The demand for chess in the United States, 1946-1990.

Chressanthis, George A.

I. Introduction

Ever since the seminal works of Becker (1965, 1975), economists have been fascinated with how consumers allocate their time among competing demands. However, far less research has been undertaken to explain the determinants of the demand for specific leisure activities. The probable reason for this void in research is the problem of securing data necessary to estimate a demand relationship.

This paper, with the help of data made available by the United States Chess Federation (USCF), will investigate the per capita demand for chess membership in the USCF from 1946-1990. Chess has long been considered an activity associated with other intellectual pursuits. The skills needed to be an accomplished chessplayer are often associated as necessary requirements to obtain success in other intellectual activities. Thus, while this study is specific to chess, it may also shed some light as to the demand for similar intellectual endeavors.

II. Chess in the United States

While its basic elements are fairly easy to learn, the game of chess is an extremely difficult and time-consuming game to master. Mastery of chess requires large investments in developing and refining human capital skills over long periods of time. For this reason, those players who have reached the highest level of play generally did so by learning the game in childhood. Only through continued study and practice for years in tournament play do individuals become master chessplayers.

Few individuals in the United States are chess professionals as measured by the attainment of the international title of grandmaster (GM). A recent listing published by the United States Chess Federation (1992), the principal governing body in this country which promotes and sponsors chess activities, names only 41 grand-masters out of a total USCF 1991 membership of 57,617.(1) Many of these internationally-titled players are emigres from other countries such as the former Soviet Union.(2) GMs try to make a living through monies won in chess tournaments here and abroad, or earned from activities such as instruction, writing articles or books, and simultaneous exhibitions. An equally small number of individuals in this country make their living through chess-related activities like selling chess equipment (i.e., chess sets, clocks, and books) and sponsoring and directing chess tournaments. Thus, for the overwhelming majority of players in this country, chess represents a leisure activity much like any other hobby or non-work endeavor.

Amateur chessplayers who join the USCF (founded in 1940), already place themselves in a distinct class of individuals from the rest of the national population. USCF members pay an annual membership fee which secures the right to enter all USCF sanctioned open events (after paying a tournament entry fee) and receive a rating (a measure of one's plying strength relative to other chessplayers). They also enjoy discounted prices for the purchasing of chess equipment, and receive a monthly magazine which keeps players abreast with chess related events here and abroad.

Players receive ratings after entering their first tournament, which can increase with wins or draws (provided the opponent has a higher rating) against other chessplayers. More points are awarded if the opponent has a higher rating. Reaching the top national rating category of master is attained by few chessplayers in the USCF (approximately 2%). However, players can lose their master title by continued poor play. Thus, attaining and keeping this elusive title is extremely difficult.

Several alternative chess-related activities are available through membership in the USCF. According to the 1991 USCF annual rating list, 28,360 USCF members played in over-the-board (OTB) games during 1991 through chess tournaments sponsored at the club, local, state, regional, and national levels. Many chess enthusiasts (approximately 11,000 as of 1991), for a variety of reasons, devote time to correspondence or postal chess. The USCF sponsors tournaments for these players, who like OTB players, can receive a postal rating and win prizes. A very small number of players devote themselves as composers of chess problems and endgame studies. Players in both of these areas can also receive international and national titles like OTB players. Lastly, since chess enthusiasts can engage in a number of different chess activities at the same time, the membership numbers provided by the USCF suggest that a significant portion of USCF members merely receive the monthly magazine and follow chess events in the U. S. and around the world. Thus, these individuals are interested enough in chess to join the USCF, though are unwilling or unable to participate further in its specific activities. A good review of the history and activities of the USCF for those not familiar with this organization is given in the 1992 yearbook issue of Chess Life published by the USCF (April 1992, pp. 43-57).

Thus, this paper will investigate the demand for a specific type of chess activity, those who choose to join the USCF. This is not to suggest that the only chessplayers in the United States are USCF players. Chess is probably played casually by tens of millions of people in this country. Although, it is probably safe to say, that those individuals who are able and willing to seek higher levels of knowledge and competition in chess do so via the USCF.

