March 9th, 2018 at 6:21:52 AM
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I am reading the articles “Deconstructing Hexbreaker” and trying to calculate the probability and wins, but I have no idea how to calculate Icon win (Treasure symbol win) for 4 mirrors and 5 mirrors from the Mirror Mirror Bonus game.

I have tried to calculate these wins using Binomial tree but I could not get the same value.

Would anybody help me to find the right way to calculate this? Many thanks.

I have tried to calculate these wins using Binomial tree but I could not get the same value.

Would anybody help me to find the right way to calculate this? Many thanks.

March 9th, 2018 at 6:41:43 AM
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Each of the five treasure symbols has an equal chance of being behind any of the 13 mirrors. This means each symbol has a 5/13 chance of behind behind any of the five broken mirrors.

Let P(n) be the probability of n symbols being revealed behind broken mirrors.

P(5) = (5/13)

P(4) = 5 x (5/13)

P(3) = 10 x (5/13)

P(2) = 10 x (5/13)

P(1) = 5 x 5/13 x 8/13

P(0) = 8/13

The expected payout for the 4-mirror bonus is P(5) x 1000 + P(4) x 125 + P(3) x 75 + P(2) x 25 + P(1) x 15 + P(0) x 0 = about 45.748237

(for those of you who want the exact number, it is 16,986,000 / 371,293)

Let P(n) be the probability of n symbols being revealed behind broken mirrors.

P(5) = (5/13)

^{5}P(4) = 5 x (5/13)

^{4}x 8/13P(3) = 10 x (5/13)

^{3}x 8/13^{2}P(2) = 10 x (5/13)

^{2}x 8/13^{3}P(1) = 5 x 5/13 x 8/13

^{4}P(0) = 8/13

^{5}The expected payout for the 4-mirror bonus is P(5) x 1000 + P(4) x 125 + P(3) x 75 + P(2) x 25 + P(1) x 15 + P(0) x 0 = about 45.748237

(for those of you who want the exact number, it is 16,986,000 / 371,293)

March 10th, 2018 at 12:46:37 AM
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Thank you for your detailed and clear explanation.

August 24th, 2023 at 3:39:20 AM
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Hi ThatDonGuy,

Finally got it the result !! Many many thanks.

Still don't get the x5, x10, x10, x5 multipliers. Can anyone explain?

Sub Main()

Dim P(0 To 5) As Double

Dim R As Double

Dim i As Long

Dim SP As Double

'16986000 / 371293

' 5+8=13

P(5) = ((5 / 13) ^ 5) * ((8 / 13) ^ 0) * 1

P(4) = ((5 / 13) ^ 4) * ((8 / 13) ^ 1) * 5

P(3) = ((5 / 13) ^ 3) * ((8 / 13) ^ 2) * 10

P(2) = ((5 / 13) ^ 2) * ((8 / 13) ^ 3) * 10

P(1) = ((5 / 13) ^ 1) * ((8 / 13) ^ 4) * 5

P(0) = ((5 / 13) ^ 0) * ((8 / 13) ^ 5) * 1

For i = 0 To 5

Debug.Print "P(" & i & ") = " & Format(P(i), "##0.00000000")

SP = SP + P(i)

Next

Debug.Print "P = " & Format(SP, "##0.00000000")

R = P(5) * 1000 + P(4) * 125 + P(3) * 75 + P(2) * 25 + P(1) * 15 + P(0) * 0

Debug.Print R ' 45.7482365678858 !!

End Sub

Finally got it the result !! Many many thanks.

Still don't get the x5, x10, x10, x5 multipliers. Can anyone explain?

Sub Main()

Dim P(0 To 5) As Double

Dim R As Double

Dim i As Long

Dim SP As Double

'16986000 / 371293

' 5+8=13

P(5) = ((5 / 13) ^ 5) * ((8 / 13) ^ 0) * 1

P(4) = ((5 / 13) ^ 4) * ((8 / 13) ^ 1) * 5

P(3) = ((5 / 13) ^ 3) * ((8 / 13) ^ 2) * 10

P(2) = ((5 / 13) ^ 2) * ((8 / 13) ^ 3) * 10

P(1) = ((5 / 13) ^ 1) * ((8 / 13) ^ 4) * 5

P(0) = ((5 / 13) ^ 0) * ((8 / 13) ^ 5) * 1

For i = 0 To 5

Debug.Print "P(" & i & ") = " & Format(P(i), "##0.00000000")

SP = SP + P(i)

Next

Debug.Print "P = " & Format(SP, "##0.00000000")

R = P(5) * 1000 + P(4) * 125 + P(3) * 75 + P(2) * 25 + P(1) * 15 + P(0) * 0

Debug.Print R ' 45.7482365678858 !!

End Sub

Last edited by: eliasp on Aug 24, 2023

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