No Formulas or Advanced Math

Forever is a long time, eventually, the 1 quadzillion to 1 swing will happen, and you will get tapped out, but I think that for any finite period of time, there is probably a liklehood that if you can survive the early flips, you will be able to survive a long time. There must be a method for estimating your survival for a given period of time, and it reminds me of a calculus problem, but I have to go to work in about 5 minutes, so I cant add more now.


Good luck,

Play well,


Bob T.

It will never be 100% as long as you have an edge on every play. It approaches 100% when your bankroll is 1 bet and your edge is close to even. It goes down exponentially as your bankroll increases (doubling bankroll squares risk of ruin). The games you mention are more difficult to analyze due to variable bets, variable payouts, and bets when your ev is negative. Still, if you have an overall edge, it is always possible to make your risk of ruin as small as you want by having a large enough bankroll relative to your bet size.

Many people are of the misconception that the likelihood of tapping out become greater the longer you play. Actually, if you don't go bust fairly early, it is even less likely that you ever will. That is, the probability of going bust has a maxima.

I computed the probability of ruin in 200 coin flips or less. I got


0.1249999829


That would seem to indicate that 1/8 is the best answer.

The reason this number is so close to 1/8 is that if you make it to 200 flips, you will almost certainly never go broke after that point.

Need to brush up on my calculus, but the answer is whatever 1/3^3 + 1/3^5 + 1/3^7 + ... comes out to be (it's definitely not 1).

OK, the answer is 1/24 (or 0.0416667).

Also, if my math is correct, if you start with X dollars, and bet $1 per coin flip with this coin weighted 2/3 in your favor, the probability that you'll ever go broke is:


0.375 * (1/3)^(x-1)


Start w/ $1 = 3/8 chance you'll ever go broke

Start w/ $2 = 1/8 chance you'll ever go broke

Start w/ $3 = 1/24 chance you'll ever go broke

Start w/ $4 = 1/72 chance you'll ever go broke

etc.

Here's how I came up with that answer


Start: $3 (All of the time)

1 Flip: $2 (1/3) $4 (2/3)

2 Flips: $1 (1/9) $3 (4/9) $5 (4/9)

3 Flips: $0 (1/27) $2 (6/27) $4 (12/27) $6 (8/27)

4 Flips: $0 (1/27 - from before) $1 (6/81) $3 (24/81) $5 (32/81) $7 (16/81)

5 Flips $0 (1/27 + 1/243) $2 (36/243)...


So the $0 component will eventually be (1/27 + 1/243 + 1/2187 + 1/19683 + ...)

Same process as above, just realized a math error...


Probability will be (1/27 + 2/81 + 4/243 + 8/729 + ... + (2^x)/[3^(x+3)])


This reduces to 1/9.