EP0688002B1 - Method for selecting stopping positions of reels in a gaming machine - Google Patents

Description

Background and Summary of the Invention
• The present invention generally relates to gamingapparatus and, more particularly, to electronic reel-type slotmachines having a plurality of reels rotatable about a commonaxis. In a typical reel-type slot machine, a payoff is made to aplayer when a winning set of symbols is displayed on the payline(s) of the machine. To start play, a button is pushed or ahandle is pulled to initiate rotation of the reels.
• In one type of design, the angular positions of thereels, after they have been stopped, is detected and theappropriate payoff amount, if any, is calculated and paid to theplayer. Another approach in modern machines uses a random numbergenerator to select the symbols to be displayed on the payline(s). The payoff is then determined based on a pay table which contains payoff amounts for the various winning symbol combinations. Payoffamounts provided by either approach are limited because there is a fixed limit on theprobability of obtaining the maximum payoff, which is the reciprocal of the number ofreel stop positions per reel raised to the power of the number of reels.
• Accordingly, it is desirable for manufacturers of reel-type slot machines toprovide new ways to increase reel-type slot machine payoff values while maintainingadequate game revenue for the operator. As the payoff amounts increase, playerinterest in the game is fostered which leads to maximized game revenue.
• One method of increasing payoff values in a prior art electronic slot machinedesign is to employ a "virtual reel". According to this method, a plurality of numbersare assigned to most of the physical reel stop positions and at least one number isassigned to every physical reel stop position. In this way, the chances of winning thelarger payoffs can be decreased by assigning these stop combinations to fewernumbers.
• Such a "virtual reel" system is described in US patent number 5102134 , wheretwo random number selectors are employed, one to select numbers on a theoreticalreel strip, and another to decide between physical reel locations if pre-assignedrandom numbers representing jackpot possibilities are chosen by the first randomnumber generator.
• EP-A-0391667 describes a slot machine in which decisions on winning hitsare also taken by a random number generator. The output of a first random numbergenerator is fed to a first judgement section which decides if a winning combination ispossible, and if so, the results of a second random number generator are used todetermine the type of winning selection.
• The present invention provides an alternative method for increasing payofflevels in electronic reel-type slot machines by the provision of a method of selectingsymbol combinations to be displayed on the payline or lines of a multi-reel slotmachine.
• The method comprises the steps of providing a symbol look-up table in amemory device either for each reel or for a combination of reels, the or each look-uptable being arranged in a tree branch structure containing tiers, each tier comprisingnodes, each node comprising either a terminal node or a descending node which leadsto a lower tier, and at least one tier reached via a descending node from a higher tier,said at least one tier also including a descending node leading to a lower tier, storingthe symbol or symbols to be displayed in the corresponding look-up table at terminalnode locations within the tree branch structure and randomly selecting a single nodein each tier which is reached, and controlling the reels to display the symbol orsymbols stored in any selected terminal node, wherein the symbols are stored atterminal node locations corresponding to desired pay-off probabilities determined bythe positions of storage locations within the or each tree branch structure.
• The odds of obtaining a particular winning symbol set can be "dialed in" byassigning each possible reel stop combination to a unique terminal node (position) in arandom number fractional branching tree. The tree comprises a maintier, a plurality of lower tiers and a plurality of terminalnodes. Each of the tiers has a number of entries which leadeither to a lower tier or to a terminal node.
