Blackjack card count probability

Hey there,
Need to start with the fact that I just love your work! I know game providers that are implementing new games and they are basing their mathematics on your calculation (more likely copying your calculations).

I work in a gambling domain, and I do all kind of statistics on historical data in order to see if occurrence rates for various scenarios are in the right "range".
When it comes to theoretical mathematic, I'm sad to say I have a long road ahead :(

I have a question that mess with my mind and on my own I can't get to the bottom of it unless I put in some serious hours of work based on historical data, but the main idea is this:
How can I calculate on Blackjack 8 deck ( 6 out of 8 decks dealt) the percentage of hands won in the scenario that someone is playing only when the true count of a shoe is = or > than 1?

Thank you for everything you do, keep it you and need to mention I will still love your work even if you won't find the time to answer me.
All the best!

Interesting question! I hope Wizard see this, but it’s probably very hard to calculate the win rate because it depends on specific rules. Let me just ask a similar but simpler question.

For an 8-deck shoe game, the probability of a blackjack is 4.745%. What is the probability of a player’s blackjack when player only plays at true count >=+1?

Quote: aceside

Interesting question! I hope Wizard see this, but it’s probably very hard to calculate the win rate because it depends on specific rules. Let me just ask a similar but simpler question.

For an 8-deck shoe game, the probability of a blackjack is 4.745%. What is the probability of a player’s blackjack when player only plays at true count >=+1?
link to original post

Some quick simulating using Hi-Lo gets around 5.435%

I only have six deck (UK rules) at 66% penetration and count winning BJs (as others are counted in the "Ties"). The base number was 16795488 (4.528%) winning BJs in 370930867 hands (100m shoes). There were 92045368 hands with count 1 or greater and 4670271 of those were winning BJs (5.074%)

Quote: ThatDonGuy

Quote: aceside

Interesting question! I hope Wizard see this, but it’s probably very hard to calculate the win rate because it depends on specific rules. Let me just ask a similar but simpler question.

For an 8-deck shoe game, the probability of a blackjack is 4.745%. What is the probability of a player’s blackjack when player only plays at true count >=+1?
link to original post

Some quick simulating using Hi-Lo gets around 5.435%
link to original post

Let me use your number to calculate the player's edge from additional blackjacks.
5.435%x(1-5.435%)x1.5-4.745%x(1-4.745%)x1.5=0.9296%.

This means a HiLo counter will be able to obtain a 0.9296% edge over the house by wonging in at the true count of greater than or equal to +1, betting one unit flat all the way. It is easy to overcome the house edge, isn't it?

Quote: aceside

Quote: ThatDonGuy

Quote: aceside

Interesting question! I hope Wizard see this, but it’s probably very hard to calculate the win rate because it depends on specific rules. Let me just ask a similar but simpler question.

For an 8-deck shoe game, the probability of a blackjack is 4.745%. What is the probability of a player’s blackjack when player only plays at true count >=+1?
link to original post

Some quick simulating using Hi-Lo gets around 5.435%
link to original post

Let me use your number to calculate the player's edge from additional blackjacks.
5.435%x(1-5.435%)x1.5-4.745%x(1-4.745%)x1.5=0.9296%.

This means a HiLo counter will be able to obtain a 0.9296% edge over the house by wonging in at the true count of greater than or equal to +1, betting one unit flat all the way. It is easy to overcome the house edge, isn't it?
link to original post

That's the (estimated) probability of you getting a blackjack. You're forgetting that the dealer is also more likely to get a blackjack.

I'll leave you to do the maths but at +1 there's only a minor advantage to the player. But you are correct wonging at +1 or more gives an advantage. On average (based on these sim figures and UK rules) it's 0.69% HE (advantage) and makes $18.36 profit per 100 hands watched for $100 bets. This is because the edge at lower counts is small and the higher opportunities don't come as often.
Here's an extract from the figures, note the sim works out count into 0.1 chunks so these are the values at 0,1,2 etc. The overall HE for the game is -0.48% (to the house).

Quote: ThatDonGuy

Quote: aceside

Quote: ThatDonGuy

Quote: aceside

For an 8-deck shoe game, the probability of a blackjack is 4.745%. What is the probability of a player’s blackjack when player only plays at true count >=+1?

Some quick simulating using Hi-Lo gets around 5.435%

Let me use your number to calculate the player's edge from additional blackjacks.
5.435%x(1-5.435%)x1.5-4.745%x(1-4.745%)x1.5=0.9296%.

This means a HiLo counter will be able to obtain a 0.9296% edge over the house by wonging in at the true count of greater than or equal to +1, betting one unit flat all the way. It is easy to overcome the house edge, isn't it?

That's the (estimated) probability of you getting a blackjack. You're forgetting that the dealer is also more likely to get a blackjack.

The (simulated) probability of getting a blackjack and the dealer not also getting a blackjack is 5.153%.

Quote: charliepatrick

I'll leave you to do the maths but at +1 there's only a minor advantage to the player. But you are correct wonging at +1 or more gives an advantage. On average (based on these sim figures and UK rules) it's 0.69% HE (advantage) and makes $18.36 profit per 100 hands watched for $100 bets. This is because the edge at lower counts is small and the higher opportunities don't come as often.
Here's an extract from the figures, note the sim works out count into 0.1 chunks so these are the values at 0,1,2 etc. The overall HE for the game is -0.48% (to the house).

Count: 0 Exp: -0.004362165317904683 Hands: 34058888 Win: 15389403 Lose: 17851740 Tie: 2998380 CHY: 0 BJk: 1542511
Count: 1 Exp: 0.0005946421593759342 Hands: 5576463 Win: 2502519 Lose: 2896196 Tie: 494838 CHY: 0 BJk: 264662
Count: 2 Exp: 0.0062002146315115495 Hands: 3095538 Win: 1381105 Lose: 1591982 Tie: 278383 CHY: 0 BJk: 153380
Count: 3 Exp: 0.009922477361631772 Hands: 1570122 Win: 695248 Lose: 801953 Tie: 142112 CHY: 0 BJk: 81523
Overall Result: Exp: -0.004796346592530947 Hands: 370930867 Win: 167589328 Lose: 194561673 Tie: 32670420 CHY: 0 BJk: 16795488

link to original post

Hands watched or hands played?

Here is the six deck analysis:

https://www.888casino.com/blog/blackjack-tips/blackjack-card-counting-vs-blackjack-side-bets-six-decks