moo321 said:
According to this formula, if you play one hand for the rest of your life, or 100 billion, you have the same risk of losing your whole bank.
The difference between 100 billion hands and infinity is insignificant in this case. The formula is raised to the power of Bank/SD so it moves very rapidly. As your bankroll shrinks, your risk increases exponentially. This means that you will likely go broke in the beginning when your bankroll is small, especially if it continues to get smaller. Similarly, as your bankroll grows, your risk decreases exponentially. The more you win, the bigger the negative swing has to be
and the less likely it is to happen. You are getting double protection. If you are betting properly then your bankroll will increase faster than the probability of hitting a big enough losing streak. Essentially you are trying to “outrun” the ruin. In this case the results from 100 billion hands will very nearly approach infinity because the exponential movement is so fast.
moo321 said:
There's no way that your lifetime risk of ruin can be the same for two people who are playing different numbers of hands.
You’re right, and that’s why we have the short-term RoR formulas. If you want to look at risk for only a certain number of hands then you have to adjust the formula a bit. But, as I explained, you have to be careful when looking at risk from such a shortsighted perspective. You have to know which formula is more relevant to your situation but you often want to know the “big picture” as well. If the players don't have a specific number of hands they plan to play before quitting, or if that number is big enough as in the case above, then Lifetime RoR is a good place to start.
moo321 said:
No bet resizing, never removing or adding money, always playing the exact same game, spread, pen, rules. From a finance perspective, it doesn't really tell us anything.
The formula above assumes that you reinvest all winnings back into the bankroll. If you want to add more money periodically then you should use the
Renewable Bankrol RoR formula. If you rely on your winnings to pay your bills and cannot reinvest all winnings then you should use a
Proportional Reinvestment RoR formula. If you plan on resizing your bets at a certain bankroll size then you can adjust the Lifetime number based on what level you plan on raising/lowering your bets (this is covered in BJA).
There are literally dozens of different RoR formulas for just about any situation. I agree that the Lifetime formula isn’t always applicable, but it is a good place to start. It will give you a general idea of what you’re up against. Once you have a very specific game plan you can start playing with the more specific formulas that will suit your needs. However, as you said, those formulas require more information than simple EV, SD and BR. That is why the Lifetime formula is often used to give ballpark figures in books and on message boards.
-Sonny-