Simulation reveals shocking conclusion (1 vs 2 hands)

[QFIT]

Hey kewljason, I agree with you about the time and stuff.
However, in practical viewpoint, in Atlantic City, I've
never been at a table alone. How much longer does it
take to deal me an extra hand when there're 2 or 3 other
random players at the table?

Now this is a good question. The fact is that an accomplished player can play two hands nearly as quickly as one hand, assuming that the dealer is reasonably quick.

 

[kewljason]

Now this is a good question. The fact is that an accomplished player can play two hands nearly as quickly as one hand, assuming that the dealer is reasonably quick.

But it's not the speed of playing the hands that will matter, although even at 2-3 seconds each that would begin to add up over 100 rounds. The factor that will really make the difference is less rounds per shoe with more hands. That means it will take more shoes to get in the 100 rounds (plus more shuffle time)

 

[QFIT]

But it's not the speed of playing the hands that will matter, although even at 2-3 seconds each that would begin to add up over 100 rounds. The factor that will really make the difference is less rounds per shoe with more hands. That means it will take more shoes to get in the 100 rounds (plus more shuffle time)

Another good point. Speed is always a factor in my mind. Shuffling time is somewhat different from waiting for the dealer come to your seat during play as it is less tiring. Energy level and its effect on performance is not something we talk about much.

 

[aslan]

My original simulation had two players at the same table.
The first player played one hand, while the second player played two hands all the time.
So, total of three hands were played against the dealer's same hand.
I assumed that the number of players at the table would have negligible impact in
6 decks.

For those who're curious about the "heads-up" results, I re-ran the simulation except
this time for 10 billion rounds.

First Table: 1 unit = $50
Number of players: 1
Bet 1 unit for TC <= 1
Bet 3 units for TC = 2
Bet 6 units for TC >= 3

Second Table: 1 unit = $25
Number of players: 1
Bet 1 unit on two hands for TC <=1
Bet 3 units on two hands for TC = 2
Bet 6 units on two hands for TC >= 3
Reset after shuffle: Unchecked (This is important to maintain two hands at all times.)
The second table has only one player who's playing two hands.

Player at Table 1 win rate: $37.77/hr
Player at Table 2 win rate: $38.55/hr
Player at Table 1 Standard Deviation: $1258.13/100 rounds
Player at Table 2 Standard Deviation: $1047.47/100 rounds
Player at Table 1 SCORE: 9.01
Player at Table 2 SCORE: 13.54

My theory is still correct. Even if you're playing heads-up, it's still better to play
two hands.

Personally, I would sacrifice yield for low variance. By lowering the standard deviation,
I'm basically buying piece of mind so I wouldn't get stomach ulcers and lose sleep at
night.
The slight increase in win rate was a pleasant bonus. But why is there an increase in
win rate at all? Maybe because more cards are dealt after the cut card,... ?
Which translates to slightly deeper penetration,... ?
But what about when both players are at the same table? Don't they get the same penetration?

Regarding playing two hands being superior to playing one hand:

I don't consider myself an expert, but it you are playing two hands all the time, then you will also be playing two hands in all positive counts, meaning that you have a decided advantage over the player playing one hand since you have twice the possibility of getting all those "good" cards. Since you will be betting max, that should make for the difference.

When you are in negative counts, you will be in no more jeopardy playing two $25 hand than the other player who is playing one $50 hand. In fact, you may be more likely to win one and lose the other, actually giving you a small advantage over the single bet player, but of this I am not totally sure.

 

[assume_R]

Thinking about it a little further: Suppose you have 3 players, Joe, Bill and Bob at the table. All play Hi/Lo with identical betting ramps. All play their hands according to basic strategy to eliminate any advantage of seat position. Joe uses $50 units while Bill and Bob each use $25 units. At the end of eternity, Bill and Bob must each win half of what Joe wins -- no???

Now let's say that seats number 2 and 3 just happened to be BillyBob -- one person playing both hands! How could BillyBob's results be any different than Bill's and Bob's added together??? Can someone help me here???

It seems to me that the important part of this is that if both BillyBob and Joe appropriately chose their bets so that they both had an equal RoR of 5%, BillyBob would be betting higher than $25 per hand and thus have a higher EV.

How, just given the exact scenario you proposed above, it's my understanding that the EV of BillyBob and Joe are equal, yet the Var of BillyBob is less than Joe. Therefore, BillyBob would have a lower N0 = Var/EV^2.

If the game were such that the covariance were a certain value (not sure the exactly value), then BillyBob and Joe would have EXACTLY the same results.

So I suppose it all comes down to BillyBob has a lower N0, and if he wants to "utilize" that by either increasing his EV (putting more than $25 out) or decreasing his Var (2x$25 instead of 1x$50) that's his choice.

Does that seem reasonable?? Just my thoughts...

 

[assume_R]

In fact, you may be more likely to win one and lose the other, actually giving you a small advantage over the single bet player, but of this I am not totally sure.

I don't think that's true...hmmmm maybe it is????

 

[QFIT]

BillyBob will have more rounds that push, and therefore lower variance. For the same risk, BB can bet 2x37 instead of 1x50. therefore, he can make more money with the same risk. You can see this with CVCX. Click the Two hands button.

The bet will decrease by less than half.
The win rate will go up.
The std dev will go up, but by less than the win rate
The risk of ruin will stay the same
SCORE will go up
N0 will go down.

 

[muppet]

kj does bring up a good point in that it takes longer to play 2 hands as opposed to 1. and if you're playing heads up this will also result in the dealer having to 'play' their hand more often.

hmm, something to think about