• During game play, one of the entries on the main tieris randomly selected by the game microprocessor. If the randomlyselected entry leads to a lower tier, then one of the entries onthat tier is randomly selected. This selection process continuesfor each successive tier until a terminal node is selected. Onereel stop combination is assigned to each terminal node. Thecombination assigned to the selected terminal node is thendisplayed on the pay line(s) of the slot machine. A payoff ismade to the player if the combination displayed corresponds to awinning symbol combination in a posted pay table.
• In an alternate embodiment of the invention, onefractional branching tree is utilized for each reel strip, eachtree having a main tier, a plurality of lower tiers and aplurality of terminal nodes. All of the symbols for each reelare assigned to unique terminal nodes in the fractional branchingtree corresponding thereto. To display a reel stop combinationon the pay line(s) of the slot machine, the selection processdescribed above is used to randomly select a terminal node andthe symbol assigned thereto for each of the reels. The selectedcombination is displayed and a payoff is made if it corresponds to a winning symbol combination in a posted pay table.
Brief Description of the Drawings
• Figure 1 shows a typical electronic reel-type slotmachine which may incorporate the present invention.
• Figure 2 illustrates one example of three reel "strips"containing symbols positioned at the stop positions.
• Figure 3 is a block diagram of a control system for thepresent invention.
• Figure 4 is a table showing the payoffs and desiredodds of obtaining a winning symbol set for the reel strips ofFigure 2.
• Figure 5 illustrates a first embodiment of a fractionalbranching tier system of the present invention.
• Figure 6 is a computer flow diagram illustrating apreferred embodiment of the invention.
• Figure 7 illustrates a second example of three reel"strips" containing symbols positioned at the stop positions.
• Figure 8 is a table showing payoffs and desired odds ofobtaining a winning symbol set for the reel strips of Figure 7.
• Figure 9 illustrates a preferred embodiment of afractional branching tier system of the present invention.
• Figure 10 illustrates one example of three reel"strips" containing symbols positioned at the stop positions foran alternate embodiment of the invention.
• Figure 11 is a table showing the payoffs and the oddsof obtaining a winning symbol set for the reel strips ofFigure 10.
• Figure 12 illustrates an alternate embodiment of afractional branching tier system of the present invention.
• Figure 13 is a computer flow diagram illustrating thealternate embodiment of the invention presented in Figures 10-12.
Detailed Description of the Preferred Embodiment
• Referring to Figure 1, an electronic reel-type slotmachine 10 is illustrated.Slot machine 10 includes ahandle 12,acoin slot 14,payout trough 22 and reels, each having aplurality of stop positions thereon. Each reel includes a system of symbols which are used to display an outcome of a game whichis played onslot machine 10. In the illustrated embodiment,slot machine 10 includes threeslot reels 16, 18 and 20, each ofwhich has eighteen stop positions each of which corresponds to asymbol. The symbols form combinations which correspond to a paytable displayed to the player.
• It must be noted thatslot machine 10 can incorporateany number of reels and that the reels can include any reasonablenumber of stop positions. Any system of symbols can be utilizeda long as there is one symbol, which may include a "blank"symbol, corresponding to each stop position on each reel. When acoin is inserted, the game start button and/or handle is enabled.By pushing the start button or pulling the handle, the playercauses the microprocessor control system to spin the reels in anattempt to win money if a winning set of symbols is chosen anddisplayed on thepay line 24.
• Figure 2 illustrates an example of three reel "strips"which can be attached to reels 16-20. Each of the reel stripscontain a system of symbols as discussed above and, in thisexample, has eighteen discrete physical stop positions at whichone of the symbols is displayed. It should be noted thatduplicate symbols can be employed on each reel. In theillustrated embodiment, reel one displays two "7s," two triplebars, four double bars, three single bars and seven blanks; reel two displays three "7s," two triple bars, two double bars, foursingle bars and seven blanks; and reel three displays two "7s,"three triple bars two double bars, four single bars and sevenblanks.
