Difference between revisions of "Slot Machine"

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'''Slot Machines''' are a mini-game found in the [[Casino]].
 
'''Slot Machines''' are a mini-game found in the [[Casino]].
  
 +
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.
 +
 +
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.
 +
 +
==Winning lines==
 +
There are 10 possible winning lines, each one giving different multipliers.
 +
{| class="wikitable sortable"
 +
|-
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!Line
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!Chance<ref name="slots"/>
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!Multiplier
 +
|-
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|[[File:Cherry.png|32px]]
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|20%
 +
|2
 +
|-
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|[[File:Cherry.png|32px]][[File:Cherry.png|32px]]
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|10%
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|3
 +
|-
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|[[File:Parsnip.png|32px]][[File:Parsnip.png|32px]][[File:Parsnip.png|32px]]
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|8%
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|5
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|-
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|[[File:Large Milk.png|32px]][[File:Large Milk.png|32px]][[File:Large Milk.png|32px]]
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|1%
 +
|30
 +
|-
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|[[File:Rainbow Trout.png|32px]][[File:Rainbow Trout.png|32px]][[File:Rainbow Trout.png|32px]]
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|0.3%
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|80
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|-
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|[[File:Nautilus Shell.png|32px]][[File:Nautilus Shell.png|32px]][[File:Nautilus Shell.png|32px]]
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|0.2%
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|120
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|-
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|[[File:Melon.png|32px]][[File:Melon.png|32px]][[File:Melon.png|32px]]
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|0.25%
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|200
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|-
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|[[File:Cherry.png|32px]][[File:Cherry.png|32px]][[File:Cherry.png|32px]]
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|0.09%
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|500
 +
|-
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|[[File:Diamond.png|32px]][[File:Diamond.png|32px]][[File:Diamond.png|32px]]
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|0.06%
 +
|1000
 +
|-
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|[[File:Stardrop.png|32px]][[File:Stardrop.png|32px]][[File:Stardrop.png|32px]]
 +
|0.01%
 +
|2500
 +
|}
  
 +
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%).
  
 +
==Expected Value Calculation==
  
−
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.
+
To calculate the expected net gain or loss from playing the slot machine, we use the formula:
 +
 
 +
'''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!
  
−
Daily [[Luck]] and the Luck buff from various food items can increase the chance of winning and your expected return when gambling. Otherwise, rolls are randomly determined.
+
==References==
 +
<references>
 +
<ref name="slots">See <samp>Slots::setSlotResults</samp> in the game code.</ref>
 +
</references>
  
 
==History==
 
==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.}}
+
{{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.}}
  
 
[[Category:Mini-games]]
 
[[Category:Mini-games]]

Latest revision as of 12:43, 15 April 2024

Slot Machine.gif
Slot Machine Rewards.png

Slot Machines are a mini-game found in the Casino.

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.

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.

Winning lines

There are 10 possible winning lines, each one giving different multipliers.

Line Chance[1] Multiplier
Cherry.png 20% 2
Cherry.pngCherry.png 10% 3
Parsnip.pngParsnip.pngParsnip.png 8% 5
Large Milk.pngLarge Milk.pngLarge Milk.png 1% 30
Rainbow Trout.pngRainbow Trout.pngRainbow Trout.png 0.3% 80
Nautilus Shell.pngNautilus Shell.pngNautilus Shell.png 0.2% 120
Melon.pngMelon.pngMelon.png 0.25% 200
Cherry.pngCherry.pngCherry.png 0.09% 500
Diamond.pngDiamond.pngDiamond.png 0.06% 1000
Stardrop.pngStardrop.pngStardrop.png 0.01% 2500

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%).

Expected Value Calculation

To calculate the expected net gain or loss from playing the slot machine, we use the formula:

Net Expected Gain/Loss = (B × Σ(Pi × Mi)) - B

Where:

  • B = Bet amount (in units)
  • Pi = Probability of the i-th outcome
  • Mi = 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 data-sort-value="100">QiCoin.png100 on a spin you can expect a net gain of data-sort-value="493">QiCoin.png493 per spin!

References

  1. ↑ See Slots::setSlotResults in the game code.

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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