point that has been made at least twice. In yet another embodiment, the craps game may include a progressive jackpot in which the casino (i.e., the house) sets aside a certain amount of house winnings to be paid upon particular occurrences.
The invention herein further includes a craps table 5 having a peripheral wall for playing the game of craps therein, the table 5 being accessible by a dealer utilizing a place bet area on the table. One form of the table includes a REPLAY™ bet wager area 40 between the table wall 7 and the traditional place bet area 37. See FIG. 1. The REPLAY™ bet wager area may be proximate both the pass line and the place bet area 37 on the table 5. The replay bet wager area 40 is sufficiently close to the peripheral wall on the table to leave open space on the table between the traditional place bet area 37 and the replay bet wager area 40. The replay bet area 40 comprises a betting position for each player at the table. In a different embodiment, shown in FIG. 2, the REPLAY™ bet wager area 40 is below the proposition bet area traditionally in the center of the table.
The game described above has a probability analysis as set forth below. The probabilities are shown for a single shooter scoring a certain dice combination a certain number of times during a single series of rolls in the game of craps before sevening out:

TABLE 1

Probability of Dice Scores in a Single Series Before Sevening Out:

Event	Probability	Odds

4 made exactly 3 times	0.02649445%	3773:1
4 made exactly 4 times	0.00170035%	58810:1
4 made exactly 5 times	0.00010945%	913658:1
4 made 6 or more times	0.00000825%	12121211:1
* * *	* * *	* * *
5 made exactly 3 times	0.09256765%	1079:1
5 made exactly 4 times	0.00931425%	10735:1
5 made exactly 5 times	0.00095610%	104591:1
5 made 6 or more times	0.00010820%	924213:1
* * *	* * *	* * *
6 made exactly 3 times	0.22437600%	445:1
6 made exactly 4 times	0.03085235%	3240:1
6 made exactly 5 times	0.00422565%	23664:1
6 made 6 or more times	0.00068120%	146799:1
* * *	* * *	* * *
8 made exactly 3 times	0.22437600%	445:1
8 made exactly 4 times	0.03085235%	3240:1
8 made exactly 5 times	0.00422565%	23664:1
8 made 6 or more times	0.00068120%	146799:1
* * *	* * *	* * *
9 made exactly 3 times	0.09256765%	1079:1
9 made exactly 4 times	0.00931425%	10735:1
9 made exactly 5 times	0.00095610%	104591:1
9 made 6 or more times	0.00010820%	924213:1
* * *	* * *	* * *
10 made exactly 3 times	0.02649445%	3773:1
10 made exactly 4 times	0.00170035%	58810:1
10 made exactly 5 times	0.00010945%	913658:1
10 made 6 or more times	0.00000825%	12121211:1

The probability table above is based on the idea of determining the number of times each REPLAY™ point is made during one series prior to the shooter sevening out. The calculations are based on the fact that dice used in a casino are weight balanced, and the probability distribution of the sum of two dice is as follows:

TABLE 2

Probability of an Individual Score by Rolling Two Dice

score

	2	3	4	5	6	7	8	9	10	11	12

prob	1/36	2/36	3/36	4/36	5/36	6/36	5/36	4/36	3/36	2/36	1/36

The casino running the craps game described herein would calculate a house edge by adjusting the pay-out for certain events. Examples of these house edge tables are set forth in Tables 3, 4, and 5 below:

TABLE 3

Sample Pay-Out Table for House Edge of 29%

Event	Probablity	Odds	Pay-Out

4 made exactly 3 times	0.02649445%	3773:1	100:1
4 made exactly 4 times	0.00170035%	58810:1	1000:1
4 made exactly 5 times	0.00010945%	913658:1	5000:1
4 made 6 or more times	0.00000825%	12121211:1	250000:1
* * *	* * *	* * *	* * *
5 made exactly 3 times	0.09256765%	1079:1	50:1
5 made exactly 4 times	0.00931425%	10735:1	500:1
5 made exactly 5 times	0.00095610%	104591:1	2500:1
5 made 6 or more times	0.00010820%	924213:1	10000:1
* * *	* * *	* * *	* * *
6 made exactly 3 times	0.22437600%	445:1	30:1
6 made exactly 4 times	0.03085235%	3240:1	100:1
6 made exactly 5 times	0.00422565%	23664:1	700:1
6 made 6 or more times	0.00068120%	146799:1	5000:1
* * *	* * *	* * *	* * *
8 made exactly 3 times	0.22437600%	445:1	30:1
8 made exactly 4 times	0.03085235%	3240:1	100:1
8 made exactly 5 times	0.00422565%	23664:1	700:1
8 made 6 or more times	0.00068120%	146799:1	5000:1
* * *	* * *	* * *	* * *
9 made exactly 3 times	0.09256765%	1079:1	50:1
9 made exactly 4 times	0.00931425%	10735:1	500:1
9 made exactly 5 times	0.00095610%	104591:1	2500:1
9 made 6 or more times	0.00010820%	924213:1	10000:1
* * *	* * *	* * *	* * *
10 made exactly 3 times	0.02649445%	3773:1	100:1
10 made exactly 4 times	0.00170035%	58810:1	1000:1
10 made exactly 5 times	0.00010945%	913658:1	5000:1
10 made 6 or more times	0.00000825%	12121211:1	250000:1

