2 Hands Heads Up
- Thread starter SleightOfHand
- Start date
depends on what you mean by something missing.
i can't see your images very well, but magnified i caught some of it, lol.
two things, looks like ror went up for the two hands scenario?
also i'm wondering assuming say the playing one hand scenario was optimal for you then i thought the orthodox thing to do if playing two hands relatively speaking you wouldn't end up betting twice as much. i forget exactly but i think it would be like the total bet for the two hands could go as high as 50% more of what it would be if you was betting one hand.
then maybe i'm wrong but i wouldn't think you'd want to bet two hands at all at a disadvantage. just one would do enough damage, it would seem, lol, especially if your exceeding your unit bet. i mean maybe you could imagine your unit bet was what your betting at two hands, but then you'd be missing out on the advantage of only betting a half of a unit at one hand, sort of thing in those disadvantage counts.
just me, i think to keep things on an even par for judging it, you would want to contrive it so as the ror are equal for the two scenarios. again i'm not sure but i think that's what betting the 50% more of what you would bet on one hand when playing two hands does, is keeps your ror in line with what you are shooting for and keeps your betting optimal, sort of thing.
i can't see your images very well, but magnified i caught some of it, lol.
two things, looks like ror went up for the two hands scenario?
also i'm wondering assuming say the playing one hand scenario was optimal for you then i thought the orthodox thing to do if playing two hands relatively speaking you wouldn't end up betting twice as much. i forget exactly but i think it would be like the total bet for the two hands could go as high as 50% more of what it would be if you was betting one hand.
then maybe i'm wrong but i wouldn't think you'd want to bet two hands at all at a disadvantage. just one would do enough damage, it would seem, lol, especially if your exceeding your unit bet. i mean maybe you could imagine your unit bet was what your betting at two hands, but then you'd be missing out on the advantage of only betting a half of a unit at one hand, sort of thing in those disadvantage counts.
just me, i think to keep things on an even par for judging it, you would want to contrive it so as the ror are equal for the two scenarios. again i'm not sure but i think that's what betting the 50% more of what you would bet on one hand when playing two hands does, is keeps your ror in line with what you are shooting for and keeps your betting optimal, sort of thing.
i can't respond on the SCORE stuff, lmao. i keep forgetting what the heck it means. :laugh:
does your cvcx have this in the help section?
"Play Two Hands - Click to estimate the effect of playing two hands. The original sim must have had at least two players."
but i think you have a updated version of cvcx from what i've got. hmm, i dunno.
just me maybe i'm way off base, is the two hands thing for cvcx kind of experimental? well it says estimate in the section above.
but what ever, i wonder about it because would maybe the true count frequencies be different if you play two hands as opposed to one? that isn't reflected by the sim though. perhaps that's why it would be an estimation?
something i think Wong wrote in Professional Blackjack about this stuff, where if you play two hands heads up you use 150% more cards than if one hand. wouldn't that represent a differing true count frequency when you want to compare this stuff?
:whip:
oh, and the number of rounds or hands per hour in your sim, would that maybe be different if you were to play one hand or two hands, sort of thing?
does your cvcx have this in the help section?
"Play Two Hands - Click to estimate the effect of playing two hands. The original sim must have had at least two players."
but i think you have a updated version of cvcx from what i've got. hmm, i dunno.
just me maybe i'm way off base, is the two hands thing for cvcx kind of experimental? well it says estimate in the section above.
but what ever, i wonder about it because would maybe the true count frequencies be different if you play two hands as opposed to one? that isn't reflected by the sim though. perhaps that's why it would be an estimation?
something i think Wong wrote in Professional Blackjack about this stuff, where if you play two hands heads up you use 150% more cards than if one hand. wouldn't that represent a differing true count frequency when you want to compare this stuff?
:whip:oh, and the number of rounds or hands per hour in your sim, would that maybe be different if you were to play one hand or two hands, sort of thing?
sagefr0g said:
i can't respond on the SCORE stuff, lmao. i keep forgetting what the heck it means. :laugh:
does your cvcx have this in the help section?
