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| '''Slot Machines''' are a mini-game found in the [[Casino]]. | | '''Slot Machines''' are a mini-game found in the [[Casino]]. |
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− | The player can bet either 10 or 100 Qi coins when using a slot machine. If the results match one of the winning lines, the player receives a multiple of their bet. If there is no match the player loses their bet. [[Luck]] has an effect on gambling odds when using the slot machines. | + | The player can bet either 10 or 100 Qi coins when using a slot machine. If the results match one of the winning lines, the player receives a multiple of their bet. If there is no match the player loses their bet. |
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− | For the PC-Version the following may help to maximize your "luck": The slot machines have certain patterns that can be exploited. By betting {{Price|100|Qi}} when expecting a win and {{Price|10|Qi}} when expecting a loss, you can quickly obtain enough {{Price||Qi}} coins to buy an item from the shop. The order of the patterns may vary depending on your luck.
| + | Daily [[Luck]] and the Luck buff from various food items can increase the chance of winning and the expected return when gambling. Otherwise, rolls are randomly determined. |
| | | |
− | On a day with a little [[Luck]] there are three patterns that occur in some order:
| + | ==Winning lines== |
− | *16 losses then W-L-W-L-W-L-W
| + | There are 10 possible winning lines, each one giving different multipliers. |
− | *14 losses then W-L-W-L-W-L-W-L-W
| + | {| class="wikitable sortable" |
− | *14 losses then W-L-W-L-W-L-W
| + | |- |
| + | !Line |
| + | !Chance<ref name="slots"/> |
| + | !Multiplier |
| + | |- |
| + | |[[File:Cherry.png|32px]] |
| + | |20% |
| + | |2 |
| + | |- |
| + | |[[File:Cherry.png|32px]][[File:Cherry.png|32px]] |
| + | |10% |
| + | |3 |
| + | |- |
| + | |[[File:Parsnip.png|32px]][[File:Parsnip.png|32px]][[File:Parsnip.png|32px]] |
| + | |8% |
| + | |5 |
| + | |- |
| + | |[[File:Large Milk.png|32px]][[File:Large Milk.png|32px]][[File:Large Milk.png|32px]] |
| + | |1% |
| + | |30 |
| + | |- |
| + | |[[File:Rainbow Trout.png|32px]][[File:Rainbow Trout.png|32px]][[File:Rainbow Trout.png|32px]] |
| + | |0.3% |
| + | |80 |
| + | |- |
| + | |[[File:Nautilus Shell.png|32px]][[File:Nautilus Shell.png|32px]][[File:Nautilus Shell.png|32px]] |
| + | |0.2% |
| + | |120 |
| + | |- |
| + | |[[File:Melon.png|32px]][[File:Melon.png|32px]][[File:Melon.png|32px]] |
| + | |0.25% |
| + | |200 |
| + | |- |
| + | |[[File:Cherry.png|32px]][[File:Cherry.png|32px]][[File:Cherry.png|32px]] |
| + | |0.09% |
| + | |500 |
| + | |- |
| + | |[[File:Diamond.png|32px]][[File:Diamond.png|32px]][[File:Diamond.png|32px]] |
| + | |0.06% |
| + | |1000 |
| + | |- |
| + | |[[File:Stardrop.png|32px]][[File:Stardrop.png|32px]][[File:Stardrop.png|32px]] |
| + | |0.1% |
| + | |2500 |
| + | |} |
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− | From playing 8 repetitions of the above patterns (14 or 16 losses followed by 4 or 5 W/L) the 5 W/L happened once. The highest observed match at the time was 3x shells.
| + | This is adjusted multiplicatively by daily Luck, increasing by 20% at best or decreasing by 20% at worst with the [[Special Charm]] adding 5%. Food buffs add 8% for every point of Luck (''e.g.,'' if daily Luck is max and luck from food is 3 then the chance to get 1 cherry is 20% * (1 + 0.2 + 0.24) = 28.8%). |
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− | On a day where the spirits are displeased this pattern was observed:
| + | ==Expected Value Calculation== |
− | *12 losses then W-L-W-L-W-L
| |
− | *16 losses then W-L-W-L-W-L
| |
− | *18 losses then W-L-W-L-W-L
| |
− | *18 losses then W-L-W-L-W-L
| |
− | *16 losses then W-L-W-L-W-L
| |
− | *18 losses then W-L-W-L-W-L
| |
− | *18 losses then W-L-W-L-W-L
| |
− | *18 losses then W-L-W-L-W-L
| |
− | *18 losses then W-L-W-L-W-L
| |
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− | The highest observed match at the time was 3x parsnips.
| + | To calculate the expected net gain or loss from playing the slot machine, we use the formula: |
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− | Starting a new round of slot play will require {{Price|300|Qi}} (18 losses x 10 = 180 + 100 high bet).
| + | '''Net Expected Gain/Loss = (B × Σ(P<sub>i</sub> × M<sub>i</sub>)) - B''' |
| + | |
| + | Where: |
| + | * ''B'' = Bet amount (in units) |
| + | * ''P<sub>i</sub>'' = Probability of the i-th outcome |
| + | * ''M<sub>i</sub>'' = Multiplier for the i-th outcome |
| + | * ''Σ'' = Sum over all possible outcomes (i=1 to n) |
| + | |
| + | After accounting for the following: |
| + | |
| + | '''Net Expected Gain/Loss = B × ((0.2 × 2) + (0.1 × 3) + (0.08 × 5) + (0.01 × 30) + (0.003 × 80) + (0.002 × 120) + (0.0025 × 200) + (0.0009 × 500) + (0.0006 × 1000) + (0.001 × 2500)) - B''' |
| + | |
| + | Which simplifies to: |
| + | |
| + | '''Net Expected Gain/Loss = B × 5.93 - B = B × (5.93 - 1)''' |
| + | |
| + | Then reducing to: |
| + | |
| + | '''Net Expected Gain/Loss = B × 4.93''' |
| + | |
| + | To simplify, if you spend {{price|100|Qi}} on a spin you can expect a net gain of {{price|493|Qi}} per spin! |
| + | |
| + | ==References== |
| + | <references> |
| + | <ref name="slots">See <samp>Slots::setSlotResults</samp> in the game code.</ref> |
| + | </references> |
| + | |
| + | ==History== |
| + | {{History|1.4|Recalculated the way random number generation is done, removing repeating pattern exploits. All [[Casino]] games now slightly favor the player rather than the house.}} |
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| [[Category:Mini-games]] | | [[Category:Mini-games]] |
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| [[de:Spielautomat]] | | [[de:Spielautomat]] |
| [[es:Tragaperras]] | | [[es:Tragaperras]] |
| + | [[fr:Machine à sous]] |
| + | [[it:Slot machine]] |
| [[ja:スロットマシン]] | | [[ja:スロットマシン]] |
| + | [[ko:슬롯 머신]] |
| + | [[hu:Pénzbedobós automata]] |
| [[pt:Caça-níqueis]] | | [[pt:Caça-níqueis]] |
− | [[ru:Слот-машина]] | + | [[ru:Игровой автомат]] |
− | [[zh:角子機]] | + | [[tr:Kumar Makinesi]] |
| + | [[zh:角子机]] |