;;Model Easy Money globals [updates race-over pause ;; controls in the procedure can-pay total-can-pay winner winnings ;; these and remaining globals are defined in INFORMATION take takes total-take extras odds-0 odds-1 odds-2 odds-3 odds-4 odds-5 bets-1 bets-2 bets-3 bets-4 bets-5 bets total-bets take-1 take-2 take-3 take-4 take-5 pay-1 pay-2 pay-3 pay-4 pay-5 pays-1 pays-2 pays-3 pays-4 pays-5 ] to setup ca crt 6 ask turtle 0[set heading 0 set shape "wolf" set size 2 set color brown setxy -9 -24] ;; the hare ask turtle 1[set heading 0 set shape "turtle" set size 2 set color black setxy -6 -24] ;; turtle 1 ask turtle 2[set heading 0 set shape "turtle" set size 2 set color blue setxy -3 -24] ;; " 2 ask turtle 3[set heading 0 set shape "turtle" set size 2 set color gray setxy 0 -24] ;; " 3 ask turtle 4[set heading 0 set shape "turtle" set size 2 set color magenta setxy 3 -24] ;; " 4 ask turtle 5[set heading 0 set shape "turtle" set size 2 set color red setxy 6 -24] ;; " 5 ask turtles[set label who] ;; turtles show ID default ;; sets default values of bets set take-% 10 ;; " " value of take-% set updates 0 ;; counts procedure steps set pause false ;; resets the pause procedure for a zero odds ask patches[ if pxcor <= 9 and pycor <= 25[set pcolor 55] ;; makes the green course if pxcor >= -9 and pxcor <= 9 and pycor = -25[set pcolor 45] ;; makes the yellow start line if pxcor = -9 and pycor >= 20[set pcolor 54.99]] ;; makes a hazard for the hare end to default set bet-1 5 ;; default value of the bet set bet-2 15 ;; " " " " " set bet-3 10 ;; " " " " " set bet-4 25 ;; " " " " " set bet-5 20 ;; " " " " " end to go ifelse updates >= 50[stop][ ;; stops the run at 50 steps bet-random ;; makes typical values of bets calc ;; calculates the odds ifelse pause = true[stop][ ;; stops go for zero odds wait 0.5 pay set total-bets total-bets + bets wait 0.5 pays wait 0.5 plot-odds set updates updates + 1]] ;; counts procedure steps end to bet-random ;; makes typical values of bets if random 40 = 1 [set bet-1 (5 * (1 + random 10))] if random 40 = 2 [set bet-2 (5 * (1 + random 10))] if random 40 = 3 [set bet-3 (5 * (1 + random 10))] if random 40 = 4 [set bet-4 (5 * (1 + random 10))] if random 40 = 5 [set bet-5 (5 * (1 + random 10))] end to calc ;; calculates the odds set bets bet-1 + bet-2 + bet-3 + bet-4 + bet-5 set take bets * take-% / 100 ;; calculates the bookie's take set can-pay bets - take ;; calculates how much left to pay the winners set odds-1 int ((can-pay / bet-1) - 1) ;; calculates odds for the bet if odds-1 = 0[set pause true] ;; the zero odds discriminant set odds-2 int ((can-pay / bet-2) - 1) if odds-2 = 0[set pause true] set odds-3 int ((can-pay / bet-3) - 1) if odds-3 = 0[set pause true] set odds-4 int ((can-pay / bet-4) - 1) if odds-4 = 0[set pause true] set odds-5 int ((can-pay / bet-5) - 1) if odds-5 = 0[set pause true] end to reset ;; resets the odds calculation after an odds = 0 found set bets 0 set take 0 set take-% 0 set can-pay 0 set odds-1 0 set odds-2 0 set odds-3 0 set odds-4 0 set odds-5 0 set pause false ;; resets the odds zero discriminant end to step-run go ;; runs go once set take-% 10 ;; sets take-% back to 10 default ;; sets bets to default values end to pay ;; calculates the pay for each bet plus stake return set pay-1 (bet-1 * odds-1) + bet-1 set pay-2 (bet-2 * odds-2) + bet-2 set pay-3 (bet-3 * odds-3) + bet-3 set pay-4 (bet-4 * odds-4) + bet-4 set pay-5 (bet-5 * odds-5) + bet-5 end to pays ;; adds the bets for each turtle set pays-1 pays-1 + pay-1 set pays-2 pays-2 + pay-2 set pays-3 pays-3 + pay-3 set pays-4 pays-4 + pay-4 set pays-5 pays-5 + pay-5 set total-can-pay total-can-pay + can-pay ;; adds up all available for paying set takes takes + take ;; adds up all the bookmakers take end to plot-odds set-current-plot "betting on turtles" set-current-plot-pen "turtle-1" plot odds-1 set-current-plot-pen "turtle-2" plot odds-2 set-current-plot-pen "turtle-3" plot odds-3 set-current-plot-pen "turtle-4" plot odds-4 set-current-plot-pen "turtle-5" plot odds-5 end to race ifelse race-over = true[stop][ ask turtle random 6[ifelse color-ahead = 45[if winner = 0[set winner who win]][ ;; racing the turtles ifelse color-ahead = 54.99[fd 0.001 * random 2][fd 0.001 * random 3]]]] ;; slowing the hare end to-report color-ahead ;; used to stop the turtles at the winning line and slow the hare report pcolor-of patch-at dx dy end to win ;; pays the winning bets and the bookmakers take plus extras if winner = 1[set winnings pays-1] if winner = 2[set winnings pays-2] if winner = 3[set winnings pays-3] if winner = 4[set winnings pays-4] if winner = 5[set winnings pays-5] set extras total-bets - takes - winnings ;; calculates the extras set total-take takes + extras set race-over true end @#$#@#$#@ GRAPHICS-WINDOW 629 10 787 437 9 25 7.8 1 10 0 1 CC-WINDOW 2 380 132 441 Command Center SLIDER 1 346 199 379 take-% take-% 0 20 10 5 1 NIL MONITOR 7 283 69 332 NIL total-bets 0 1 MONITOR 260 298 340 347 NIL total-can-pay 2 1 MONITOR 201 348 258 397 NIL take 2 1 SLIDER 1 48 140 81 bet-1 bet-1 5 50 20 5 1 NIL SLIDER 1 99 138 132 bet-2 bet-2 5 50 40 5 1 NIL SLIDER 2 148 138 181 bet-3 bet-3 5 50 30 5 1 NIL SLIDER 2 196 138 229 bet-4 bet-4 5 50 35 5 1 NIL SLIDER 2 246 138 279 bet-5 bet-5 5 50 25 5 1 NIL MONITOR 201 47 258 96 NIL pay-1 2 1 MONITOR 202 97 259 146 NIL pay-2 2 1 MONITOR 201 147 258 196 NIL pay-3 2 1 MONITOR 201 197 258 246 NIL pay-4 2 1 MONITOR 201 247 258 296 NIL pay-5 2 1 BUTTON 20 10 124 43 setup setup NIL 1 T OBSERVER MONITOR 142 47 200 96 NIL odds-1 0 1 MONITOR 142 97 200 146 NIL odds-2 0 1 MONITOR 142 147 200 196 NIL odds-3 0 1 MONITOR 141 197 199 246 NIL odds-4 0 1 MONITOR 140 247 198 296 NIL odds-5 0 1 MONITOR 332 350 393 399 NIL extras 2 1 MONITOR 76 283 133 332 NIL bets 0 1 MONITOR 259 47 314 96 NIL pays-1 2 1 MONITOR 260 97 315 146 NIL pays-2 2 1 MONITOR 260 147 315 196 NIL pays-3 2 1 MONITOR 260 197 314 246 NIL pays-4 2 1 MONITOR 260 247 314 296 NIL pays-5 2 1 MONITOR 202 297 258 346 NIL can-pay 2 1 MONITOR 261 349 330 398 NIL takes 2 1 BUTTON 512 403 617 436 run race race T 1 T OBSERVER MONITOR 396 350 463 399 total take total-take 2 1 PLOT 318 10 625 263 betting on turtles updates odds 0.0 50.0 0.0 20.0 true true PENS "turtle-1" 1.0 2 -16777216 true "turtle-2" 1.0 2 -16776961 true "turtle-3" 1.0 2 -7566196 true "turtle-4" 1.0 2 -65281 true "turtle-5" 1.0 2 -65536 true MONITOR 395 299 462 348 NIL winnings 0 1 MONITOR 533 352 583 401 NIL winner 0 1 MONITOR 395 401 462 450 NIL total-bets 0 1 BUTTON 177 10 283 43 run/pause go T 1 T OBSERVER TEXTBOX 635 437 777 467 0 1 2 3 4 5 MONITOR 531 264 585 313 updates updates 0 1 BUTTON 152 401 252 434 reset odds reset NIL 1 T OBSERVER BUTTON 267 402 373 435 step run step-run NIL 1 T OBSERVER @#$#@#$#@ MODEL EASY MONEY --------------- This model was made to illustrate the apparent ease with which a "book" might be made to provide a guaranteed take, that is, if the Bookmaker follows these simple rules: RULE 1. No bet should be accepted until the set of proposed bets of which it is a member have had the procedure run to determine the ODDS for the bets and no ODDS is zero. The ODDS will be zero if any bet in the set is too high to be covered by the other bets in the set. RULE 2. If a bet is not covered the Bookmaker may reduce the take* and the take should be restored upwards as soon as conditions permit. Alternatively the bet should be refused at that time or perhaps put aside until it can be associated with a set** of proposed bets that will cover it.