2 Hands Heads Up

[Kasi]

Is that not the purpose of SCORE? A Standard Comparison of Risk and Expectation? When betting Kelly (13.5% RoR), the SCORE is what our WR would be (or at least thats what I understand). So, even at a lower risk, the WR would be better for 2 hands than 1.

The reason I ask this question is because people are always saying that when heads up, playing 1 hand is better than 2. But looking at the results of my sim, that statement seems to be false.

PS: Sorry for the bad image, but the SCORE from playing 2 hands is clearly better than 1 (~41 vs 60)

Well, you may have me a little conflicted here lol.

I agree with your def of SCORE - win rate will equal SCORE when playing with a $10K roll and betting optimally.

Also, it makes sense to me that if SCORE was 41.45 (if that's what it is) in the first sim it would be 60.45 in the second sim on the "optimal" lines. Since one would bet 73% of the original optimal bet if playing 2 hands per round. And 41.45*1.46=60.51 which is pretty close.

On the other hand, like you suggest, Don's Table 2.4 suggests one should always bet only one hand when playing heads-up due to the "card-eating" effect and that one would get more "top-bets" (total $'s wagered) out playing heads-up with one hand versus 2 hands per 100 top-bet opportunities seen.

At the moment, and maybe for a while, I can't reconcile both thoughts in my head lol.

While Don's table applies to only "top-bet" opportunities, I don't know how it would effect always doing it at every count.

I think he does go on to say the effect is one of those "theoretical" effects that doesn't nake a whole lot of difference in real life. Like you wouldn't be real far off either way. So you can rest easy while I will remain tormented and not even doing it lol.

Still, I'd guess a precise use of a sim could maybe reveal the answers?

And, keep in mind, if SCORE in your sims is what you say it means, the SCORE won't change no matter how improperly you bet your roll. Like, in this case, doubling orig (optimal) bet amount on each of 2 simultaneous hands. That's as wrong as the day is long is my guess.

Don't feel bad. There's alot I don't understand about QFIT's software. Whether "hds/hr" means "rds/hr" if playing more than one hand. Whether N0 is expressed per 100/seen or physically played when back-counting. Why, when back-counting, the frequencies still seem to sometimes add to 100% even though only 75% of the hands are actually being played. I guess maybe "normalizing" or something but it causes me headaches lol. Sometimes it seems maybe to me SD is expressed per hand as some kind of average of per round per hour based on 100 rds/hr seen as opposed to just what it is in a physical round. So when you add a few players, per/round stuff changes per hour maybe even though it's really the same per physical round played lol.

Why co-variance is not chosen to be displayed at each TC when playing more than 1 hand per round. What would be so darn hard about that? Katrina can do it in her SP21 book. I don't even know if the co-variance is "behind the scenes" included in the SD at each TC or not - it seems to me (my guess) it is not and just completely calculated invisibly to the user. I'm pretty sure the co-variance is not constant at each TC but that's really just a guess too.

Trust me, I'm so easily confused, it's pathetic lmao.

 

[rukus]

The betting was the same except the 2 hands were 2 hands of what 1 would have had. ex: bet 1x3 units at TC of 3 / bet 2x3 units at TC of 3. So, I suppose that it would not have been optimal assuming the same BR, but SCORE would have taken care of that. SCORE does not take your specific betting scheme into consideration, just the size of the ramp (or so I believe).
....
You are correct that I forgot to consider that aspect, but at least in my CVCX sim, I used the automatic bet feature and it still showed a ~50% improvement in SCORE/WR with the same RoR.

the sentence i highlighted alone would cause your WR and SCORE to increase since you are putting more money down on the table in advantageous situations. but i am curious how you managed to achieve the same ROR for the 2 scenarios with the bet sizes just doubled and split between two hands. i dont have CVCX so maybe i am missing something, particularly this "automatic bet" thing?

 

[SleightOfHand]

the sentence i highlighted alone would cause your WR and SCORE to increase since you are putting more money down on the table in advantageous situations. but i am curious how you managed to achieve the same ROR for the 2 scenarios with the bet sizes just doubled and split between two hands. i dont have CVCX so maybe i am missing something, particularly this "automatic bet" thing?

