INDOOR GOLF RULES A GAME OF GOLF DICE. The colours in sequence Red, White, Blue, Yellow and Green determine shot from tee to green.

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1 Golf Dice Some years ago my late father picked up a delightful set of five six-sided dice in a little leather case resembling a golf bag; the game has been published in other forms, both for sale and promoti. Essentially it is a variati poker dice; e of my first tasks was to transcribe the very fragile printed rules rule for posterity: INDOOR GOLF RULES A GAME OF GOLF DICE Every roll plays a hole 18 rolls 18 holes Par 72 The Five Dice are rolled e at a time. The colours in sequence Red, White, Blue, Yellow and determine shot from tee to green. Read the dice in the above order counting each dice a shot Unless penalty or extra shots are designated dice until the dice shows you are the green then putts are added for total score the hole. Obviously, if the third or fourth shot show holed out the score for hole is determined as no putts are necessary. If the first (red) or secd (white) shows the green putts must be added for score hole even though the yellow or blue may show holed out. Par each hole is FOUR. The lowest possible score is TWO (drive green and e putt). The highest possible score is NINE. Indoor Golf can be played match (by hole) or medal (by 18 hole score) with competitive interest the same as regular golf TWO BALL FOUR BALL and SUNNINGDALE etc. The colours of the dice have matured to varying degrees over the years: whilst red is still red, white has become cream, blue is midnight blue bordering black, yellow is reminiscent of Stroudley s Improved Engine whilst green itself is now best described as n-descript. Let s have a look at the dice, not forgetting each face substitutes the A-K-Q-J-10-9 of the poker dice, or if you prefer the of a cventi die. These are presented exactly as the faces except the dice text is capitalised:

2 One Red 150 Yards Outbound Bunker Yards 250 Yards Two White in Bunker short over 2 Water 1 Penalty 4 Three Blue Holed out short Four Yellow Holed out 4 & 5 in Bunker 6 5 Five 1 Putt Putt The titles have been arranged reading from left to right such that the best outcome can be read face up, being equivalent to the six a normal die; the latter so placed for comparis with five the vertical face to the right and therefore four to the frt. The ly excepti to this was the fifth, putting die, which, because it has two best outcomes, was opted with the worst at the five positi. The first point to note is that unlike a cvential arrangement of opposites; 6&1, 5&2 and 4&3 symmetrical, the three repeated outcomes Blue, Yellow and are not placed e each opposite pairs of faces; rather two of the three are opposite each other. That said at least the two 1-Putt are opposite each other. INDOOR GOLF probabilities The probabilities for straightforward Par 4 golf as defined by the rules are as follows, with the actual text substituted by interpretati; for example the actual Yardages One/Red are meaningless. In theory for five different six-sided dice of distinguishing colour there are 7776 individual combinatis but since more than e face e or more dice has the same outcome, according to the dice rolled, then there are a number of different outcomes for even the most extreme results: Die One/Red: 1/6 refer to Dice 5 1/6 Out of Bounds; in four via bunker refer to Dice 5 4/6 refer to Dice 2

3 Dice Two/White: 1/6 refer to Dice 5 1/6 in four via water refer to Dice 5 4/6 not refer to Dice 3 Dice Three/Blue: Dice Four/Yellow: Dice Five/ 1/6 holed out from off the 3/6 refer to Dice 5 2/6 not refer to Dice 4 1/6 holed out from off the 3/6 the refer to Dice 5 1/6 the in five refer to Dice 5 1/6 the in six via bunker refer to Dice 5 2/6 e putt 3/6 two putts 1/6 three putts The probabilities for each hole depend the cditial result of at least two of the dice. Therefore the probability of each outcome depends the product (multiplicati) of the probability of each individual relevant die. For example, to score an Eagle, two under par, this can ly be achieved by rolling (1/6) the Red and 1 Putt the (1/3). These individual probabilities are multiplied together, giving us 1 in 18 or as a decimal percentage to four figures. To score a Birdie, e under par, this can be achieved by: a) Specific (1/6) and 2 (3/6) making 1/12 b) Other (4/6), (1/6) with the White and 1 Putt (1/3) c) Other (4/6), not (4/6) and Holed out (1/6) with the Blue. This gives a cumulative probability of 1/12 plus 1/27 plus 2/27, which is 21/108 or 7/36 7 in 36 works out as but is does seem rather odd to be twice as likely to Birdie with the third from off the green rather than in two and hole out with a single putt The complete breakdown of outcomes is as follows: Shots Title Percentage Fracti 1 in 2 Eagle / Birdie / Par / Bogey / Double Bogey / Triple Bogey / Quadruple Bogey / /