*** RULE 3. In calculating the ODDS for a bet always round down to the integer. *Reducing the take, even to zero, is a good option because much of the total take comes from the extras made by rounding down to the integer in the ODDS calculation. **Waiting for a set of bets to cover each other is the simplest of methods guaranteeing a take; also the delay involved, very little in a busy office, can probably be made acceptable to most gamblers. ***In this model these actions take place automatically when RESET ODDS and STEP RUN are pressed in sequence to clear a zero ODDS condition. THE CALCULATIONS ---------------- To gain clarity the model has been kept simple. For example, it has been made to accept only bets to win, (no place bets); also a set of bets, on all turtles, is made at each step of the procedure; also ODDS less than one are not considered. The algebra of the procedure in this model is: (for a SINGLE RACE with 5 turtles and 1 hare competing; also it uses turtle-1 where necesary as the example; also no one bets on the hare, a known loser.). bet-1 = value of a bet made on turtle 1. odds-1 = odds for " " " " " " bets = the sum of bets proposed but not yet accepted, = bet-1 + bet-2 + bet-3 + bet-4 + bet-5 in this model. total-bets = the sum of ALL BETS ON THIS RACE TO THIS TIME, also see below. take = bets x (take-% / 100), (preceeds the odds calculation.) can-pay = bets - take, (preceeds the odds calculation.) odds-1 = integer((can-pay/bet-1) - 1), (the - 1 allows for return of the stake; also rounding down to the integer makes extras for the Bookmaker.) pay-1 = (bet-1 x odds-1) + bet-1, (the + bet-1 is return of the stake for a winning bet.) pays-1 = addition of pay-1's. total-can-pay = " " can-pay's. takes = " " take's. extras = gain from rounding down to the integer in the odds calculation. total take = takes + extras. total-bets = winnings + total take (after the race this checks the overall arithmetic.) USING THE MODEL --------------- SETUP will clear all and bring the turtles and hare to the starting gate and set to default values the BETS and TAKE-% RUN/PAUSE will illustrate 50 steps of betting with random changes of bet values; also the odds change in accordance with the rule that high values of bets will reduce the odds, including to zero, in which case the procedure automatically freezes. RESET ODDS will unfreeze the procedure and set take-% to zero (temporarily), so that the high value bet is covered. STEP RUN will run the procedure for one step to check that the freezing condition has been cleared and it will reset take-% and the bets to the default values. RUN/PAUSE will continue the run. PAUSE will pause the procedure to enable experimental manual setting of the bet and take sliders. RUN RACE will run the race and complete the calculations to reveal the winner plus the winnings. Readers of fables will no doubt note that the HARE with ID 0, lives up to its reputation. FURTHER READING --------------- The author has no experince of gambling or bookmaking and consequently is not in a position to make suggestions under this heading. However the author would be pleased to receive comments and information that would remedy this situation. The author Derek Rush may be contacted by Email at derekrush@beeb.net June 2003. @#$#@#$#@ default true 0 Polygon -7566196 true true 150 5 40 250 150 205 260 250 ant true 0 Polygon -7566196 true true 136 61 129 46 144 30 119 45 124 60 114 82 97 37 132 10 93 36 111 84 127 105 172 105 189 84 208 35 171 11 202 35 204 37 186 82 177 60 180 44 159 32 170 44 165 60 Polygon -7566196 true true 150 95 135 103 139 117 125 149 137 180 135 196 150 204 166 195 161 180 174 150 158 116 164 102 Polygon -7566196 true true 149 186 128 197 114 232 134 270 149 282 166 270 185 232 171 195 149 186 149 186 Polygon -7566196 true true 225 66 230 107 159 122 161 127 234 111 236 106 Polygon -7566196 true true 78 58 99 116 139 123 137 128 95 119 Polygon -7566196 true true 48 103 90 147 129 147 130 151 86 151 Polygon -7566196 true true 65 224 92 171 134 160 135 164 95 175 Polygon -7566196 true true 235 222 210 170 163 162 161 166 208 174 Polygon -7566196 true true 249 107 211 147 168 147 168 150 213 150 Polygon 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