• Figure 3 is a block diagram of a control systemsuitable for practicing the present invention.Coin detector 24sends a signal tomicroprocessor 26 when a coin is inserted intocoin slot 14. The microprocessor then randomly selects thesymbol set to be displayed on the pay line. If a player wins,thenmicroprocessor 26 signals theconventional coin mechanism 28to dispense a payoff to the player viacoin payout trough 22.
• Reel motor andstep controller 30 rotates the reels 16-20in response to a signal frommicroprocessor 26. The signal isgenerated after a coin input and player operation of thehandle12 or the start button.Controller 30 stops the reels atpositions determined by the microprocessor such that the reelsdisplay three symbols on thepay line 22.
• During the reel spin,microprocessor 26 randomlyselects one of the reel stop combinations for display on the payline. To ensure that the selected reel stop combination isdisplayed,detector 32 provides feedback signals tomicroprocessor 26 which are representative of the rotationalposition of each reel relative to payline 22. Feedback of this type is utilized in accordance with well known techniques in thisart.
• Figure 4 shows a symbol table which lists the winningsets of symbols A-F and the losing sets of symbols G that can bedisplayed onpay line 22 for the reel strips of Figure 2. Alsolisted in Figure 4 are the number of physical reel stopcombinations and the desired win percentages which correspond tothe symbol sets A-G. The odds of obtaining a particular symbolset can be controlled by assigning each possible reel stopcombination to a unique terminal node in a random numberbranching tree. The location in the tree affects the likelihoodof the symbol combination being selected. By way of example, thedesired odds listed in Figure 4 are implemented by the fractionalbranchingtree 38 of Figure 5.
• Branchingtree 38 includes a plurality of tiers 40-54having level values of 0.10 to 0.00001 and a plurality of entrieswhich lead either to lower tiers or to terminal nodes. The treeis a conceptual device which is used to explain the method of theinvention. In actuality, each reel stop combination is stored ina ROM memory look-up table corresponding to its terminal nodelocation intree 38. Each one of the possible reel stopcombinations is assigned only once in the tree structure and thusto only one memory location inROM 34.
• The odds for each of the symbol sets A-G, as listed inFigure 4, may be calculated from the tree as follows. For eachtier intree 38, the number of terminal nodes associated with aparticular symbol set is multiplied by that tier's level value.These numbers are then summed to compute the odds.
• For example, the desired odds of obtaining three triplebars, symbol set B, is .00180. Referring to Figure 5, one "B" isplaced attier 46 and eight "B" are placed attiers 50 and 52.Thus, the desired odds of obtaining three triple bars is (1 *.001) + (7 * .0001) + (1 * .0001) = .0018.
• The third term in the calculation requires explanation.It relates to the sub-tier 51 dropping fromtier 50. Note thatFigure 4 requires 12 unique ways to display three triple bars.To include all of these combinations and still obtain the desiredodds, it is necessary to lower one of the B combinations to asub-tier in which all of the nodes are set B. The remainingnumber of nodes in the sub-tier is equal to the number ofcombinations not used in setting the odds. Thus, sub-tier 51 hasfour nodes set to B.
• If the entry leading to the sub-tier 51 is selected,the probability of obtaining a B combination is 1.0, the onlyquestion being which B combination.Microprocessor 26 randomlyselects one of the nodes of the sub-tier to determine which reel stop combination is displayed on the pay line. A similarexercise is employed to implement the probabilities for each ofthe other symbol groups A and C-G.
• It should be noted that the implementations of theFigure 5 embodiment is accomplished principally using decimaltiers. That is, only ten entries per tier. The use of sub-tiersof varying size, each sub-tier having a probability of 1 for theassigned symbol set, permits the use of all possible reel stopcombinations so that no combinations of stop positions need beused or stored in memory more than once. Thus, for example, todisplay three sevens in twelve unique ways without changing theodds, a sub-tier 159, having three terminal nodes, one for eachadditional reel stop combination for displaying three sevens, isprovided in place of an "A" combination ontier 54.
• Note that the desired odds could be implemented withoutthe use of sub-tiers. In that case, however, not all of thepossible combinations of the symbol sets would be displayed. Asit is desirable to be able to display each possible combinationfor a symbol set, the use of sub-tiers is preferred.
