bicgus1
Joined: Mar 31, 2010
• Posts: 1
March 31st, 2010 at 7:12:26 PM permalink
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?
mustangsally
Joined: Mar 29, 2011
• Posts: 2463
March 10th, 2012 at 4:48:50 PM permalink
removed first reply but the worksheet still works for the Gambler's Ruin Formula

ok
a = (18/37)^15
b = (19/37)^15

something like this
0.307675671

Sally
I Heart Vi Hart
98Clubs
Joined: Jun 3, 2010
• Posts: 1728
March 14th, 2012 at 6:59:07 AM permalink
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.

Some people need to reimagine their thinking.
edward
Joined: Jan 18, 2012
• Posts: 76
March 14th, 2012 at 8:35:31 AM permalink
@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.
mustangsally
Joined: Mar 29, 2011
• Posts: 2463
March 14th, 2012 at 1:19:41 PM permalink
removed
silly
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buzzpaff
Joined: Mar 8, 2011
• Posts: 5328
March 14th, 2012 at 2:10:20 PM permalink
The answer depends on how many times black has appeared consecutively before placing you first bet.
edward
Joined: Jan 18, 2012
• Posts: 76
March 15th, 2012 at 12:21:58 PM permalink
Quote: mustangsally

I 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.
mustangsally
Joined: Mar 29, 2011
• Posts: 2463
Thanks for this post from:
June 8th, 2018 at 9:48:02 AM permalink
Quote: bicgus1

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?

the calculation does not take into account the time required for hitting target or ruin.
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:

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):0.3680312p(ruin):0.6319688mean Trials:97.6569mean given Goal:97.6569mean 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):0.3076757p(ruin):0.6923243mean Trials:213.48mean given Goal:213.48mean given Ruin:213.48`

I found this interesting
(formula and formula found in SN Ethier book, Doctrine of Chances)
Sally
I Heart Vi Hart