If the $250,000 pay-out in the above table is reduced to $100,000 as indicated in the following table, then the house edge is 31%.

TABLE 4

Pay-out Schedule with 31% House Edge

Event	Probablity	Odds	Pay-Out

4 made exactly 3 times	0.02649445%	3773:1	100:1
4 made exactly 4 times	0.00170035%	58810:1	1000:1
4 made exactly 5 times	0.00010945%	913658:1	5000:1
4 made 6 or more times	0.00000825%	12121211:1	100000:1
* * *	* * *	* * *	* * *
5 made exactly 3 times	0.09256765%	1079:1	50:1
5 made exactly 4 times	0.00931425%	10735:1	500:1
5 made exactly 5 times	0.00095610%	104591:1	2500:1
5 made 6 or more times	0.00010820%	924213:1	10000:1
* * *	* * *	* * *	* * *
6 made exactly 3 times	0.22437600%	445:1	30:1
6 made exactly 4 times	0.03085235%	3240:1	100:1
6 made exactly 5 times	0.00422565%	23664:1	700:1
6 made 6 or more times	0.00068120%	146799:1	5000:1
* * *	* * *	* * *	* * *
8 made exactly 3 times	0.22437600%	445:1	30:1
8 made exactly 4 times	0.03085235%	3240:1	100:1
8 made exactly 5 times	0.00422565%	23664:1	700:1
8 made 6 or more times	0.00068120%	146799:1	5000:1
* * *	* * *	* * *	* * *
9 made exactly 3 times	0.09256765%	1079:1	50:1
9 made exactly 4 times	0.00931425%	10735:1	500:1
9 made exactly 5 times	0.00095610%	104591:1	2500:1
9 made 6 or more times	0.00010820%	924213:1	10000:1
* * *	* * *	* * *	* * *
10 made exactly 3 times	0.02649445%	3773:1	100:1
10 made exactly 4 times	0.00170035%	58810:1	1000:1
10 made exactly 5 times	0.00010945%	913658:1	5000:1
10 made 6 or more times	0.00000825%	12121211:1	100000:1

If the $30 pay-out in the above table is raised $50 and the $50 pay-out is raised to 75, as indicated in the following table, then the house edge is 18%.

TABLE 5

Pay-out Schedule with 18% House Edge

Event	Probablity	Odds	Pay-Out

4 made exactly 3 times	0.02649445%	3773:1	100:1
4 made exactly 4 times	0.00170035%	58810:1	1000:1
4 made exactly 5 times	0.00010945%	913658:1	5000:1
4 made 6 or more times	0.00000825%	12121211:1	100000:1
* * *	* * *	* * *	* * *
5 made exactly 3 times	0.09256765%	1079:1	75:1
5 made exactly 4 times	0.00931425%	10735:1	500:1
5 made exactly 5 times	0.00095610%	104591:1	2500:1
5 made 6 or more times	0.00010820%	924213:1	10000:1
* * *	* * *	* * *	* * *
6 made exactly 3 times	0.22437600%	445:1	50:1
6 made exactly 4 times	0.03085235%	3240:1	100:1
6 made exactly 5 times	0.00422565%	23664:1	700:1
6 made 6 or more times	0.00068120%	146799:1	5000:1
* * *	* * *	* * *	* * *
8 made exactly 3 times	0.22437600%	445:1	50:1
8 made exactly 4 times	0.03085235%	3240:1	100:1
8 made exactly 5 times	0.00422565%	23664:1	700:1
8 made 6 or more times	0.00068120%	146799:1	5000:1
* * *	* * *	* * *	* * *
9 made exactly 3 times	0.09256765%	1079:1	75:1
9 made exactly 4 times	0.00931425%	10735:1	500:1
9 made exactly 5 times	0.00095610%	104591:1	2500:1
9 made 6 or more times	0.00010820%	924213:1	10000:1
* * *	* * *	* * *	* * *
10 made exactly 3 times	0.02649445%	3773:1	100:1
10 made exactly 4 times	0.00170035%	58810:1	1000:1
10 made exactly 5 times	0.00010945%	913658:1	5000:1
10 made 6 or more times	0.00000825%	12121211:1	100000:1