• Referring to Figure 6, a computer flow diagram is shownwhich illustrates the steps executed bymicroprocessor 26 toselect a reel stop combination to be displayed on the pay line.The steps illustrated in Figure 6 are stored as a computer program in read onlymemory 34 which is executed bymicroprocessor 26 when the game is played. Current game data isstored in a random access memory (RAM) 36. Figure 6 is a flowdiagram which illustrates the essential program steps of theinvention permitting it to be implemented on any type of computersystem desired.
• The program begins atstart step 38. The random numbergenerator function ofmicroprocessor 26 is used to randomlyselect one of the entries on themain tier 40 of the branchingtree (steps 58-64). With reference to the branching tree ofFigure 5,microprocessor 26 randomly selects an integer from 1 to10 (or 0 to 9) which is used to select one of the ten entries onthemain tier 40. If the selected entry is not a terminal node,step 66, then the program drops to the next lower tier (step 68)and repeats steps 58-64 until a terminal node is selected.
• If the selected entry is a terminal node, the uniquereel stop combination assigned thereto is displayed on the payline and the appropriate payoff, if any, is determined,step 70.The payoff amounts are stored in a look-up table inROM 34 foreach of the winning symbols sets A-F (Figure 4). The reels whichspin while the selection process is implemented (or spin afterselection, as desired) are stopped to display the selected reelstop combination and the appropriate award is paid (steps 72-76).
• Figure 7 illustrates a second example of three reel"strips" which can be attached to reels 16-20. The winning setsof symbols A-F and the losing sets of symbols G that can bedisplayed onpay line 22, the corresponding payoffs and thedesired win odds are listed in the table shown in Figure 8.
• Figure 9 illustrates a second embodiment of afractional branching tree which implements the desired odds forthe example of Figures 7 and 8. For clarity, the number ofentries on each tier leading to terminal nodes or to lower tiersis labeled in theform 1/X (1 out of X) where X is the number ofentries for the tier. The number of reel stop combinations for agiven symbol set located on a tier is labeled directly below thetier in parenthesis, if numerous. The tiers have differentvalues of X as necessary to implement each possible reel stopcombination for a given symbol set at the desired odds.
• The use of variable length tiers, particularly for thelower tiers, allows the odds to be precisely dialed in with aminimum number of iterations of steps 60-66 (Figure 6). Thedesired odds of obtaining a particular set of symbols requiresonly a minimum number of drops to successive tiers from the maintier. For example, the desired odds of obtaining three triplebars (Group B in Figure 8) can be implemented by repeating steps60-66 three times. Thus, the desired odds (.001818) isimplemented by dropping fromtier 78 to sub-tier 88 viatier 80.
• More specifically, if the RNG function selects thecorresponding entry of tier 78 (the .1 level), a drop is made totier 80 (the .01 level). Another iteration of the RNG cyclecould result in a further drop to sub-tier 88. Sub-tier 88 has22 terminal nodes of which four represent the four possible reelstop combinations for displaying three triple bars. Thus, thedesignation B(4) is shown at sub-tier 88. The odds of selectingany one of the B group terminal nodes equals 1/10 * 1/10 * 4/22 =.001818.
• Similarly, the desired odds for obtaining three doublebars, group C, is implemented by dropping to sub-tier 100 viatiers 78, 80 and 98. The desired odds of .0018 are obtained byassigning one of the eight possible reel stop combinations totier 98 and the remaining seven combinations to sub-tier 100.Thus, the desired odds equal (1/10 * 1/10 * 1/10) + (1/10 * 1/10* 1/10 * 7/9) = .001 + .000777 = .001777.
• Calculations similar to those illustrated above can beused to implement the desired odds for the remaining sets ofsymbols resulting in the tree structure of Figure 9. After allof the odds for the winning sets of symbols are implemented, theremaining terminal nodes in the branching tree are "filled out"with losing reel stop combinations. Thus, the desired odds ofobtaining a losing symbol set, Group G in Figure 8, equals (1/10* 7) + (1/10 * 1/10 * 5) + (1/10 * 1/10 * 5/10) + (1/10 * 1/10 * 18/22) + (1/10 * 1/10 * 75/77) + (1/10 * 1/10 * 3) + (1/10 * 1/10* 3) + (1/10 * 1/10 * 1/10 * 6) + (1/10 * 1/10 * 1/10 * 2/9) =.839144.