"Play Two Hands - Click to estimate the effect of playing two hands. The original sim must have had at least two players."
but i think you have a updated version of cvcx from what i've got. hmm, i dunno.
just me maybe i'm way off base, is the two hands thing for cvcx kind of experimental? well it says estimate in the section above.
but what ever, i wonder about it because would maybe the true count frequencies be different if you play two hands as opposed to one? that isn't reflected by the sim though. perhaps that's why it would be an estimation?
something i think Wong wrote in Professional Blackjack about this stuff, where if you play two hands heads up you use 150% more cards than if one hand. wouldn't that represent a differing true count frequency when you want to compare this stuff?:whip:
oh, and the number of rounds or hands per hour in your sim, would that maybe be different if you were to play one hand or two hands, sort of thing?
does your cvcx have this in the help section?
"Play Two Hands - Click to estimate the effect of playing two hands. The original sim must have had at least two players."
but i think you have a updated version of cvcx from what i've got. hmm, i dunno.
just me maybe i'm way off base, is the two hands thing for cvcx kind of experimental? well it says estimate in the section above.
but what ever, i wonder about it because would maybe the true count frequencies be different if you play two hands as opposed to one? that isn't reflected by the sim though. perhaps that's why it would be an estimation?
something i think Wong wrote in Professional Blackjack about this stuff, where if you play two hands heads up you use 150% more cards than if one hand. wouldn't that represent a differing true count frequency when you want to compare this stuff?
:whip:oh, and the number of rounds or hands per hour in your sim, would that maybe be different if you were to play one hand or two hands, sort of thing?
As for the count frequency, I don't think that there would be any difference in it, as multiple players do not affect your advantage.
Finally, hands per hour. There probably will be a slightly lower hands/hr, but I doubt its going to be half that of 1 hand, which would still give me both a higher SCORE and WR.
lol, ok it would be interesting to look at QFIT's update information and see what he says about playing two hands thing needing multiple players thing, like for my version and yours.
score:whip: lol, your gonna make me read up on that again aren't you, lmao. but now i think you have two estimation considerations. one the estimation that cvcx makes and two the difference in the rate of estimation that you make playing one hand versus playing two hands. which is more accurate when heads up with the dealer? per Wong page, i think it's 210 it would be the playing one hand guy.
don't stop thinking, that's a good thing but think again on the count frequency and multiple players and if in fact multiple players affect your advantage. and wouldn't count frequency heads up with the dealer be different playing one hand compared to playing two hands? your simulation doesn't reflect that.
but yeah the hands per hour might not be all that significant, just it's a part of the equation if you want to compare the two modes of play in the quest for wondering if your missing something. lol. now that is a glorious and honorable quest, imho.:1st:
all i really wonder at this point is if Wong is wrong or not. some how i doubt it. but at least we are thinking, asking questions and maybe learning something even if it is right or wrong.
lmao i named the sim's below twohands this and that, lol, but yeah i realize it's just done for one hand.:whip:
anyway the first image is for heads up, the second for two players, the third for (five players)
edit: lmao to do penance i looked at the definition for score in encyclopedia of 21, lmao of course i still don't understand it but found a interesting link in the process. http://www.bjmath.com/bjmath/efficien/ssstrat.htm (Archive copy)
score
:whip: lol, your gonna make me read up on that again aren't you, lmao. but now i think you have two estimation considerations. one the estimation that cvcx makes and two the difference in the rate of estimation that you make playing one hand versus playing two hands. which is more accurate when heads up with the dealer? per Wong page, i think it's 210 it would be the playing one hand guy.don't stop thinking, that's a good thing but think again on the count frequency and multiple players and if in fact multiple players affect your advantage. and wouldn't count frequency heads up with the dealer be different playing one hand compared to playing two hands? your simulation doesn't reflect that.
but yeah the hands per hour might not be all that significant, just it's a part of the equation if you want to compare the two modes of play in the quest for wondering if your missing something. lol. now that is a glorious and honorable quest, imho.:1st:
all i really wonder at this point is if Wong is wrong or not. some how i doubt it. but at least we are thinking, asking questions and maybe learning something even if it is right or wrong.
lmao i named the sim's below twohands this and that, lol, but yeah i realize it's just done for one hand.