CVCX has an option that will automatically place the optimal Kelly (or its proportional counterpart) bet given your BR and spread size.

 

[sagefr0g]

CVCX has an option that will automatically place the optimal Kelly (or its proportional counterpart) bet given your BR and spread size.

it's interesting. are you able to compare these results with similar parameters for cvdata?
what is that spinner in the two hand simulation across from the play two hands check box? is that for number of players?
edit: oh never mind i see the spinner gives you two hands played at all tc's
http://www.blackjackinfo.com/bb/showpost.php?p=139218&postcount=8

 

[rukus]

Sleight, do you have CVdata? If not, you can send me your inputs (including optimal bet ramps as spit out from CVCX) and I probably have some time this wknd to run it for you. Full blown sim would settle this though I'm sure cvcx gives a very good estimate.

For true comparison purposes you need the one hand optimal bet ramp for whatever BR you want. Then take each of those and multiply by about .73 to get the two hand bets and run that. Then you should be able to fairly compare score and winrate across sims.

And Froggy you are correct. I think ppl above mean c-SCORE.

 

[sagefr0g]

Sleight, do you have CVdata? If not, you can send me your inputs (including optimal bet ramps as spit out from CVCX) and I probably have some time this wknd to run it for you. Full blown sim would settle this though I'm sure cvcx gives a very good estimate.

For true comparison purposes you need the one hand optimal bet ramp for whatever BR you want. Then take each of those and multiply by about .73 to get the two hand bets and run that. Then you should be able to fairly compare score and winrate across sims.

And Froggy you are correct. I think ppl above mean c-SCORE.

sounds like a plan.

maybe two hands heads up can be better, maybe i'm miss-interpreting Wong in PB where he says, "...pg 211.. Generally, if you are alone with the dealer you are better off playing one hand, and if there are other players you are better off playing two hands when you have an edge."

on that SCORE stuff maybe i got some of it right but i'm a lost puppy far as understanding it.
SCORE, c-SCORE & classic coke, lmao...

 

[bjcount]

sounds like a plan.

maybe two hands heads up can be better, maybe i'm miss-interpreting Wong in PB where he says, "...pg 211.. Generally, if you are alone with the dealer you are better off playing one hand, and if there are other players you are better off playing two hands when you have an edge."

on that SCORE stuff maybe i got some of it right but i'm a lost puppy far as understanding it.
SCORE, c-SCORE & classic coke, lmao...

If I have it correct, you play 1 hand heads up so you will get more rounds in a shoe when the counts positive.
You'll play 2 hands when there are other players at the table when the counts positive so you will get a larger percentage of the cards dealt.

Now let's see if I have this correct too:
You will have lower variance playing two hands, but you will require a larger bankroll to handle the larger action and higher RoR.

If you guys are going to look at sims comparing the TC frequencies, SCORE, win rates etc... first you need to have the "PEN" set all the same.

Froggy, In your sims earlier in the thread you ran them using 50% pen so your SCORE and all other results will be awful.

In SoH sims you keep changing the pen too, 1.25/2 & 1.33/2. In a DD game just a 1 card difference in pen makes a big change in the results.

CVData will also give you more accurate results than CVCX.



BJC

 

[sagefr0g]

..

Froggy, In your sims earlier in the thread you ran them using 50% pen so your SCORE and all other results will be awful.
...
BJC

right, i was only trying to show with those sims that the tc frequencies do change according to how many players are at the tabel, and by inference that playing one hand heads up and playing two hands heads up would still involve changing tc frequencies.... something apparently cvcx doesn't reflect for the instances of going from one hand to two hands heads up with the dealer.

 

[Kasi]

Now let's see if I have this correct too:
You will have lower variance playing two hands, but you will require a larger bankroll to handle the larger action and higher RoR...

I'd guess, if betting optimally, with the same roll, game, system etc, you'd have more total variance per round playing 2 hands than 1, more EV too, but all with the same risk to your roll.

Why would you willingly submit your roll to different risks just because you want to play 2 hds/rd?

Bet optimally so that one's EV and one's variance both increase in the right proportions to keep the risk to your roll the same in either case.

Yes, more EV per round. Yes, more variance per round. Same risk to roll.

That's the point of spreading.