• Figure 10 illustrates an alternate embodiment of theinvention and three exemplary reel "strips" which can be attachedto reel 16-20 shown in Figure 1. Each of the reel stripscontains a system of symbols and, in this example, there are fivediscrete physical stop positions at which one of the symbols isdisplayed. The symbols for each reel are assigned to uniqueterminal nodes in a fractional branching tree corresponding toeach reel. In the illustrated embodiment, each reel displays onetriple bar, one double bar, one single bar and two blank symbols.
• Figure 11 is a table which lists the winning symbolsets that can be displayed on the payline 22 (Figure 1) for thereel strips of Figure 10. Also listed in Figure 11 are thenumber of physical reel stop combinations and the win percentageswhich correspond to the winning symbol sets. The odds ofobtaining a particular symbol set are determined by assigningeach symbol to a terminal node in a random number branching treefor each of the reels. The location in the tree determines theprobability of the symbol being selected.
• The probability of selecting a combination of threesymbols is calculated by multiplying the odds for each reel. By way of example, the odds listed in Figure 11 are implemented bythree iterations through the fractional branchingtree 150 shownin Figure 12. It will be appreciated, however, that only onetree is necessary for the reels in the illustrated embodimentbecause each reel contains the same system of symbols. Ifmultiple systems of symbols are used, then a separate fractionalbranching tree would be utilized for each of the different systemof symbols.
• Referring to Figure 12, fractional branchingtree 150includes a plurality oftiers 152, 154, 156 and 158 each havingentries which lead either to lower tiers or to a terminal node.As with the first embodiment, it should be emphasized that eachof the possible symbols is assigned only once in the treestructure and, therefore, to only one memory location in ROM 34(Figure 3).
• The probability for selecting each of the winningsymbol sets, as listed in Figure 11, may be calculated from threeiterations through the tree 150 (or through three separate treesif separate symbol sets are used) as follows. For each tier intree 150, the number of terminal nodes associated with aparticular symbol is divided by the number of terminal nodes inthat tier. If the tree contains the same symbol at differentlevels, then this computation is repeated for each symbol, theresults being summed to arrive at the odds of selecting that symbol for a particular reel. This process is repeated threetimes until a symbol is selected for each of the three reelstrips shown in Figure 10. Finally, the numbers obtained fromeach iteration through therandom number tree 150 are multipliedto compute the probability of obtaining a particular combinationof symbols.
• For example, the odds of obtaining three triple bars,is 0.000244. Referring to Figure 12, one triple bar is placed attier 158 and, therefore, the odds of obtaining a triple bar onone reel is 0.5 x 0.5 x 0.5 x 0.5 = 0.0625. Thus, the odds ofobtaining a triple bar on each reel equals (0.0625 x 0.0625 x0.0625 = 0.000244). The odds of obtaining the blank symbol onone reel is (0.5 x 0.5 x 0.5 x 0.5) + 0.5 = 0.5625. Therefore,the odds of obtaining a winning combination of three blanksymbols is (0.5625 x 0.5625 x 0.5625 = 0.177979).
• Figure 13 is a computer flow diagram illustrating theoperation of the alternate embodiment of the invention shown inFigures 10-12. As with the first embodiment, the random numbergenerator function ofmicroprocessor 26 is used to randomlyselect entries on the main tier of the branching treecorresponding to the first reel until a terminal node is reached(steps 160-174). The unique symbol assigned thereto is storedfor display,step 176. Steps 160-174 are repeated for each ofthe reels of the slot machine,step 178, using the same or a different branching tree depending on the similarity of the reelstrips. After symbols have been selected for all reels, thereels are spun and stopped to display that combination on the payline and the appropriate payoff, if any, is determined and made,steps 180-186.
• While the invention has been illustrated and describedin detail in the drawings and foregoing description, the same isto be considered as illustrative and not restrictive in character.Thus, for example, larger reel strips can be employed andaccommodated simply by expanding the tree structure.