:whip:anyway the first image is for heads up, the second for two players, the third for (five players
)edit: lmao to do penance i looked at the definition for score in encyclopedia of 21, lmao of course i still don't understand it but found a interesting link in the process. http://www.bjmath.com/bjmath/efficien/ssstrat.htm (Archive copy)
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here is some of the stuff about going to two hands in cvcx:
http://www.qfit.com/blackjack-simulator-update-cvcx4.htm
http://www.qfit.com/blackjack-simulator-update-cvcx4.htm
lol, i don't know. i don't have that version. but i want it. like apparently cvdata could do that sort of stuff and the website says the estimates compare well with cvdata, sort of thing.
just, wondering if the displayed tc frequencies change when you do all that switching and stuff, with your version? maybe it goes on internal for the program but not opaque for the user?
but i don't understand why you don't see a problem multihands playall.
wouldn't that be the most important consideration since it calls for playing
multiple hands at a disadvantage?
just me maybe but not even thinking about the sim, me it's just knowing your playing two hands in disadvantage situations. just me maybe, but i can't imagine that being a good thing in play all scenerio.
then the other thing, like Wong writes in PB and the guy in the link
http://www.bjmath.com/bjmath/efficien/ssstrat.htm (Archive copy)
writes gives me the impression one would want to go to the potty in negative counts a lot and stuff like how you might could run into the problem of exceeding the table limit. i'd quote out of Wong's book, but it's kind of wordy. just when you get your book, check it out page 210, lol.
what ever, this stuff is of interest to me, like for instance Y and i like to play together. ok but what that does is push's my preferred unit bet to double, and then say the count goes negative, (which it does a lot) and i want to leave the table, well, lmao Y doesn't know perfect basic strategy so....
then ok, say she leaves the table, then still i'm stuck playing negative counts for at least one hand. then Y doesn't like leaving the table once she sits, lol.
that's that thing if you remember Matt at the bash dinner asking me if that was an act between me and her when she stormed away from the table.:laugh:
not an act, lmao but me trying to get us both off a table with a crap count.
so but i turned it into an act. :cat:
what ever this stuff is also why i asked you about playing two hands when we all had the 'back room' meeting at the bash.
so really the point could be two hands all the time could fit in with your risk stipulations and cover requirements, so what the heck do what you want sort of thing.
still i wonder if Wong isn't right, thing is the whole question is probably even more complex than just the things we've discussed or considered. when you read Wong on the matter i think you'll see what i mean by that. he looks at it from various angles in mind sort of thing.
like apparently cvdata could do that sort of stuff and the website says the estimates compare well with cvdata, sort of thing.just, wondering if the displayed tc frequencies change when you do all that switching and stuff, with your version? maybe it goes on internal for the program but not opaque for the user?
but i don't understand why you don't see a problem multihands playall.
wouldn't that be the most important consideration since it calls for playing
multiple hands at a disadvantage?
just me maybe but not even thinking about the sim, me it's just knowing your playing two hands in disadvantage situations. just me maybe, but i can't imagine that being a good thing in play all scenerio.
then the other thing, like Wong writes in PB and the guy in the link
http://www.bjmath.com/bjmath/efficien/ssstrat.htm (Archive copy)
writes gives me the impression one would want to go to the potty in negative counts a lot and stuff like how you might could run into the problem of exceeding the table limit. i'd quote out of Wong's book, but it's kind of wordy. just when you get your book, check it out page 210, lol.
what ever, this stuff is of interest to me, like for instance Y and i like to play together. ok but what that does is push's my preferred unit bet to double, and then say the count goes negative, (which it does a lot) and i want to leave the table, well, lmao Y doesn't know perfect basic strategy so....
then ok, say she leaves the table, then still i'm stuck playing negative counts for at least one hand. then Y doesn't like leaving the table once she sits, lol.
that's that thing if you remember Matt at the bash dinner asking me if that was an act between me and her when she stormed away from the table.:laugh:
not an act, lmao but me trying to get us both off a table with a crap count.
so but i turned it into an act. :cat:
what ever this stuff is also why i asked you about playing two hands when we all had the 'back room' meeting at the bash.
so really the point could be two hands all the time could fit in with your risk stipulations and cover requirements, so what the heck do what you want sort of thing.
still i wonder if Wong isn't right, thing is the whole question is probably even more complex than just the things we've discussed or considered. when you read Wong on the matter i think you'll see what i mean by that. he looks at it from various angles in mind sort of thing.