The game described herein is set forth further in the claims below.

Claims

1. A method of playing the game of craps with a series of dice rolls and with winning payout rates based on the respective probabilities of accumulating specified numbers of occurrences of particular pairs of dice roll combinations having identical total point values, the method comprising:

identifying an established point by rolling dice having a total point value selected from the group consisting of 4, 5, 6, 8, 9, and 10, wherein the established point is equal to the total point value of the dice;

converting said established point into a made point by rolling dice within a single series of dice rolls such that the dice have the same total point value as said established point;

accumulating multiple occurrences of any made point to a specified number of occurrences within a single series of dice rolls, wherein each roll in the series has a point value other than 7 and wherein the specified number of occurrences of a single made point determines a payout for bettors.

2. A method of playing the game of craps according to claim 1, wherein the series of dice rolls is complete upon the event of any dice roll having a total point value of 7.

3. A method of playing the game of craps according to claim 1, wherein the specified number of occurrences the single made point leading to a payout for bettors is between 3 and 6.

4. A method of playing the game of craps according to claim 1, further comprising the step of paying bets according to the payout rates for the specified number of occurrences of a single made point accumulated prior to completing the series by rolling a 7.

5. A method of playing the game of craps according to claim 1, further comprising the step of indicating on a craps table the established points in the series with an established point indicator.

6. A method of playing the game of craps according to claim 5 further comprising indicating established points with a REPLAY™ puck.

7. A method of playing the game of craps according to claim 6, further comprising the step of indicating on a craps table the made points in the series of dice rolls.

8. A method of playing the game of craps according to claim 7, wherein the step of indicating made points comprises moving the REPLAY™ puck to a made point location on the craps table.

9. A method of playing the game of craps according to claim 8, further comprising the step of converting multiple established points to made points during the series of dice rolls.

10. A method of playing the game of craps according to claim 9, further comprising the step of converting to a made point, more than once, at least one of the points selected from the group consisting of 4, 5, 6, 8, 9, and 10.

11. A method of playing the game of craps according to claim 10, further comprising the step of placing a REPLAY™ chip on the REPLAY™ puck for those established points converted to made points more than once during the series of dice rolls.

12. A method of playing the game of craps according to claim 11, further comprising the step of placing multiple REPLAY™ chips on a puck, wherein each REPLAY™ chip bears an indicia showing how many times the point has been converted from an established point to a made point in a single series of dice rolls.

13. A method of playing the game of craps according to claim 1, further comprising placing bets on the accumulation of multiple occurrences of a single made point in a series of dice rolls, wherein bets placed during the series are dealer-placed bets.

14. A method of playing the game of craps according to claim 1, further comprising paying the bettor a payout corresponding to the payout rate for the made point having the highest number of accumulated occurrences during a single series of dice rolls.

15. A method of playing the game of craps according to claim 14, further comprising paying the bettor a payout that is the highest payout available when multiple made points have the same number of accumulated occurrences during a single series of dice rolls.

16. A method of playing the game of craps according to claim 1, further comprising the step of players making an insured bet that pays out when a single point is established and made two times during a single series of dice rolls along with a different point being established at least once.

17. A craps table having a peripheral wall for playing the game of craps therein, the table being accessible by a dealer utilizing a place bet area on the table, the table comprising a REPLAY™ bet wager area between the wall and the place bet area.

18. A craps table according to claim 17, wherein the REPLAY™ bet wager area is proximate both the pass line and the place bet area on the table.

19. A craps table according to claim 18, wherein the REPLAY™ bet wager area is sufficiently close to the peripheral wall on the table to leave open space on the table between the place bet area and the REPLAY™ bet wager area.

20. A craps table according to claim 17, wherein the REPLAY™ bet area comprises a betting position for each player at the table.