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March 31st, 2010 at 7:12:26 PM
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How do you calculate this? For example, how do you calculate the chance of winning 15 units at european roulette betting plain 1 unit on black all the time, BEFORE you lose 15 units?

March 10th, 2012 at 4:48:50 PM
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removed first reply but the worksheet still works for the Gambler's Ruin Formula

ok

a = (18/37)^15

b = (19/37)^15

answer = a/a+b

something like this

0.307675671

Sally

ok

a = (18/37)^15

b = (19/37)^15

answer = a/a+b

something like this

0.307675671

Sally

I Heart Vi Hart

March 14th, 2012 at 6:59:07 AM
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I have what I think is an interesting extension... note ties and lose 1/2.

Suppose the House collects its vigorish by losing half on certain wagers. For example, lets say in 1000 wagers:

WIN 450

LOSE 450

TIE 50

LOSE 1/2 50

Should I consider the outcome as WIN 450 LOSE 475 TIE 50? and how does the TIE factor in, if at all, since its not a resolved wager?

At first glance it appears that my bank is at 975 after 1000 rounds: Keeping 900 for WINS, 50 for TIES and 25 for HALF-LOSSES.

Thanks much in advance.

Suppose the House collects its vigorish by losing half on certain wagers. For example, lets say in 1000 wagers:

WIN 450

LOSE 450

TIE 50

LOSE 1/2 50

Should I consider the outcome as WIN 450 LOSE 475 TIE 50? and how does the TIE factor in, if at all, since its not a resolved wager?

At first glance it appears that my bank is at 975 after 1000 rounds: Keeping 900 for WINS, 50 for TIES and 25 for HALF-LOSSES.

Thanks much in advance.

Some people need to reimagine their thinking.

March 14th, 2012 at 8:35:31 AM
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@Sally,

the formula is nice but is a little counterintuitive.

For example if i set a goal of 3 units having a 3 unit bank, the formula says that i have 85% chance to win 3 units before losing 3 units?! However i think that it rather means that i have an 85% chance of 50% (doubling) before losing all. That would mean that im better off putting straight ahead 3 units on the black.

Correct me if i'm wrong.

Thanks.

the formula is nice but is a little counterintuitive.

For example if i set a goal of 3 units having a 3 unit bank, the formula says that i have 85% chance to win 3 units before losing 3 units?! However i think that it rather means that i have an 85% chance of 50% (doubling) before losing all. That would mean that im better off putting straight ahead 3 units on the black.

Correct me if i'm wrong.

Thanks.

March 14th, 2012 at 1:19:41 PM
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removed

silly

silly

I Heart Vi Hart

March 14th, 2012 at 2:10:20 PM
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The answer depends on how many times black has appeared consecutively before placing you first bet.

March 15th, 2012 at 12:21:58 PM
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Quote:mustangsallyI find no problem with the formula.

See if you can find the error or any error :)

(I tried to upload to Windows Live but it does not upload using certain ISPs.)

Here is a link to my Excel worksheet. It has no macros.

Gambler's Ruin Calc

How to derive the formula is in a link to Don Catlin's article.

The Wizard has a solution on his math page from a post in the above link.

Hi Sally,

nope - there is no error and i didnt intend to search for an error necesarilly.

Btw, the excel file is beautiful, thx again for sharing.

June 8th, 2018 at 9:48:02 AM
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the calculation does not take into account the time required for hitting target or ruin.Quote:bicgus1For example, how do you calculate the chance of winning 15 units at european roulette betting plain 1 unit on black all the time, BEFORE you lose 15 units?

that is a different formula (from the Gambler's Ruin formula)

Many do want to know the results after X number of trials or resolved bets in a casino.

that requires a slightly different method (a transition matrix raised to a power, for example)

R code for the OP question(s), 2nd R code module here:

https://sites.google.com/view/krapstuff/risk-of-ruin

for the OP title example of 10 into 20

> gambler.ruin(10,10, 18/37, "0 Roulette evens bet")

[1] "0 Roulette evens bet"

[1] "Stake: 10"

[1] "Target: 20"

p(goal):

0.3680312

p(ruin):

0.6319688

mean Trials:

97.6569

mean given Goal:

97.6569

mean given Ruin:

97.6569

15 into 30

> gambler.ruin(15,15, 18/37, "0 Roulette evens bet")

[1] "0 Roulette evens bet"

[1] "Stake: 15"

[1] "Target: 30"

p(goal):

0.3076757

p(ruin):

0.6923243

mean Trials:

213.48

mean given Goal:

213.48

mean given Ruin:

213.48

I found this interesting

(formula and formula found in SN Ethier book, Doctrine of Chances)

Sally

I Heart Vi Hart