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)
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)
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like i don't understand SCORE, well i did skim read BJA on it some, man Don S is wordy sometimes. the square of DI, sharpes ratio stuff, investing and risk management and manglieodio (spielling?) in the economy and all, lol.
so but from just skim reading about it, did i miss the mark by concluding that SCORE is essentially a way to estimate the relative values of games for a gambler with given bankroll using a given count and kelly approach?
and did i understand correctly Don S.'s warning or cautionary note regarding the abuse and misuse of the concept of SCORE? lmao, notice i'm now capitalizing the word as that is what Don S would want us to do.
i mean i guess i understood that in the orthodox sense, SCORE has some very specific underpinnings and conditions. what?, originally set up with hi/lo in mind and with a ten grand roll, sort of thing. then it's hooked up with DI and that 13% ror of kelly stuff. so but just in my confusion what SCORE does is somehow gives one a way of comparing games values for a gambler with specific conditions the gambler is limited by, by standardizing in an absolute sense risk and win rate.:whip:
just the question comes to my mind the way your comparing SCORES of the same game but with the difference being one hand and two hands approach with betting essentially doubled for what i guess is the same bankroll, the only difference being number of hands played .
the idea being i guess you hope to end up with SCORES that show an estimate of relative desirability of the two approaches in terms of risk and expectation all rolled up in one neat little package, ie. SCORE.
just a thought, would it be possible for you to tweak your simulation of either the one hand simulation or the two hand simulation so that the same amount is bet at the same true counts for both approaches? then maybe compare SCORE or what ever you want to compare. would that then be a fair comparison? i still wonder about the point of differing tc freq's, adv and sd in all of that though. but maybe QFIT has tweaked your version so that cvcx can handle two hands for a one on one simulation.:whip:
by the way i did just recently order an upgrade for my version as a result of these conversations.
now it's my turn to ask, what am i missing? at the very least i might learn some more about the concept of SCORE.:whip:
and really i guess it wouldn't hurt to understand the derivation and meaning of DI.:whip:
so but from just skim reading about it, did i miss the mark by concluding that SCORE is essentially a way to estimate the relative values of games for a gambler with given bankroll using a given count and kelly approach?
and did i understand correctly Don S.'s warning or cautionary note regarding the abuse and misuse of the concept of SCORE? lmao, notice i'm now capitalizing the word as that is what Don S would want us to do.
i mean i guess i understood that in the orthodox sense, SCORE has some very specific underpinnings and conditions. what?, originally set up with hi/lo in mind and with a ten grand roll, sort of thing. then it's hooked up with DI and that 13% ror of kelly stuff. so but just in my confusion what SCORE does is somehow gives one a way of comparing games values for a gambler with specific conditions the gambler is limited by, by standardizing in an absolute sense risk and win rate.
:whip:just the question comes to my mind the way your comparing SCORES of the same game but with the difference being one hand and two hands approach with betting essentially doubled for what i guess is the same bankroll, the only difference being number of hands played .
the idea being i guess you hope to end up with SCORES that show an estimate of relative desirability of the two approaches in terms of risk and expectation all rolled up in one neat little package, ie. SCORE.
just a thought, would it be possible for you to tweak your simulation of either the one hand simulation or the two hand simulation so that the same amount is bet at the same true counts for both approaches? then maybe compare SCORE or what ever you want to compare. would that then be a fair comparison? i still wonder about the point of differing tc freq's, adv and sd in all of that though.
but maybe QFIT has tweaked your version so that cvcx can handle two hands for a one on one simulation.:whip:by the way i did just recently order an upgrade for my version as a result of these conversations.
now it's my turn to ask, what am i missing? at the very least i might learn some more about the concept of SCORE.
:whip:and really i guess it wouldn't hurt to understand the derivation and meaning of DI.
:whip:
Sage
"Back Room Meeting At The Bash", nice that you mentioned that:grin:, that was one of the highlites for me, really cool, made me feel like the breakfast scene from Reservoir Dogs, and you even tried to lift my coins:laugh:
Good times!:grin:
CP
sagefr0g said:
lol, i don't know. i don't have that version. but i want it. like apparently cvdata could do that sort of stuff and the website says the estimates compare well with cvdata, sort of thing.
just, wondering if the displayed tc frequencies change when you do all that switching and stuff, with your version? maybe it goes on internal for the program but not opaque for the user?
but i don't understand why you don't see a problem multihands playall.
wouldn't that be the most important consideration since it calls for playing
multiple hands at a disadvantage?
just me maybe but not even thinking about the sim, me it's just knowing your playing two hands in disadvantage situations. just me maybe, but i can't imagine that being a good thing in play all scenerio.