Claims (13)

1. A method of setting the probability of selection of symbol combinations to bedisplayed on the payline or lines of a mult-reel slot machine (10) in which each reelcarries a specified set of symbols, characterised by:

   (a) providing a symbol look-up table in a memory device either for eachreel or for a combination of reels, the or each look-up table being arranged in a treebranch structure (38, 150) containing tiers, each tier comprising nodes, each nodecomprising either a terminal node or a descending node which leads to a lower tierand at least one tier (44, 154) reached via a descending node from a higher tier (40,152) said at least one tier (44, 154) also including a descending node leading to alower tier (48, 156);

   (b) storing the symbol or symbols to be displayed in the correspondinglook-up table at terminal node locations within the tree branch structure (38, 150); and

   (c) randomly selecting a single node in each tier which is reached, andcontrolling the reels to display the symbol or symbols stored in any selected terminalnode, wherein the symbols are stored at terminal node locations corresponding todesired pay-off probabilities determined by the positions of the storage locationswithin the or each tree branch structure.
2. The method according to claim 1 further including the steps of:

   (d) randomly selecting a node in the first tier (40, 152) of said treestructure (38, 150);

   (e) determining if the selected node is a terminal node or a descendingnode;

   (f) in the event that a descending node is determined, dropping to thereferenced lower tier (44, 154) in said tree and repeating steps (d) and (e) for suchlower tier; and

   (g) in the event that a terminal node is determined, displaying thesymbol or symbols stored at the terminal node for each reel or combination of reels.
3. The method according to claim 2 wherein step (d) comprisesdetermining the number of nodes in the tier, N, and randomly selecting a number from1 to N to select a node.
4. The method according to claim 1 or 2 wherein each tier in the treestructure (38, 150) corresponds to an order of magnitude less than the tier above it,thereby permitting accurate placement of symbol combinations within said treestructure to obtain the desired pay-off probabilities.
5. The method according to any of claims 1 to 3 wherein at least one tierin said tree structure (38) has 10 nodes.
6. The method according to claim 5 wherein the initial tier in said treestructure (38) has 10 nodes.
7. The method according to any preceding claim wherein at least some ofthe tiers in said tree structure (38) have different numbers of nodes.
8. The method according to any of claims 1 to 7 wherein each of saiddesired pay-off probabilities corresponds to a specific multi-reel combination ofsymbols to be displayed on said pay line.
9. The method according to claim 8 wherein said multi-reel combinationsare grouped into multi-reel combination groups, each multi-reel combination in aparticular group having an identical award associated therewith and a desiredprobability of obtaining that reward;
   wherein said step of storing said multi-reel combinations at terminal locationsin said tree structure (38) comprises establishing the probability of reaching saidlocations and assigning the multi-reel combinations in a particular group to terminallocations such that the sum of the probabilities of reaching the locations associatedwith a particular multi-reel combination group is equal to the desired probability ofobtaining the reward associated with said group.
10. The method according to claim 9 wherein at least one of said tiers insaid tree structure has a sub-tier (51), linked via a descending node, which is not anorder of magnitude less than the associated tier, said sub-tier (51) serving to permitthe display of additional multi-reel combinations in a symbol group without alterationof the desired outcome probabilities.
11. A method according to claim 9 or 10 wherein the desired probability ofobtaining the reward associated with said group is the number of multi-reelcombinations in the group divided by the total number of possible multi-reelcombinations.
12. A method according to any of claims 1 to 7 comprising one or morefurther trees (150), each of said trees corresponding to a reel on said multi-reel slotmachine, each of said terminal node locations corresponding to one of said symbolson the associated reel.
13. A method according to claim 12, wherein each reel contains a differentset of symbols and a separate look-up table for each reel is stored in said memorydevice.

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