III. Demand Estimation

The demand regression equation for chess ([q.sub.t]*) over time t must contain determinants consistent with an ordinary demand function specification such as a vector of prices ([P.sub.t]) and income ([m.sub.t]) variables, a vector of exogenous variables ([x.sub.t]) that will change the demand for chess activity, the work-leisure tradeoff ([w.sub.t]), the tradeoff amongst alternative leisure ([l.sub.t]) activities, and changes in effort by the USCF ([e.sub.t]) that can effect chess membership.(3) Thus, the estimation problem can be written as follows:

[q.sub.t]* = q([p.sub.t], [m.sub.t], [x.sub.t], [w.sub.t], [l.sub.t], [e.sub.t]) (1)

where aside from the usual price effects, [q.sub.2][is greater than]0, [q.sub.4][is less than]0, [q.sub.5][is less than]0, and [q.sub.6][is greater than]0 are the signs for the expected marginal effects. The expected signs suggest that chess is a normal good, that increased time spent on work (w) and other leisure (l) activities will decrease demand, and increased effort by the USCF to promote chess (e) will increase demand.

Data and Empirical Model

The empirical model attempts to explain annual variations in per capita USCF membership, as indicated in Figure 1, over the period 1946-1990.(4) The data for this study came from the USCF national office and monthly issues of Chess Life (formerly entitled Chess Life & Review) dating back to 1946 for all chess-related variables, and traditional government-based publications for all remaining socio-economic variables in the model.(5)

The specification of the empirical model conforms to theoretical expectations. The regression equation contains explanatory variables consistent with a traditional ordinary demand function. In addition, the model contains variables which capture allocation of time decisions that are expected to alter the per capita demand for chess membership over time:

[MEMBERSHIP.sub.t] = [Alpha] + [[Beta].sub.1][PRICE.sub.t] + [[Beta].sub.2] [YOUTH.sub.t] + [[Beta].sub.3] [SCHOLASTIC.sub.t] + [[Beta].sub.4] [INCOME.sub.t] + [[Beta].sub.5] [FISCHER.sub.t] + [[Beta].sub.6] TV [STATIONS.sub.t] + [[Beta].sub.7][ WORK.sub.t] + [[Beta].sub.8] [TOURNAMENTS.sub.t] + [[Beta].sub.9] [OBSSQ.sub.t] + [[Epsilon].sub.t] (2)

where t = 1946, 1947, . . ., 1990. Table 1 provides all definitions of variables employed in the empirical model along with expected signs for all coefficients.

The dependent variable is USCF membership per 100,000 U.S. civilian population greater than or equal to 5 years of age (MEMBERSHIP). Civilian population (which includes armed forces overseas) is used since membership rights are open to and chess tournaments are held for USCF members in the military stationed abroad. The age of five years is approximately the age at which individuals can begin to learn chess.(6)

The list of independent variables comprising an ordinary demand function begins with the one-year regular membership price adjusted for consumer inflation (PRICE). The expected sign on the coefficient is negative, given the law of demand. The next two variables, YOUTH and SCHOLASTIC, represent the enactment of alternative prices for individuals age 19 and under. The YOUTH membership pricing structure, which began in 1967, offers younger individuals full membership benefits at about TABULAR DATA OMITTED half the regular membership rate. The SCHOLASTIC membership pricing structure, which began in 1976, offers younger individuals full membership benefits at a rate about half the youth membership rate, but excludes the monthly magazine. Both YOUTH and SCHOLASTIC are specified as zero-one dummy variables. The existence of both pricing structures are expected to increase USCF membership. The variable INCOME accounts for changes in real disposable income per capita. The assumption is that the demand for chess is a normal and/or luxury good, thus attaining a positive coefficient for this variable. In addition, the INCOME specification also measures the effect from changes in cyclical trends over time. Given the costs associated with travelling to and entering in OTB tournaments, INCOME measures the ability of members to absorb these costs.(7)

