Betting Multiple Hands

[SleightOfHand]

Lets say I use a 16:1 spread where my max bet is 2 hands of 8 units. Is there a difference if I bet 1 hand of 5 and another hand of 11? I would think that it seems like I am more of a ploppy if I bet 2 hands of 8, lose 1 and win the other, and transfer some of the "loser" bets into the "winner" bets.

 

[rukus]

Lets say I use a 16:1 spread where my max bet is 2 hands of 8 units. Is there a difference if I bet 1 hand of 5 and another hand of 11? I would think that it seems like I am more of a ploppy if I bet 2 hands of 8, lose 1 and win the other, and transfer some of the "loser" bets into the "winner" bets.

it will increase your variance while keeping your EV the same when compared with 2 hands of even amounts.

 

[cardcounter0]

betting 2 hands of 8 is not a 16:1 spread, it is a 12:1 spread.

 

[SleightOfHand]

betting 2 hands of 8 is not a 16:1 spread, it is a 12:1 spread.

Ehhh semantics :grin: I just want to know the effect of transfering checks.

it will increase your variance while keeping your EV the same when compared with 2 hands of even amounts.

Any idea how much? Is it too much to utilize?

 

[rukus]

Any idea how much? Is it too much to utilize?

it varies based on how much is in each hand. should be proportional to the square of how much you bet on each hand, something like (A)x(#hands)x(Bet^2), where A is composed of other numbers (including variance/covariance, etc).

for 2 hands of 8 it might be (A)x(2)x(8^2) = 128xA
for 1 hand of 11 and 1 hand of 5 it might be = (A)x(1)x(11^2) + (A)x(1)x(5^2) = 146xA

the equation might not be precisely correct, but it should give you an idea of how straying from two hands of equal amounts in either direction increases variance.

now we care about standard deviation when looking at risk, so maybe the real difference we are talking about here is SQRT(A)*[SQRT(146) - SQRT(128)], or approximately SQRT(A), actually a little less. so it all depends on the size of A, and to a lesser degree how much you bet on each hand.

 

[Sonny]

The variance per hand is the same, it’s just the covariance that changes. I would estimate that the covariance jumps to about 0.75 instead of the usual 0.5. Instead of per-round variance of 1.83 squared units it would be closer to 2 squared units.

-Sonny-

 

[rukus]

The variance per hand is the same, it’s just the covariance that changes. I would estimate that the covariance jumps to about 0.75 instead of the usual 0.5. Instead of a per-round SD of 1.83 units it would be closer to 2 units.

-Sonny-

yup i was actually about to go in and edit my post and say id probably expect a difference of maybe 1 unit.

now assuming covariance going to 0.75 from 0.5 as you say, the total variance for a hand is ~1.15 + 0.75 ~ 1.9. this is my A above. the square root of A, or 1.9, is about 1.4. So it seems to me your per round variance will increase by a about 1.4 units [less actually since sqrt(146) - sqrt(128) ~ 0.75].
So, 0.75x1.4 ~ 1 unit.
what do you think about that reasoning Sonny?

 

[SleightOfHand]

Ooooooh

Wow! Great job guys. So with just a difference of 1 unit, that seems like it could be a useful little variance cost camo to make it seem like I consider 1 box luckier than another, looking more superstitious.

 

[Sonny]

...recalculating...

I think my initial estimate of 0.75 may have been wrong.

 

[rukus]

Just be careful about mixing variance and standard deviation. They are two different units that cannot be combined. The total variance for a round is 1.33 + 0.75 = 2.08 squared units. The total SD for a round is sqrt(2.08) = 1.44 units. The typical SD for a round when betting two hands of equal amounts is sqrt(1.83) = 1.35 so we are increasing our SD by about 0.09 units by using this cover technique.

-Sonny-

yup you caught me! should have been 1.33 + 0.75 in my example above...

 

[bjcount]

yup you caught me! should have been 1.33 + 0.75 in my example above...

Do you guys use these formulas everyday, if not, I need to get one of those cheat sheets too.

Do they have a plastic formula card i can carry around like the BS cards others use? :grin:

BJC

 

[1357111317]

betting 2 hands of 8 is not a 16:1 spread, it is a 12:1 spread.

Could you explain the math behind this?

 

[SleightOfHand]

Could you explain the math behind this?

It was calculated in BJA. When utilizing any spread, the optimal covariance and spread for 2 hands is gained by betting 3/4 of the desired unit size. Example: If a bet calls for 20 units, and you want to spread to 2 hands, its best to bet 2 hands of 15.

Spreading to 3 hands calls for 50% of the units.

So actually, its a 1:10.66 (8*4/3) spread, but thats just more semantics.

