GAM 



GAN 



TABLE, 



Showing 1 the Odds of Winning in any Game, when the number of Games wanting 

 does not exceed Six, and the Skill of the Contenders is equal. 



The above proportions are found by 

 the binomial theorem in a very easy way. 

 Suppose the games wanting 1 and 5, 

 raise a+6 to the fifth power, being the 

 number of games which must determine 

 the bet. a=b in this case, as the skill is 

 equal: a5+5,a* b + 19, a3 b 1 + 10, a- 63 

 -f- 5, a b* + 65, the first five coefficients 

 are the chances of him who has 1 game 

 to get, viz. 1 + 5 + 10 -f- 10 + 5 31, 

 and the other, viz. 1, the chance of him 

 who has five to get, 



Suppose the games wanting are 2 and 

 5, then a 6 +6, a* b + 15, a* b~ + 20, a3 63 

 + 15, a 1 6* + 6, a fr + b 6 , the chances 

 for him wanting two are 1 + 6 + 15 + 

 20+15 =57; but for him wanting 5, 

 are 6 -|- 1 = 7 according to table 57 : 7. 



Suppose the games wanting 4 and 6, 

 then a9+9, a 8 6+36, a 7 b 1 + 84, a 6 63 + 

 126, 5 64 -f 126, rt* 65 + 84, a3 b 6 + 36, 

 fl 47 + g t 6 8 +69; therefore for him 

 wanting 4 games, 1 -|- 9 -f- 36 -f 84 + 

 126 -f 126 = 382, and to him wanting 6 

 are 84 + 36 + 9 + 1 = 130 : the odds 

 are 382: 130 according to table. 



When the skill is not equal, or when 

 the chances for winning are not equal: as, 



1. If A and B play together, and A 

 wants 1 game of being up, and B wants 

 2 ; but the chances whereby B may win 

 a game are double to the number of 

 chances whereby A may win the same. 

 Here the number of games are two. And 

 = 1 and b == 2 .-. a z + 2 a 6 -f 6> will 

 give the probability of each. A = 1 + 

 4 = 5 and B = 4 or the probabilities are 

 A: B::5:4. 



1. A wants 3 games of being up, B 

 7; the proportion of chances 3 to 5, what 

 is the proportion of chances to win the 

 set? here the number of games will be 

 9, a =36 = 5, therefore raise a + 6)9 

 and the three last terms -=- by a + 69 

 will express the chances of B, which sub- 



VOL. V. 



tracted from unity gives the chances of 

 A : thus, 



a 9 + 9, a 8 6+35, a? 6 + 84, a 6 63 + 126, 

 5 b* + 126, a4 65 + 84, as b 6 + 36, a 1 6? 

 + 9, a 6* +69. 



X 5 s + 324 X 5|7 



B =- 



J|7 x 25+27 .5 + 324 37812500 



8|9 ~~ 1342 17728' 



GAMMONING, among seamen, de- 

 notes several turns of rope taken round 

 the bowsprit, and reeved through holes 

 in knees of the head, for the greater 

 security of the bowsprit. 



GAMMUT, GAM, GAMMA, or GAJT- 

 MAUT, in music, a scale, whereon we 

 learn to sound the musical notes, nt, re, 

 mi, fa, sol, la, in their several orders and 

 dispositions. 



GANG, in sea affairs, a select number 

 of a ship's crew appointed on any par- 

 ticular service, and commanded by an 

 officer suitable to the occasion. 



GAITG board, is a plank with several 

 steps nailed to it, for the convenience of 

 walking into or out of a boat upon the 

 shore, where the water is not deep 

 enough to float the boat close to the 

 landing place. 



GAXG tvay, a narrow platform, ofr 

 range of planks, laid horizontally along 

 the upper part of a ship's side, from the 

 quarter-deck to the forecastle, and is 

 peculiar to ships that are deep waisted, 

 for the convenience of walking more ex- 

 peditiously fore and aft than by descend- 

 ing into the waist: it is fenced on the out- 

 side by iron stanchions, and ropes or 

 rails, and in vessels of war with a netting, 

 in which part of the hammocks are stow- 

 ed. In merchantmen, it is frequently 

 called the gang-board. The same terra 

 is applied to that of a ship's side, 



Mm 