 

[creeping panther]

Sleight

I have played both ways in heads up, with out the "h" rule I prefer one spot but will swing to 2 at the right moment. I play so much with the "H" rule that playing heads up without it is a great treat.

With another player at the table I much prefer 2 spots.

But if you can move from 1 to 2 and back and forth, I believe in taking advantage of that.

Hope all is well with you.

CP

 

[sagefr0g]

Sleight, do you have CVdata? If not, you can send me your inputs (including optimal bet ramps as spit out from CVCX) and I probably have some time this wknd to run it for you. Full blown sim would settle this though I'm sure cvcx gives a very good estimate.

For true comparison purposes you need the one hand optimal bet ramp for whatever BR you want. Then take each of those and multiply by about .73 to get the two hand bets and run that. Then you should be able to fairly compare score and winrate across sims.

.....

thinking about this and the original post regarding the question of which is better when playing heads up with the dealer, one hand or two, i've come to the conclusion that the only fair way to compare the two scenarios would be to have each scenario betting the same exact amount at the same exact true count per round. then examine the risk involved for each. the risk involved should be the determining factor not win rate.

this approach would i believe better fit the spirit of Wongs advice that it is in general better to play one hand when playing heads up with the dealer.

Wong's idea that one can bet some fractional amount more when playing two hands and there are other players at the table there by getting more money on the table with relatively the same risk is a separate issue, but it illustrates the spirit of the idea.

 

[SleightOfHand]

thinking about this and the original post regarding the question of which is better when playing heads up with the dealer, one hand or two, i've come to the conclusion that the only fair way to compare the two scenarios would be to have each scenario betting the same exact amount at the same exact true count per round. then examine the risk involved for each. the risk involved should be the determining factor not win rate.

this approach would i believe better fit the spirit of Wongs advice that it is in general better to play one hand when playing heads up with the dealer.

Wong's idea that one can bet some fractional amount more when playing two hands and there are other players at the table there by getting more money on the table with relatively the same risk is a separate issue, but it illustrates the spirit of the idea.

Unless I'm mistaken, playing 2 hands, betting the same amount as 1 (ie. 1x10 vs 2x5) will definately lower your RoR due to the covariance. However, that is not the optimal bet, as the Kelly equation considers variance (~advantage*BR/variance). That is why the rule of thumb is to play 150% of what you would with 1 hand when spreading to 2 (when you desire the same risk). Playing the same amount as 1 hand will achieve the same WR but a lower RoR.

If I have it correct, you play 1 hand heads up so you will get more rounds in a shoe when the counts positive.
You'll play 2 hands when there are other players at the table when the counts positive so you will get a larger percentage of the cards dealt.

Now let's see if I have this correct too:
You will have lower variance playing two hands, but you will require a larger bankroll to handle the larger action and higher RoR.

If you guys are going to look at sims comparing the TC frequencies, SCORE, win rates etc... first you need to have the "PEN" set all the same.

Froggy, In your sims earlier in the thread you ran them using 50% pen so your SCORE and all other results will be awful.

In SoH sims you keep changing the pen too, 1.25/2 & 1.33/2. In a DD game just a 1 card difference in pen makes a big change in the results.

CVData will also give you more accurate results than CVCX.



BJC

The sims that are being compared have the same pen. So, it doesn't really make a big difference. Also, I did use CVData, and achieved similar results (although my method may not have been completely accurate, but still achieved a SCORE much better than the one for 1 hand).

 

[SleightOfHand]

Bja

I lent my BJA to a friend that is learning to count. Can someone tell me exactly what DS says about why 1 hand is better than 2? If I remember, it had to do with a slightly less amount of $ being put out vs cards eaten. Why is this important? What does it matter to make the TC last temporally longer, if we are experiencing a much higher playing speed? Is this not like just playing slower in a high TC so it lasts longer?