then the other thing, like Wong writes in PB and the guy in the link
http://www.bjmath.com/bjmath/efficien/ssstrat.htm (Archive copy)
writes gives me the impression one would want to go to the potty in negative counts a lot and stuff like how you might could run into the problem of exceeding the table limit. i'd quote out of Wong's book, but it's kind of wordy. just when you get your book, check it out page 210, lol.
what ever, this stuff is of interest to me, like for instance Y and i like to play together. ok but what that does is push's my preferred unit bet to double, and then say the count goes negative, (which it does a lot) and i want to leave the table, well, lmao Y doesn't know perfect basic strategy so....
then ok, say she leaves the table, then still i'm stuck playing negative counts for at least one hand. then Y doesn't like leaving the table once she sits, lol.
that's that thing if you remember Matt at the bash dinner asking me if that was an act between me and her when she stormed away from the table.:laugh:
not an act, lmao but me trying to get us both off a table with a crap count.
so but i turned it into an act. :cat:
what ever this stuff is also why i asked you about playing two hands when we all had the 'back room' meeting at the bash.
so really the point could be two hands all the time could fit in with your risk stipulations and cover requirements, so what the heck do what you want sort of thing.
still i wonder if Wong isn't right, thing is the whole question is probably even more complex than just the things we've discussed or considered. when you read Wong on the matter i think you'll see what i mean by that. he looks at it from various angles in mind sort of thing.
like apparently cvdata could do that sort of stuff and the website says the estimates compare well with cvdata, sort of thing.just, wondering if the displayed tc frequencies change when you do all that switching and stuff, with your version? maybe it goes on internal for the program but not opaque for the user?
but i don't understand why you don't see a problem multihands playall.
wouldn't that be the most important consideration since it calls for playing
multiple hands at a disadvantage?
just me maybe but not even thinking about the sim, me it's just knowing your playing two hands in disadvantage situations. just me maybe, but i can't imagine that being a good thing in play all scenerio.
then the other thing, like Wong writes in PB and the guy in the link
http://www.bjmath.com/bjmath/efficien/ssstrat.htm (Archive copy)
writes gives me the impression one would want to go to the potty in negative counts a lot and stuff like how you might could run into the problem of exceeding the table limit. i'd quote out of Wong's book, but it's kind of wordy. just when you get your book, check it out page 210, lol.
what ever, this stuff is of interest to me, like for instance Y and i like to play together. ok but what that does is push's my preferred unit bet to double, and then say the count goes negative, (which it does a lot) and i want to leave the table, well, lmao Y doesn't know perfect basic strategy so....
then ok, say she leaves the table, then still i'm stuck playing negative counts for at least one hand. then Y doesn't like leaving the table once she sits, lol.
that's that thing if you remember Matt at the bash dinner asking me if that was an act between me and her when she stormed away from the table.:laugh:
not an act, lmao but me trying to get us both off a table with a crap count.
so but i turned it into an act. :cat:
what ever this stuff is also why i asked you about playing two hands when we all had the 'back room' meeting at the bash.
so really the point could be two hands all the time could fit in with your risk stipulations and cover requirements, so what the heck do what you want sort of thing.
still i wonder if Wong isn't right, thing is the whole question is probably even more complex than just the things we've discussed or considered. when you read Wong on the matter i think you'll see what i mean by that. he looks at it from various angles in mind sort of thing.
, that was one of the highlites for me, really cool, made me feel like the breakfast scene from Reservoir Dogs, and you even tried to lift my coins:laugh:Good times!:grin:
CP
sagefr0g said:
like i don't understand SCORE, well i did skim read BJA on it some, man Don S is wordy sometimes. the square of DI, sharpes ratio stuff, investing and risk management and manglieodio (spielling?) in the economy and all, lol.
so but from just skim reading about it, did i miss the mark by concluding that SCORE is essentially a way to estimate the relative values of games for a gambler with given bankroll using a given count and kelly approach?
and did i understand correctly Don S.'s warning or cautionary note regarding the abuse and misuse of the concept of SCORE? lmao, notice i'm now capitalizing the word as that is what Don S would want us to do.