The remaining variables account for additional exogenously and endogenously-defined shifts that will change the demand for chess over time. The variable FISCHER accounts for the explosive impact on American chess from Robert Fischer winning the world championship against Boris Spassky in Reykjavik, Iceland in 1972. Fischer's reign as the first official American world champion went from 1972-1975.(8) The specification of the variable FISCHER, defined as 1946-1971 = 0, 1972-1975 = 2, and 1976-1990 = 1, represents that Fischer's effect has been long-standing on American chess, going well beyond the years in which he held the title.(9) This specification also suggests the Fischer's effect on USCF membership has been less pronounced after his title reign than during his years as world champion. A simple 0-1-0 dummy scheme to account for the periods before, during, and after his world championship reign, wrongly suggests that Fischer has had no effect on USCF membership and American chess after he forfeited the title to Anatoly Karpov in 1975. Fischer's world championship victory and personal mystique have been kept alive by a plethora of chess books and writings in the popular press as to his whereabouts after he left the public arena in 1972. As evidence of his longlasting impact on chess and potential effect on USCF membership, that despite an absence from chess competition in public for 20 years since his world championship match with Spassky in 1972, Fischer's return to chess in September 1992 in a rematch against Spassky has generated excitement and controversy unmatched by anyone currently playing in American chess. Last, and most important of all, Fischer's victory in 1972 brought exposure to chess, stimulating an attention to the game that goes well beyond his world title years.

The next two variables account for alternative uses of time from the context of leisure and work that tend to reduce USCF membership. The variable TV STATIONS represents the number of commercial television stations per capita, adjusted for percent of total households having at least one television.(10) The expected negative sign implies that the growth of this form of entertainment occupies more of people's time to the exclusion of other activities. In addition, the growth of television is expected to have a negative distracting influence on younger individuals to engage in chess activities, compromising the ability of the USCF to attract new members. The variable WORK represents the percent of time per week individuals are working, thus capturing the work-leisure trade-off. Given the time-consuming nature of playing chess, this variable is expected to have a negative sign.

The variable TOURNAMENTS measures changes in effort by the USCF national office to raise membership through the sponsorship of national OTB tournaments.(11) A more desired measure of effort is an annual count of USCF-affiliated chess clubs around the country. Unfortunately, such data has not been calculated or kept over the long sample time period in question. However, the variable TOURNAMENT does measure indirectly the increased development and activities by local clubs over time since national tournaments are coordinated with the assistance from organizers at the local level. National tournament cites are bid for by local clubs and state organizations as an additional way to promote chess in their immediate area or region. Thus, an increased ability for the USCF to hold more national tournaments in varied locations around the country does suggest a greater local organizational network to support and promote chess. An alternative proxy variable could be to calculate degree of urbanization in the United States since chess clubs and tournament activities are primarily located in cities. Again however, this measure is also not readily available.(12)

The last variable in the model is a time-counter squared measure (OBSSQ) to account for non-linearity in the trend of per capita USCF membership. As Figure 1 illustrates, the data exhibits an increasing rate growth path up through the Fischer title years while illustrating a more stabilized membership pattern afterwards. The expected negative sign suggests that per capita membership follows a general cubic function relationship. Table 2 Provides for the descriptive statistics of all variables in the empirical model.

Empirical Results

The empirical results for the regression equation displayed in Table 3 exhibit excellent statistical characteristics in terms of the adjusted [R.sup.2], Durbin-Watson, and F statistics. Moreover, no rejections of hypothesis tests concerning the anticipated signs on coefficient estimates occurred, and most estimates attained highly significant t-statistics. Unstandardized and standardized coefficients are provided in Table 3, the latter estimates allowing for direct comparisons of the coefficients to determine the relative importance of the independent variables [see Pindyck and Rubinfeld (1991, p. 85)].

The regression equation was respecified to account for expected simultaneity bias between MEMBERSHIP and TOURNAMENTS, using the procedure developed by Hausman (1978) and recommended by Pindyck and Rubinfeld (1991, pp. 174-176 and 303-305). The variable TOURNAMENTS was determined to be a function of MEMBERSHIP, INCOME, FISCHER, a year time trend, and the percent of U. S. civilian population ([greater than or equal to] age 5) that is white male. A reduced-form equation was formulated for TOURNAMENTS using the equation for MEMBERSHIP, and estimated using OLS. The residual value for TOURNAMENTS was calculated (RTOURNAMENTS) and applied directly into the OLS regression equation for MEMBERSHIP. The application of the Hausman specification test provided for the variable TOURNAMENTS to be significant with a positive coefficient sign as expected while accounting the for potential simultaneity bias in the OLS estimation.(13)

TABLE 2
Descriptive Statistics

 Standard
Dependent Variable Mean deviation Minimum Maximum
MEMBERSHIP 12.22 10.80 0.73 30.38