 

[sagefr0g]

Unless I'm mistaken, playing 2 hands, betting the same amount as 1 (ie. 1x10 vs 2x5) will definately lower your RoR due to the covariance. However, that is not the optimal bet, as the Kelly equation considers variance (~advantage*BR/variance). That is why the rule of thumb is to play 150% of what you would with 1 hand when spreading to 2 (when you desire the same risk). Playing the same amount as 1 hand will achieve the same WR but a lower RoR.
...

yes, i believe that is correct.

lmao, well obviously i don't understand it.
doesn't mean i can't still think, question or wonder about the issue, lol.
maybe revise, thoughts on the issue, cause still i'm reluctant to believe Wong is so far off on this issue.

thinking about what you stated above makes me wonder, if there is another issue here that we haven't considered as a 'fairness' point of contention over the matter. i'm thinking that would be a matter of 'effective' spread (for lack of a better word) between the two scenarios.
point being the one hand guy is spreading Xunits to Yunits with some ramp, but what is the 'effective' spread and ramp of the two hand guy? it would seem, a greater spread and ramp, no?
thought being, if the spread issue were to be equalized, while the betting action was kept equalized, then what would the comparable risk of ruins be?:whip:
i'm pretty sure if the spread was increased for the one hand player the ROR would drop significantly. so if the 'effective' spread for both players was equalized while the amount of action was equalized perhaps we'd get a 'fairer' picture in terms of risk. i dunno. :whip:

edit: oh, and i'll take a look in my BJA and see what Don S. has to say about this issue........

 

[sagefr0g]

I lent my BJA to a friend that is learning to count. Can someone tell me exactly what DS says about why 1 hand is better than 2? If I remember, it had to do with a slightly less amount of $ being put out vs cards eaten. Why is this important? What does it matter to make the TC last temporally longer, if we are experiencing a much higher playing speed? Is this not like just playing slower in a high TC so it lasts longer?

i guess this stuff out of Blackjack Attack, pg 27 is what your referring to...

""How do I know whether to bet the one hand, two, or three?"
Here is how I suggest we figure it.
It is not sufficient to simply "get the greatest amount of money on the table" (obviously, the three hands) for any one given round, thereby assuming that this strategy will get the greatest amount on the table by the time one has finished playing. Each spot played uses up cards. We must consider, for any given shoe, how much money will actually be put on the table with each one of the approaches. it is only after considering the total "global" wager that one can determine the best approach. The "correct' answer is neither obvious no intuitive.
Let us assume that, if we play long enough ( just how long is easy to calculate), we will eventually have the opportunity to place 100 maximum bets (true of +5 or above). Furthermore, for the purposes of this demonstration, let head-up play against the dealer in a 6-deck, deal 4 1/2 (75%) game be the norm. Now consider the effect of playing one, two, or three hands on the number of cards used per round. [Note: 2.7 cards per completed hand is average. Therefore, head-on play uses 5.4 cards per round, and each additional hand at the table adds 2.7 cards to that total.] Consider, also, the effect of other players at the table. The following chart indicates exactly how many hands can be played under varying conditions, give our above scenario. In addition I have multiplied hands played by dollar amount of wager to produce, in each box a total amount of money wagered.
To determine, for any given box, how many hands (maximum = 100) can be played, use 5.4 as the numerator of a fraction. Next determine the total number of hands being played for the box in question. For example, playing with two other players and playing two hands equals five hands. Multiply the number of hands by 2.7 (in this case, 5 x 2.7 = 13.5) Use the result as the denominator of the fraction. Thus, 5.4/13.5 = 2/5 = 40%. Multiply100 by this resulting fraction (for example, 40 hands).
On each horizontal line (Table 2.4), the maximum dollar amount is in bold print, indicating the optimal play.
.........text skipped.......
Now, there is one instance, even when playing alone, when spreading to a second hand is a must. If you are proficient in eyeballing the discard tray and "know" when the last hand in the shoe is about to be dealt, then by all means, spread to the second hand. It doesn't matter anymore that you are eating up extra cards."

 

[SleightOfHand]

i guess this stuff out of Blackjack Attack, pg 27 is what your referring to...

So, looking at this, it only considers how much money is being put on the table. However, it does not say anything about covariance. With a ~2% loss in $$ being put on the table, I wonder if the loss can be offset by the covariance. Doesn't seem like a big hurdle...