 

[Kasi]

Could you explain the math behind this?

I think he probably meant spreading to 2 hands of 8 units would give about the same variance had he played just 1 hand with 12 units. But higher EV since more money is out on the table.

Still, I guess maybe I'd call it a 1-8 spread lol?

Afterall, it's the 8 unit bet you'd need to square to figure out SD per round. At least when they are both 8 units. I think lol.

No idea what bet size I'd square with one hand of 5 units and one of 11 units.
Still 8 maybe and guess at the total variance for the round?

Still, if 1 hand was one-half unit and the other 15.5 units, it's not hard to see it's almost the same as maybe betting 1 hand of 16 units?

 

[EasyRhino]

I'll leave it to the squints for the math, but if you're talking about max bet range, and you're betting aggressively (near full kelly) for your bankroll, BE CAREFUL with significantly varying bet sizes.

From a merely intuitive perspective, what happens if you beginning splitting the hands win/loss, but you keep losing the gigantor hands?

In addition, if you ever end up with a truly small bet on one hand in a + count, then you're effectively "eating cards" from yourself and you'd be better off not betting that spot at all.

One voodoo gambit you can use is switching between one hand of x and two hands of .7x to change the Sacred Flow of the cards.

 

[zengrifter]

Lets say I use a 16:1 spread where my max bet is 2 hands of 8 units. Is there a difference if I bet 1 hand of 5 and another hand of 11? I would think that it seems like I am more of a ploppy if I bet 2 hands of 8, lose 1 and win the other, and transfer some of the "loser" bets into the "winner" bets.

Its a good cover move while increasing the variance.
Should average out quickly, though, IF you keep shifting - chasing the winning hand. zg

 

[celadore]

Betting more than 2 hands

So I gathered from reading in numerous places that when you spread your bets to 2 boxes - you need to bet 75% of your normal bet on each hand. Been doing this for a while now.

What about when you go to 3,4,5,6 or even 7 boxes?
(Yes - I am allowed to bet all 7 boxes. Gone up to 5 so far - bet 75% of max bet at the time - but figure I must be overbetting).

I think it is a great way to camoflauge bets - but am worried that will be overbetting if I don't scale the bets down appropriately, and it is increasing my RoR.

 

[SleightOfHand]

So I gathered from reading in numerous places that when you spread your bets to 2 boxes - you need to bet 75% of your normal bet on each hand. Been doing this for a while now.

What about when you go to 3,4,5,6 or even 7 boxes?
(Yes - I am allowed to bet all 7 boxes. Gone up to 5 so far - bet 75% of max bet at the time - but figure I must be overbetting).

I think it is a great way to camoflauge bets - but am worried that will be overbetting if I don't scale the bets down appropriately, and it is increasing my RoR.

There is another problem with spreading to more than 2 hands. You are putting out more money and effectively eating more cards. Heads up with 2 hands , you are putting out 150% of your normal bet and using 150% of the cards. Therefore no gain. Heads up, in positive situations, stick with 1 hand.

With, say, 3 others, you will be betting 150% of your bet eating 120% of the cards. Here, there is a good gain.

But with your question of optimal bet sizes for multiple hands, it was in DS's BJA. I recall 2 hands called for ~75% and 3 hands called for ~50%. Any more than that, there is minimal gain from spreading to more. As for camo, there is a play called the Grifters Gambit, apparently popularized by zg. Spread from 3 x 1u in minus to 1x3u in moderate to 1 x 7u in high or something like that. Needs a 1000u bankroll to keep a low RoR though.

 

[Sonny]

So I gathered from reading in numerous places that when you spread your bets to 2 boxes - you need to bet 75% of your normal bet on each hand.

You don’t have to, but you can if you want to. When you bet 75% of your regular bet you are preserving the same level of risk and increasing your EV. If you just play 50% of your regular bet you are preserving your EV and reducing your risk. It all depends on what your goal is.

What about when you go to 3,4,5,6 or even 7 boxes?

From the Frequently Asked Questions thread:

Q: Should I play multiple hands? How should I bet if I do?
A: Playing multiple hands is a good way to increase your win rate and/or reduce your risk. Here are some threads about playing multiple hands:

http://www.blackjackinfo.com/bb/showthread.php?t=3069
http://www.blackjackinfo.com/bb/showthread.php?p=16488

-Sonny-

 

[rollem411]

Heads up with 2 hands , you are putting out 150% of your normal bet and using 150% of the cards. Therefore no gain. Heads up, in positive situations, stick with 1 hand.

This is not true. If you play 2 hands at high counts one vs one at 150% of your normal betting spread than you will be making more money. Play 2 hands heads up.