Independent Variables
PRICE 19.96 4.82 11.32 29.94
YOUTH 5.33 0.50 0.00 1.00
SCHOLASTIC 0.33 0.48 0.00 1.00
INCOME 8599.24 2290.35 5227.68 12422.34
FISCHER 0.51 0.66 0.00 2.00
TV STATIONS 0.25 0.12 1.42E-06 0.43
WORK 22.30 1.15 20.54 24.23
TOURNAMENTS 8.67 4.61 2.00 17.00
OBSSQ 720.49 655.71 1.00 2116.00

The significant variables in the model are PRICE, INCOME, FISCHER, TV STATIONS, WORK, TOURNAMENTS, OBSSQ, and RTOURNAMENTS [residual calculation of TOURNAMENTS to account for simultaneity bias as suggested by Hausman (1978)] as well as the CONSTANT. The empirical results reveal that variations in per capita USCF membership vary systematically according to implications of the law of demand. PRICE has a negative coefficient as expected and INCOME exhibits a positive coefficient sign, confirming the normal demand for chess as a leisure good. Moreover, changes in tastes and preferences towards chess, embodied by the variable FISCHER, and competing uses of time, measured by TV STATIONS and WORK, all reveal expected effects. Also, the significant positive coefficient on TOURNAMENTS confirms expectations that the demand for chess increases with greater effort by the USCF to promote chess activities and membership. In addition, the significance of the CONSTANT in the positive direction suggests that there are possible unobservable factors at work in bringing people to organized chess activities unrelated to the factors expressed in the model. Finally, the significance of OBSSQ suggests non-linearity in the trend of per capita USCF membership over time, as expected. An examination of the per capita membership data displayed in Figure 1 also reveals a national threshold function, where the trend since 1975 (the year Fischer lost his world title) has been fairly flat. This suggests the possibility of longer-term socio-economic, demographic, and/or cultural factors working against the ability of the USCF to raise per capita membership. The relative importance attached to OBSSQ, given the standardized coefficient estimate of -1.153, the largest measure in absolute value among all standardized coefficients, would confirm this assertion.

An examination of the remaining standardized coefficient reveals results consistent with expectations. Not surprisingly, the variable TOURNAMENTS has the highest positive standardized coefficient estimate of .801. This result supports the importance of the national and local organizational chess network to encourage greater chess activities and stimulate membership. The variable INCOME also has a high positive standardized coefficient of .636. This is consistent with the economic and educational background of individuals attracted to chess as a leisure activity. In addition, given the large number of members who are not active OTB players (50% for the year 1990), the demand for USCF membership can be viewed as a method used by individuals to achieve intellectual status of which income would be the most important determinant. Furthermore, the inactivity of many members may also explain why various attempts to model prices of complementary goods that are evident in OTB chess did not reveal statistical significance. Finally, the low ratio of OTB players to total USCF membership and the intellectual status that can be attached to USCF membership may also explain why the effects from PRICE and TV STATIONS are less than the effects from INCOME and WORK. While the increased popularity of chess brought by Fischer's victory (FISCHER) is evident (.308), dominating the effect from PRICE (-.117) and just slightly more than TV STATIONS (-.280), the effect from WORK (-.713) is more than twice as great in the opposite direction. These results suggest that studying chess and playing in tournaments is a very time-consuming process, and thus the impact of work time is quite revealing.

TABLE 3

OLS Estimates of the Determinants of the Demand for Chess in the United
States, 1946-1990

 Dependent variable Standardized
Explanatory variables MEMBERSHIP coefficients

CONSTANT 146.816(a*)
 (3.007)
PRICE -0.263(c) -.117
 (-1.520)
YOUTH 0.843
 (0.245)
SCHOLASTIC -0.891
 (-0.382)
INCOME 0.003(b) .636
 (2.076)
FISCHER 5.036(a) .308
 (5.117)
TV STATIONS -24.241(b) -.280
 (-1.919)
WORK -6.692(a) -.713
 (-3.137)
TOURNAMENTS 1.879(b) .801
 (1.877)
OBSSQ -0.019(a) -1.153
 (-3.491)
RTOURNAMENTS(**) -1.763(b)
 (-1.838)

Adjusted [R.sup.2] .968
D-W 2.296
F 132.421
N 45

Notes: t-statistics are given in parentheses. All hypotheses tests are
one-tailed.

* Unstandardized coefficient estimates.

