if 6 decks only play half deck

[bjcount]

I get your point now. However, I believe the OP was looking for info on the 26th cards all played at one go as in a CSM.

how often can we get an advantage hand

Based on my sim, playing with one other person, your betting 1u on 1 hand at all TC's under +1 & then betting 2 boxes at 25u ea at TC+1, you will have an advantage 3.65% of the time if the HE is 0.08% using a lvl 2 count.

The 26th card will come out around the 3rd - 4th round.

Using a $10unit you'll win about $2.28/hr on $2,166/hr in action

BJC

 

[k_c]

Chessplayer,

The numbers you quote above are on the last round of play which is the 26th card dealt, and thats if the last round ends once the 26th card is dealt. In essence a RC+6 is achieve 3.5% of the time when the 26 card is dealt. Your not considering all the hands/rounds where the percentage is lower or zero.

If you look at the RC +6 when the 9th card is dealt the RC+6 is acheived only 1% of the time. There is never a RC of +6 in the first 5 cards. What I believe you should do is average all the RC+6's probabilities and see what percentage of the time you see a RC+6. I came out with 1.79%. I would consider the results of my posted sim as accurate. (look at the TC distribution image in green)

If you add up all the RC greater then +6 which appear to be a rarity, I would guesstimate that you will come closer to my average 3.65% for all TC =>+1 then your single RC example which is taken from the extreme end.

Are there any other opinions out there from the math guys?

BJC

Please keep in mind that I don't pretend to have all answers to all possible problems. Here are a couple of observations, though.

1. When it comes to betting, the main info needed relative to a count is pre-round RC and pen (i.e. TC.) However, here pen is not completely random because a game of blackjack in progress determines how and when a round ends. For example there is no such thing as a pen of 1, 2, or 3 cards (heads up) for betting purposes but a pen of 4 cards is probably pretty likely, relatively speaking. Rounds that can abruptly end when a hand busts with a ten value card and other blackjack phenomena contribute to making pre-round pen not totally random. This is where a sim can be of the most assistance imho. Every sim I have done shows that the average pre-round (HiLo) RC is negative. This means there will be a preponderance of negative TCs over positive TCs subject to how they are grouped (rounded, floored, etc.) This seems most definitely to be the case when shuffle point is determined by a cut card. When shuffle point is determined by a fixed number of rounds I have seen in 2 very small sample sims that average pre-round (HiLo) RC was reduced to a value closer to 0, but still slightly negative. I don't know (long run) whether or not determining shuffle point by a fixed number of rounds effectively reduces average pre-round (HiLo) RC to 0 or just makes it closer to 0.

2. When it comes to playing, calculated RC/pen frequencies would apply because cards are just being continuously dealt with no side conditions (that I can think of.) This would open up the possibility, if not the likelihood, of computing playing indices. This would be quite a convenience. Insurance indices are pretty straightforward to compute.
Hit/stand/double/split/surrender indices would be more complicated.

 

[k_c]

Chessplayer,

The numbers you quote above are on the last round of play which is the 26th card dealt, and thats if the last round ends once the 26th card is dealt. In essence a RC+6 is achieve 3.5% of the time when the 26 card is dealt. Your not considering all the hands/rounds where the percentage is lower or zero.

If you look at the RC +6 when the 9th card is dealt the RC+6 is acheived only 1% of the time. There is never a RC of +6 in the first 5 cards. What I believe you should do is average all the RC+6's probabilities and see what percentage of the time you see a RC+6. I came out with 1.79%. I would consider the results of my posted sim as accurate. (look at the TC distribution image in green)

If you add up all the RC greater then +6 which appear to be a rarity, I would guesstimate that you will come closer to my average 3.65% for all TC =>+1 then your single RC example which is taken from the extreme end.

Are there any other opinions out there from the math guys?

BJC

Please keep in mind that I don't pretend to have all answers to all possible problems. Here are a couple of observations, though.

1. When it comes to betting, the main info needed relative to a count is pre-round RC and pen (i.e. TC.) However, here pen is not completely random because a game of blackjack in progress determines how and when a round ends. For example there is no such thing as a pen of 1, 2, or 3 cards for betting purposes but a pen of 4 cards is probably pretty likely, relatively speaking. Rounds that can abruptly end when a hand busts with a ten value card and other blackjack phenomena contribute to making pre-round pen not totally random. This is where a sim can be of the most assistance imho. Every sim I have done shows that the average pre-round (HiLo) RC is negative. This means there will be a preponderance of negative TCs over positive TCs subject to how they are grouped (rounded, floored, etc.) This seems most definitely to be the case when shuffle point is determined by a cut card. When shuffle point is determined by a fixed number of rounds I have seen in 2 very small sample sims that average pre-round (HiLo) RC was reduced to a value closer to 0, but still slightly negative. I don't know (long run) whether or not determining shuffle point by a fixed number of rounds effectively reduces average pre-round (HiLo) RC to 0 or just makes it closer to 0.

2. When it comes to playing, calculated RC/pen frequencies would apply because cards are just being continuously dealt with no side conditions (that I can think of.) This would open up the possibility, if not the likelihood, of computing playing indices. This would be quite a convenience. Insurance indices are pretty straightforward to compute.
Hit/stand/double/split/surrender indices would be more complicated.

 

[k_c]

Chessplayer,

The numbers you quote above are on the last round of play which is the 26th card dealt, and thats if the last round ends once the 26th card is dealt. In essence a RC+6 is achieve 3.5% of the time when the 26 card is dealt. Your not considering all the hands/rounds where the percentage is lower or zero.

If you look at the RC +6 when the 9th card is dealt the RC+6 is acheived only 1% of the time. There is never a RC of +6 in the first 5 cards. What I believe you should do is average all the RC+6's probabilities and see what percentage of the time you see a RC+6. I came out with 1.79%. I would consider the results of my posted sim as accurate. (look at the TC distribution image in green)

If you add up all the RC greater then +6 which appear to be a rarity, I would guesstimate that you will come closer to my average 3.65% for all TC =>+1 then your single RC example which is taken from the extreme end.

Are there any other opinions out there from the math guys?

BJC

Please keep in mind that I don't pretend to have all answers to all possible problems. Here are a couple of observations, though.

1. When it comes to betting, the main info needed relative to a count is pre-round RC and pen (i.e. TC.) However, here pen is not completely random because a game of blackjack in progress determines how and when a round ends. For example there is no such thing as a pen of 1, 2, or 3 cards for betting purposes but a pen of 4 cards is probably pretty likely, relatively speaking. Rounds that can abruptly end when a hand busts with a ten value card and other blackjack phenomena contribute to making pre-round pen not totally random. This is where a sim can be of the most assistance imho. Every sim I have done shows that the average pre-round (HiLo) RC is negative. This means there will be a preponderance of negative TCs over positive TCs subject to how they are grouped (rounded, floored, etc.) This seems most definitely to be the case when shuffle point is determined by a cut card. When shuffle point is determined by a fixed number of rounds I have seen in 2 very small sample sims that average pre-round (HiLo) RC was reduced to a value closer to 0, but still slightly negative. I don't know (long run) whether or not determining shuffle point by a fixed number of rounds effectively reduces average pre-round (HiLo) RC to 0 or just makes it closer to 0.

2. When it comes to playing, calculated RC/pen frequencies would apply because cards are just being continuously dealt with no side conditions (that I can think of.) This would open up the possibility, if not the likelihood, of computing playing indices. This would be quite a convenience. Insurance indices are pretty straightforward to compute. Hit/stand/double/split/surrender indices would be more complicated.