 

[sagefr0g]

So, looking at this, it only considers how much money is being put on the table. However, it does not say anything about covariance. With a ~2% loss in $$ being put on the table, I wonder if the loss can be offset by the covariance. Doesn't seem like a big hurdle...

beats the heck out of me, at this point i'm wore out and more confused :whip: than ever, lmao. but not ready to stop examining the issue, lol.

just i'd suspect and only voodoo reasoning here, what i'd expect to find at the bottom of the question far as which is better one hand or two, heads up against the dealer once one levels the playing field and makes the comparison fair, the thing i'd bet would be the ultimate deciding factor will be risk. perhaps for example, that 'effective' spread question i raised.

just me agreeing with Wong maybe playing those zero tc and negative tc hands doubled up is some bad stuff and unnecessary.
i dunno maybe then when it's multiple players, they eat up some of the zero and negative tc hands, sort of thing if your playing two hands or more, plus you'd be increasing your chances of a 'good' hand when the count is positive.
that sort of an 'offset' isn't working for you when your heads up with the dealer.

 

[Kasi]

So, looking at this, it only considers how much money is being put on the table. However, it does not say anything about covariance. With a ~2% loss in $$ being put on the table, I wonder if the loss can be offset by the covariance. Doesn't seem like a big hurdle...

Well, the reason he is betting 2 hands at $365 each is because, due to co-cariance, this is 73% of the optimal 1-hand $500 bet. What thiis does is make the risk the same in both cases.

So he is taking co-variance under consideration, kind of like The Wise One said above, risk is the deciding factor in deciding questions like this. (I think lol). Risk must be the same in both cases so one is comparing apples to apples.
So, since risk is the same, the scenario that gets more $out on the table in the same amount of time is the better one to choose.

Not much point in spreading to $1000/hd on 7 spots and concluding it's "better" just becasue you now have a higher $EV per round, hr etc.
You won't have the same risk lol.

Anyway, what I was trying to get at before regarding your first 2 sims when the risk was triple in one scenario than the other.

In Don's scenario, analyzing 100 top-bet opportunities, it was easy to calculate just how long it would take for one to have 100 top-bet opportunities. Hence, seeing only 67 top-bet opportunities if betting 2 hands of $365 in the same amount of time.

To me, it's pretty much, while perhaps true, useless theoretical cr*p anyway lol. Not many can increase the optimal 1 hand by 73% to keep their risk the same when betting 2 hands.

But, on the other hand, why does not one at least try, when spreading in the same game, even with diff pen levels, playing different games, playing in different ways, back-counting, wonging-out, heads-up, number of players etc, at least make an attempt to play all of that variety by betting in such a way so as to at least keep one's risk more-or-less as constant as possible?

I've never really understood what often seems to me like a lopsided fixated fascination with EV only lol.

Don't mean you lol.

 

[itrack]

The only thing that I can find wrong with that table posted above is that he assumes 2.7 cards each as the norm, whether the player is playing heads up or not. Sure the players hand might be 2.7 cards average still, but the dealers hand will surely not be 2.7 cards average I assume? Or even better yet (or worse), if you were playing a game with no dealer holecard dealt. I would assume that the number of cards played/round would decrease alot, and make it even more profitable to play only 1 hand heads up.

 

[Kasi]

The only thing that I can find wrong with that table posted above is that he assumes 2.7 cards each as the norm, whether the player is playing heads up or not. Sure the players hand might be 2.7 cards average still, but the dealers hand will surely not be 2.7 cards average I assume? Or even better yet (or worse), if you were playing a game with no dealer holecard dealt. I would assume that the number of cards played/round would decrease alot, and make it even more profitable to play only 1 hand heads up.

Well, I'd imagine you have a point - obviously, I'd guess anyway, the dealer will have fewer avg cards per round when playing heads up since he will never take another card every time his heads-up opponent busts but would likely have to take another card at a full table sice every player will likely not have busted.

I'd guess the avg cards per round for dealer vs player are different with the most difference being heads-up. Don't really know.

I'd guess the difference on avg, if it exists, after being diluted by 2 or more players, on a per round basis, isn't much different than the 2.7 per round per player including the dealer.

Probably, even if all my guesses may have some validity, or, even if they don't lol, it won't amount to much$ regardless.

To the extent such differences may or may not exist weighs into the equation of whether to buy CVDATA or not. My guess is, on this question alone, it might take a while to justify the expense.



No idea what Don's tables take into account at that level.