4 As an exercise you can if you wish work out the probabilities for Par and all the Bogies. It might be easier starting with 9 (the worst possible score) followed by 8 and 7; as a starting point work out the permutatis of shots to achieve each required total, then work out each e, bearing in mind csistent element so two or more permutatis. So how do these figures translate towards overall understanding? 1. The chances of a score of below par (2 or 3) is exactly 1 in 4 or The chances of a double-bogey or worse is just under 1 in 3 or The chances of a double-bogey or better is marginally better than 9 in 10 or The chances of a triple-bogey or worse is marginally less than 1 in 10 or The average per hole is giving a Standard Scratch Score (SSS) for Par 72 of or +17.7% The game may be simply modified to allow for Par 3 and Par 5 holes as follows: On Par 3 Four of six alternates are ruled the in e and putt; Out of Bounds is the in two and putt. 150 is also ruled the in two and putt unless White die shows On, and both Blue and Yellow dice both show Holed Out as well, in which case it is a hole-in-e. Shots Title Percentage Fracti 1 in 1 Eagle/Hole in e / Birdie / Par / Bogey / Double Bogey / Note that because we allow for the possibility of a hole in e, the fracti for a Par can ly be simplified by a factor of two, and not at all for either Bogey. On Par 4 Such holes cannot be driven. If this face is disclosed the Red Dice, 300 yards or 250 yards, then is ruled the in two shots unless in the bunker or in four via the water. Over, Short and are therefore additial classed as the. So ly if the secd shot is in the bunker is there a need to go to the Blue and then possibly the Yellow die.

5 If 150 yards, the secd cannot be short so there are two chances of ending the with the White die. The dice are ly played totally cventially if the initial is topped. The original Par 4 table is therefore modified to: Shots Title Percentage Fracti 1 in 2 Eagle n/a n/a 3 Birdie / Par / Bogey / Double Bogey / Triple Bogey / Quadruple Bogey / / On Par 5 Such holes cannot be driven. If this is disclosed the Red Dice, or 300 yards, automatically regard as being the in two. This reflects the greater chance of a sub-par score such holes. The Out of Bounds the Red Dice is still taken as being the green in four; the worst possible score a Par 5 is still a 9 but now a quadruple bogey. Shots Title Percentage Fracti 1 in 3 Eagle / Birdie / Par / Bogey / Double Bogey / Triple Bogey / Quadruple Bogey / The statistics alter as follow. A Par 3 has an average of or %, a Par 4 has an average of or +18.7% whilst a Par 5 has an average of or 6.049% Notice that the shot average the Par 4s has actually ge up slightly because of the eliminati and e Putt What has been created from the basic game with relatively little adjustment is the beginning of a mathematical model. So the game could be played using the layout of any course you choose.

6 Another alternative is to create your own course with water, Out of Bounds and perhaps even bunkers assigned to certain holes ly. If there is no possibility of e or more of these three outcomes a particular hole, then the penalty stroke is ignored; as a csequence the overall score for the round would be a little less. House rules can further establish the influence scores specific holes: for example if there is water a Par three, the ball is ly in the water if Outbound is thrown Red and Water White and by rule the in three, raising the possibility of a six. Another rule might be created to allow for a 10 in an extreme case a certain hole or holes, maybe balanced by a Par 5 being capable of resulting in an Albatross (two shots; three under par) with the 300, White On, both Blue and Yellow dice show Holed Out and the as 3 just ce face opti per die; the same likelihood as rolling five sixes five cvential dice. The same logic and dice combinati could also be extended to e or two of the Par4s; say e the outward nine and e the back nine but with rather than 300.