Inverse Gambler's Ruin

First posted
Tuesday October 23, 2012 09:44
Updated
Thursday October 25, 2012 06:20

____


Gamblers can theoretically win by increasing the amount risk at each wager until the gambler recoups all lost on previous wagers plus a profit.

Gambler's ruin [google for more citations] is that a gambler cannot withstand losses which result loss of gambler's capital to the point the gambler can no longer fund the next bet.

But inverse gambler's is playing to win without capital problems.

Bill does this frequently because it is an interesting mindless activity which can be done in the background while thinking-out solutions to other problems.

Beats ceiling staring?

And it relates to pseudorandom numbers.

Look for William Harris Payne in index of Art of Computer Programming, Volume 2: Seminumerical Algorithms (3rd Edition)
Play first



until you win.

Then play



until you win.

$ restriction on winning removed. :)

Theoretically you may never win either but, in practice, you eventually will ... unless you are REALLY UNLUCKY.

And, given enough people trying this, someone will really be really unlucky.

Skill level at both games helps.

There is a practical dark side to this which will not be explained but we hope you see.



Assume the gambler starts with fixed capital of $X.

How long can the gambler continue to place wagers if the gambler continues to want to gamble?



Geometric gamblers ruin
is usually

Bet $1.

Win. Stop playing with $1 profit.

Lose [$1 invested] bet $2.

Win. Stop playing with $1 profit.

Lose [$3 invested] bet $4.

Win. Stop playing with $5 profit.

Lose [$7 invested] bet $16.

Win. Stop playing with $25 profit.

Lose [$23 invested] bet $32.

Win. Stop playing with $41 profit.

Lose [$54 invested] bet $64.

Win. Stop playing with $74 profit.

...

When, and if, you finally win and wish to continue gambling resume by betting $1.


Arithmetic gambler's ruin.

Probability of win in 1/2, assume.

Bet $1.

Win. Stop playing with $1 profit.

Lose Bet $2.

Win. Stop playing with $3 profit.

Lose [$3 invested] Bet $2.

Win. Stop playing with $1 profit.

Lose [$5 invested] Bet $3.

Win. Stop playing with $1 profit.

Lose [$8 invested] Bet $5.

Win. Stop playing with $2 profit.

Lose [$13 invested] Bet $7.

Win. Stop playing with $1 profit.

Lose [$20 invested] Bet $11.

Win. Stop playing with $1 profit.

Lose [$31 invested] Bet $16.

Win. Stop playing with $1 profit.

Lose [$47 invested] Bet $24.

Win. Stop playing with $1 profit.

Lose [$71 invested] Bet $35.

Win. Stop playing with $1 profit.

...

When, and if, you finally win and wish to continue gambling resume by betting $1.

Guaranteed gambling gains must be placed in your Gambling Bank so that you can use your won money the next time you gamble.

Cash out once you have achived your desired percentage return.

You might wish to check these two suggested gambling strategies out.

Options are:

1 mathematical modeling.

2 simiuation using a pseudogranom number generator, such as the GFSR.

NVIDIA is reported to have implemented the GFSR, without Professor Fushimi's modifiction, in hardware on one of its chaips, we were told.

3 Verbally. The liberal arts 'eeucated' approach.

This page is formatted with CSS by the author