** Defined as TOURNAMENTS -- (fitted value of TOURNAMENTS) to account for
simultaneity bias as suggested by Hausman (1978).

a,b,c Statistical significance at the 1%, 5%, 10% level respectively.

IV. Conclusions and Implications

This paper develops estimates of the demand for chess in the United States for the period 1946-1990. The statistical results conform to prior expectations regarding coefficient estimates on price, income, and tastes changes as suggested by the law of demand as well as factors measuring significant alternative uses of time which could lessen people's ability or desire to play chess through the USCF and efforts by the USCF to increase membership and chess activities. Also, the results are insensitive to alternative variable and model specifications. Although not measured in this study, it would be of interest for future research work to determine the effect on chess and other intellectual activities from the rise of electronic and computer games (including chess), cable television, and VCR's. This study along with future research may yield additional insights into the determinants of demand for other intellectual endeavors.

Recently, the USCF has acted more aggressively in ways that are consistent with implications from these empirical findings that occur too late in the sample period to be included in this analysis. First, the USCF has reached out to younger children in city neighborhoods through exhibitions and special events in order to develop a greater enthusiasm for the game. In addition, the USCF has promoted non-rated beginner events and rated beginner opens for low-rated or unrated players as a way to increase membership and promote greater OTB chess activity by players. The USCF also arranges "chess camps" to encourage and promote young promising talent, and further, advocates the use of chess in the schools and inner city neighborhoods as an educational aid and a tool against drug use. Second, the USCF has also allowed faster time controls for full-rated games, allowing individuals to get more chess activity within a smaller time frame. While chess purists have objected to the increased speed of chess games, a typical 5-round tournament that once took an entire weekend to complete can be finished in one day. Thus, the savings in time reduces costs for players and tournament organizers alike. In addition, the quickening pace of chess games with "sudden death" time controls have enlivened games that could drag on for hours beyond the initial time control making chess more appealing to younger players who are attracted to other games that offer greater excitement at a faster pace.(14) Third, the USCF was active in securing the location for the first 12 games of the 24-game Kasparov-Karpov word championship match played in New York City in the fall of 1990. Fourth, current world champion Gary Kasparov has been active in recent years promoting chess in the United States, targeting in particular young and promising talent.

Finally, and in a "move" unexpected by the chess establishment, the return of Bobby Fischer in September 1992 with his winning $5 million rematch with Boris Spassky ($3.35 and $1.65 million to the winter and loser respectively) in Sveti Stefan, Yugoslavia has brought chess once again national and international attention. While his return has been marked by controversy, something certainly not uncommon with Fischer, his reentry into the public chess arena will fuel discussion as to whether he will once again compete for the world title. Given the empirical evidence presented here, all of these actions and events should increase the accessibility, awareness, and popularity of chess in this country, ceteris paribus.

Notes

1. There are also 59 International Masters (IMs) and 19 International Women Masters (IWMs) in the United States as given in the April 1992 issue of Chess Life published by the USCF. However, a larger proportion of these players may not rely on chess as their primary source of income than players with a GM title.

2. Players from the former Soviet Union have dominated the world chess scene since before WWII when Russian Dr. Alexander Alekhine defeated Cuban Jose Capablanca in 1927. Aside from two brief world title reigns by Dr. Max Euwe (Holland, 1935-1937) and Robert Fischer (United States, 1972-1975), the world champion as been a Soviet player. Lastly, while the countries that comprise the former Soviet Union have the world's most GMs, Iceland has the most GMs per capita.

3. The price vector should comprise only the membership price and complementary good price effects. Since the USCF is the only national chess organization in the U. S., there are no true substitute goods for people who seek chess competition with others.

4. Although the USCF was created in 1940, the choice of starting the empirical analysis in 1946 was done to avoid the special circumstances specific to the years during Word War II.

5. The USCF national office provided annual membership data dating back to 1940 while the membership price information was retrieved from each January issue of the USCF magazine with assistance from the USCF national office.

6. The empirical results did not vary when U. S. resident population was used without any age restriction. The age 5 was used since the USCF holds a national championship tournament for elementary students as early as kindergarten. These empirical results are available from the author upon request.

