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# Thread: Bankroll Requirements for Two Hands

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## Bankroll Requirements for Two Hands

I have a standard deviation of 54 units per 100 hands and a win rate per 100 hands of 2.5 units when I play one hand per my playing strategy. How would I calculate my ROR percentage with no goal and an infinite time to play if I simply played two hands with that exact same system? My initial thoughts were to double the std. dev. and win rate but I do not think this method is correct.

Thank you!

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Without actually doing the math on this one, just winging it, but, you're either going to have to double your HPH in the formula, or double your HPH and adjust your average bet out as some places require a 2x table min (if you were flat betting then raising with count).

But really, the bankroll requirement is a byproduct of average bet and average hands per hour, among a few others. Two hands requires knowledge of your average "long run" hand bet, and hands per hour.

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Understood and thank you. Doubling the HPH makes sense to me, but I am wondering about the covariance as well with regard to playing two hands. And no need to worry about the double on the table min because my min bet on one hand is already twice the table min.

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Originally Posted by player1
understood and thank you. Doubling the hph makes sense to me, but i am wondering about the covariance as well with regard to playing two hands. And no need to worry about the double on the table min because my min bet on one hand is already twice the table min.

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Because of covariance you can increase your total bet without increasing ror as follows:

If your bet with one hand is \$100
Your bet with two hands would be 2 X \$74
Your bet with three hands would be 3 x \$56

If your standard deviation is \$5.40 per hand, your standard deviation per 100 hands is SQ Rt of 100 X STD Dev per hand. You do not just multiply Std Dev

Your win rate is proportional to hands per hour and average dollars bet. It appears your advantage is 2.5% so HPH X AVG BET X 2.5% should be your win in dollars.

Professional Blackjack, Blackjack Attack and CVCX should answer any questions you have.

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Thank you. I have the two books you mentioned as well as CVCX. I cannot use CVCX because I have a custom betting strategy. Thus, I use CVData. When I do a sim on CVData for my two hand strategy, the results are per seat and not combined to account for two hands. I want to know what data do I input in the simple ROR calculator in CVdata to account for two hands. See below:

Facts: SD of 54 units per 100 hands and a win rate per 100 hands of 2.5 units when I play one hand per my playing strategy
Bankroll: 2500 units

--------------------
The simple ROR calculator only requires three points of data which are below. Would what I input into the simple ROR CVdata tool for two hands being played with the exact same bet spread and BS deviations be any one of the two examples below?

Bankroll: 2500 units
Std. Dev. per 100 hands: 54 units
Win rate per 100 hands: 2.5 units
Risk of Ruin = 1.37% - this seems very low in my opinion for two hands being played the exact same way at the same table with the facts above. Therefore, I cannot simply enter only the Std. Dev. and Win Rate for 1 hand when I am trying to evaluate two hands.
OR
Double the Std. Dev and double the win Rate due to playing two hands the exact same way. I am not playing two hands at 75% of my normal bet.

Bankroll: 2500 units
Std. Dev. per 100 hands: (54*2)=108 units
Win rate per 100 hands: (2.5 *2)=5 units
Risk of Ruin = 11.71% - this seems much more reasonable but there may be more than just doubling the SD and win rate.

I know I am really drilling down on this simple question but I appreciate all the help!

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Originally Posted by Player1
Thank you. I have the two books you mentioned as well as CVCX. I cannot use CVCX because I have a custom betting strategy. Thus, I use CVData. When I do a sim on CVData for my two hand strategy, the results are per seat and not combined to account for two hands. I want to know what data do I input in the simple ROR calculator in CVdata to account for two hands. See below:

Facts: SD of 54 units per 100 hands and a win rate per 100 hands of 2.5 units when I play one hand per my playing strategy
Bankroll: 2500 units

--------------------
The simple ROR calculator only requires three points of data which are below. Would what I input into the simple ROR CVdata tool for two hands being played with the exact same bet spread and BS deviations be any one of the two examples below?

Bankroll: 2500 units
Std. Dev. per 100 hands: 54 units
Win rate per 100 hands: 2.5 units
Risk of Ruin = 1.37% - this seems very low in my opinion for two hands being played the exact same way at the same table with the facts above. Therefore, I cannot simply enter only the Std. Dev. and Win Rate for 1 hand when I am trying to evaluate two hands.
OR
Double the Std. Dev and double the win Rate due to playing two hands the exact same way. I am not playing two hands at 75% of my normal bet.

Bankroll: 2500 units
Std. Dev. per 100 hands: (54*2)=108 units
Win rate per 100 hands: (2.5 *2)=5 units
Risk of Ruin = 11.71% - this seems much more reasonable but there may be more than just doubling the SD and win rate.

I know I am really drilling down on this simple question but I appreciate all the help!
I can't tell you the math on this right off the top of my head as it is late, but it looks like the relation to RoR and Bankroll size in 1h vs 2h is about right, so I believe you might have your numbers pretty close there.

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The simplest and most accurate way is to change the CVData sim to one player with two hands.

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Rule of thumb when playing two hands = take the bet ramp you use for one hand and bet 75% of that ramp for two hands and you will maintain the same ROR.

EI: one hand ramp is 1-15 spread = 25, 50, 125, 250, 375
Then two hands would be roughly 20x2, 35x2, 100x2, 190x2, 280x2 (depending on which way you want to round). This gives you the same ROR.

I believe that Norm outlines the math in his book.

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