Two box RoR maths question for the experts!!

Guys, your help would be greatly appreciated,

I am using this forumla for working out RoR on two boxes:

1.32 / (1.32 + 0.48 * (n-1) )


My question is, are the "1.32" and "0.48" parts of the formula affected if you have the ESA (early surrender against ace) rule (european tables).. If so, what would the revised formula be?

Thanks so much for your help!

Sorry, its not my area. zg

Anyone got any ideas? :grin:

Can you give us a bit more information on this formula?

What do the constants 1.32 and .48 even STAND for?
What does the variable 'n' represent?
The placement of the multiplication symbol in the divisor is confusing. Are you sure you have all the parentheses in their proper place?
Perhaps my most pertinent question: Where did this formula even COME from?

Maybe I can help if I can understand this a bit more.

He is using some form of the formula from http://wizardofodds.com/blackjack/appendix4.html (search for "covariance" in the document) but there shouldn't be a division unless you specifically divided for some reason.

0.48 is the covariance, and 1.32 is the variance. This would indeed change based on the rules, and you can get the variance from cvdata for the specific set of rules you are playing with.

Again, I am not sure you are using the correct formula, so you need to give us more information for clarity.

I am not sure that you are using a correct formula for the Risk Of Ruin (ROR). As people have indicated 1.32 represents the variance of a hand of blackjack and 0.48 represents the covariance. These values are dependent on the rules of the game, and early surrender will reduce the variance.

Now as far as you question, you don't play two hands to reduce your ROR, you play two hands to make larger bets (increasing your return) while maintaining the same risk of playing only one hand.

In any case that is not how you should go about this, you first determine the level of risk you are comfortable to play with, once that is set, you determine your betting ramps for (one hand or two hands) based on your bankroll, game rules, penetration, betting and playing strategy. Memorize it and hit the casino!

I am terribly sorry, I was very misleading in my original question.

I am using this formula to work out the percentage I have to lower my bets if I want to play "n" number of boxes to keep the ROR the same as I was playing 1 box. Is that clearer?

For example risk of ruin of a given BR is, say, $20,000 playing 1 box with a given betting ramp. To work out how to keep the ROR the same by playing two boxes, I just plug 2 (for 2 boxes) in place of "n" to work out the percentage of the bets to keep ROR the same on the two boxes.

1.32 / (1.32 + 0.48 * (n-1) )

= 1.32 / (1.8 * (2-1) )

= 1.32 / 1.8

=0.73

Therefore I have to bet 73% of my one-box bets to keep the ROR the same ($20,000 in this example) on two boxes.


Another example:

3 boxes

1.32 / (1.32 + 0.48 * (n-1) )

= 1.32 / (1.32 + 0.48 * (3-1) )

= 1.32 / (1.32 + 0.96)

= 1.32 / 2.28

= 0.58

Therefore I have to bet 58% of my original 1-box bet on all there boxes to keep the risk of ruin the same as the 1-box game.


My question is, if we change to rules to Early Surrender (anything, ace included), what will the revsied formula be?

BTW, I got the original formula from assume_r in this thread:

http://www.blackjackinfo.com/bb/showthread.php?t=19626

Thanks again for your help.

As I had mentioned in my above post the variance and covariance will change slightly with early surrender however due to rounding and the need to simplify bet for practical purposes it will really make no difference at the end.

So for two hands you will have 2x0.75 of one hand bet
For 3 hands you will have 3x0.60 of one hand bet
For 4 hands you will have 4x0.50 of one hand bet ...

Thanks icountntrack.

Can I also ask, say my hourly rate is 100 dollars an hour on one box. If I play 2 boxes, will my hourly rate be 200 dollars an hour? If I play 7 boxes will my hourly rate be 700 dollars am hour?

If this is no the case can you give me a formula for working out hourly rate on multiple boxes, given that I know what it is on one box.

Thanks.

Your hourly rate is equal to your hourly total action (total amount bet) multiplied by your expectation value.

Your expectation value does not change but your total action is 1.5 (2x0.75) times larger if you playing two hands, 1.8( 3*0.60) times larger if you playing 3 hands..., which means that in theory your hourly rate should be 1.5 or 1.8 times larger. However they are typically a litte less than that due to other factors like card eating and simplified bets, so the best way to determine your hourly rate is to run a simulation.

Ah yes, I forgot about that old formula I came up with - in that case, I'd have to say of course the formula is 100% correct! :laugh: Note that formula is only for determining how much you'd have to change your bet to keep the same RoR, which you probably already know.

But seriously, just change the 0.48 and 1.32 to the covariance and variance of your specific game, and the formula stands. I think iCnT has answered most of your other questions. Is everything clear?