7. A variety of complementary good prices were added to the regression, though each specification did not reveal any significance. Price indices for postcard rates (postal chess), fuel for automobiles, consumer goods, and public transportation (all representing costs associated with travel to tournaments) were employed. Data for developing a chess book price index was not readily available. Buying many chess books is not necessary for becoming a member and attaining a reasonable rating, though being a master requires more effort and expenditures on books. In addition, a price index for tournament entry fees was also not readily available, although these and other prices are captured in part by the consumer price index which was employed without success. Given the historical evidence of a low ratio of OTB players to USCF membership as measured by the annual rating list published by the USCF, the insignificance of variable measures to approximate changes in expenditures related to OTB chess activity should not be surprising. Lastly, prices for chess sets and clocks were also not readily available. However, unlike the other expenditures previously mentioned which can occur on an annual basis if someone chooses to be an active OTB or postal player, buying chess equipment is more of a one-time expenditure which can last for many years. The statistical results mentioned above are available from the author upon request.

8. Paul Morphy (1837-1884), a native of New Orleans, is considered by many chess historians to be the first American world champion, though no official title match was ever played.

9. Fischer was formally crowned as world champion on September 3, 1972 and officially lost the title on April 25, 1975. There are a variety of reasons for specifying 1972 as part of Fischer's reign as world champion, even though he formally won the title rather late in the year. First, anticipation about his title chase was abound after his convincing 1970 victories (score in parentheses) in the qualifying inter-zonal tournament at Palma de Majorca, Spain (18.5-4.5), the Buenos Aires International (152), and the Herceg Novi Five Minute World Championship (19-3), where former world champion Mikhail Tal finished a distant second at 14.5 points. Second, Fischer then easily disposed of GMs Mark Taimanov (Soviet Union) and Bent Larsen (Denmark) by the scores of 6-0 in early 1971 in challenger elimination matches. Such scores against GM competition are rare. Third, he then convincingly disposed of former world champion Tigran Petrosian (Soviet Union) 6.5-2.5 in October 1971, the final obstacle before the world championship match with Spassky. Thus, the Fischer-Spassky match had been known since October 1971 and officially started in July 1972, with many chess experts predicting and expecting a Fischer win. The final Fischer-Spassky score was 12.5-8.5 [New York Times Company (1972, 1973) and Chess Life & Review (various issues)].

10. A theoretically better measure would be average television viewing time per week per household. while Nielsen data on television viewing was obtained as early as 1950, data for many of the intervening years were not readily available. However, using a simple regression based upon time with 19 years of data available, the remaining years were estimated (a monotonically rising function). This variable (average viewing time per week adjusted for household coverage of television sets), also revealed a statistically significant negative coefficient sign. These results are available from the author upon request.

11. USCF sponsorship of national tournaments include the following championships: U. S. Championship, U. S. Open, U. S. Women's Championship, U. S. Junior Invitational, U. S. Amateur, National Open, National Elementary, National Junior High, National High School, U. S. Amateur Team, U. S. Cadet, U. S. Junior Open, U. S. Senior, U. S. Class, Arnold Denker Tournament of High School Champions, U. S. Action, U. S. Blind, and Pan Am Intercollegiate Team [USCF (April 1992, pp. 54-56)]. The specific years when each of these tournaments were held are available from the author upon request.

12. Data on USCF expenditures was not readily available over the entire period as a possible alternative specification for USCF effort to raise membership. However, most dues monies goes toward funding the monthly magazine. In 1992 for example, $21 of every regular membership price of $30 goes toward the subscription to Chess Life.

13. The variable TOURNAMENTS did not reveal significance in the OLS estimation without the correction for simultaneity bias. These statistical results are available from the author upon request.

14. All rated OTB chess games must be timed by a chess clock which keeps track of the time used up (and thus remaining) for each player. Typical first time controls without "sudden death" are for example 40 or 50 moves in 90 minutes or 2 hours respectively for each player. If a game is not over after the first time control (assuming that each player has made the allotment of moves within the time frame given, and if not, the first person violating the time control loses the game), then secondary time controls are instituted such as the next 20 or 30 moves in 1 hour (unused time from the first time control is carried over to the next time control). Thus a 70 move game can last around 6-7 hours. A "sudden death" time control can be as fast as 30 minutes to each player for the entire game. The game will either be decided on the board or by the clock, whomever violates time control first. More importantly however, the game will be over in only 1 hour instead of potentially 6-7 hours.

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