i mean i guess i understood that in the orthodox sense, SCORE has some very specific underpinnings and conditions. what?, originally set up with hi/lo in mind and with a ten grand roll, sort of thing. then it's hooked up with DI and that 13% ror of kelly stuff. so but just in my confusion what SCORE does is somehow gives one a way of comparing games values for a gambler with specific conditions the gambler is limited by, by standardizing in an absolute sense risk and win rate.:whip:
just the question comes to my mind the way your comparing SCORES of the same game but with the difference being one hand and two hands approach with betting essentially doubled for what i guess is the same bankroll, the only difference being number of hands played .
the idea being i guess you hope to end up with SCORES that show an estimate of relative desirability of the two approaches in terms of risk and expectation all rolled up in one neat little package, ie. SCORE.
just a thought, would it be possible for you to tweak your simulation of either the one hand simulation or the two hand simulation so that the same amount is bet at the same true counts for both approaches? then maybe compare SCORE or what ever you want to compare. would that then be a fair comparison? i still wonder about the point of differing tc freq's, adv and sd in all of that though. but maybe QFIT has tweaked your version so that cvcx can handle two hands for a one on one simulation.:whip:
by the way i did just recently order an upgrade for my version as a result of these conversations.
now it's my turn to ask, what am i missing? at the very least i might learn some more about the concept of SCORE.:whip:
and really i guess it wouldn't hurt to understand the derivation and meaning of DI.:whip:
so but from just skim reading about it, did i miss the mark by concluding that SCORE is essentially a way to estimate the relative values of games for a gambler with given bankroll using a given count and kelly approach?
and did i understand correctly Don S.'s warning or cautionary note regarding the abuse and misuse of the concept of SCORE? lmao, notice i'm now capitalizing the word as that is what Don S would want us to do.
i mean i guess i understood that in the orthodox sense, SCORE has some very specific underpinnings and conditions. what?, originally set up with hi/lo in mind and with a ten grand roll, sort of thing. then it's hooked up with DI and that 13% ror of kelly stuff. so but just in my confusion what SCORE does is somehow gives one a way of comparing games values for a gambler with specific conditions the gambler is limited by, by standardizing in an absolute sense risk and win rate.
:whip:just the question comes to my mind the way your comparing SCORES of the same game but with the difference being one hand and two hands approach with betting essentially doubled for what i guess is the same bankroll, the only difference being number of hands played .
the idea being i guess you hope to end up with SCORES that show an estimate of relative desirability of the two approaches in terms of risk and expectation all rolled up in one neat little package, ie. SCORE.
just a thought, would it be possible for you to tweak your simulation of either the one hand simulation or the two hand simulation so that the same amount is bet at the same true counts for both approaches? then maybe compare SCORE or what ever you want to compare. would that then be a fair comparison? i still wonder about the point of differing tc freq's, adv and sd in all of that though.
but maybe QFIT has tweaked your version so that cvcx can handle two hands for a one on one simulation.:whip:by the way i did just recently order an upgrade for my version as a result of these conversations.
now it's my turn to ask, what am i missing? at the very least i might learn some more about the concept of SCORE.
:whip:and really i guess it wouldn't hurt to understand the derivation and meaning of DI.
:whip:
At least one purpose in SCORE is to create a standardized way to measure the strength of the game that you are playing. However, it does not take into account things like heat, camo, etc.
As for Don's warning, I believe it has something to do with the fact that (at least experienced) counters would choose a heads up game in a 6D game vs a full DD game. Well, not always, but the point is that while SCORE is nice, WR is what we want. However, this question is one of curiosity as to why it is suggested to play 2 hands in a heads up game vs 1 hand. In BJA, I read that there is a very small loss in playing 2 hands vs 1, but it seems to be related to advantage. But since we are increasing our hands/hr (not rounds/hr), I would still desire 2 hands vs 1. Also, the covariance experienced from playing 2 hands would help decrease the long run variance of the game, which (I believe) is the reason for the improvement in SCORE.
Also, last night, I ran a 2 billion round CVData sim comparing the two strategies, and once again, found that playing 2 hands heads up is still quite superior to 1 hand. There was a 50% improvement in WR and (surprisingly) found that there was a small improvement in advantage (.07%).
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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).
As for TC distribution, there is actually a WIDER distribution for 2 hands. Probably has something to do with getting slightly better pen due to the multihands.
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.
As for TC distribution, there is actually a WIDER distribution for 2 hands. Probably has something to do with getting slightly better pen due to the multihands.
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.