Blackjack House Edge Variation

I have been working on a new Blackjack variant and running a game simulation to test the game and whilst running the game test I have seen a variation when running with 1 player or multiple players. Through my logic I have determined that this is due to more cards in play thus less cards to draw from which ultimately affects the results and thus alters the HE. Does this seem a reasonable explanation?

On from that this also makes me wonder what HE I should give the game, the results from the tests with 1 player, 7 players or the average across 1 to 7 players. What is the view on this?

Thanks for your time in reading and responding (if you do) :-)

I realize there are some features that might depend upon the cards in other players hands (the Envy Bonus comes to mind.)

I don't understand any of the specifics of your situation. Certainly quoting a range would be an option, such as House Edge = x.xx% (1 player) to X.XX% (7 players).

Quote: UKMark

Does this seem a reasonable explanation?...

There are some bets, such as 777vs7 on Spanish where the player could receive an Envy if another player has the hand. This means that there is an additional possibility, albeit small, of getting something for each additional player at the table. I should imagine the House Edge is calculated depending on playing solo with annote that for each additional player there is a small increase.

However your question suggests that having other players at the table affects the House Edge. This might be the case if you had a bet that paid if your hand was the highest at the table or if it was a jackpot style bet where other players might possibly be paid first, so a player would rceive less if there were two jackpot hands (depending on whether the rule is the second gets the reset value rather than the meter value or they share the meter value.)

However if the game was, say, depending on the number of cards/7s/something else then what cards are in other people's hand should be irrelevant. The mathematics is the odds are the same whether you deal your hand first of the other player first. For instance if they have some of the 7s you want your chances are less, but suppose they had no 7s then your chance would be better. This is the same logic as the ploppie's play at the end affects your result, it doesn't.

I know there's a difference in House Edge if you shuffle up every hand rather than deal further into the shoe - personally I've never really understood why - so you may have one of those situations. The House Edge is usually stated as the first hand of the shoe, i.e. you only know the cards dealt from the current hand with one player.

Quote: charliepatrick

<snip>I know there's a difference in House Edge if you shuffle up every hand rather than deal further into the shoe - personally I've never really understood why - so you may have one of those situations. The House Edge is usually stated as the first hand of the shoe, i.e. you only know the cards dealt from the current hand with one player.

charliepatrick,

First, let me say that the portion of your post that I snipped off was very well-written!

As for this portion's phenomenon, which is also known as the "Cut-Card Effect" (or CCE), here's my explanation:

Say you're playing single-deck BJ heads-up at the infamous El Cortez (colloquially, and accurately, known as the "Sweaty Spaniard"). "Current Blackjack News" reports the house edge on their SD game as 0.18%, so if the dealer were to shuffle every round, your IBA (Initial Bet Advantage, also called "EV" for Expected Value) on every round would be -0.18%.

Now instead of shuffling every round, assume after each shuffle the dealer inserts a Cut Card (CC) between the sixth and seventh cards from the top of the deck: in other words, setting the penetration to exactly 6 cards. What would this CCE do to your IBA?

Well since the dealer burns the top card after the shuffle, the only times you'll see a 2nd round in the deck is if the 1st round uses EXACTLY 4 cards: any more, and the CC will either emerge during round 1, or will be on the top of the deck (and so prompt a shuffle) after round 1 is finished.

So what types of rounds use exactly 4 cards? Well, if you or the dealer (or both) have a BJ, round 1 will use exactly 4 cards. Otherwise, the only situations will be if both stand on their 2-card hands.

Assuming you follow at least Basic Strategy (in other words, you don't stand on a hand of, say, a 3 and a 4), these 4-card rounds will NEVER use more Small cards (2's through 6's) than Big cards (10's, faces, and aces). This means that the count on Round 2 will NEVER be positive: at best, it'll be zero (for example, AK vs 34, or 89 vs 89), but much more likely it'll be negative (for example, QJ vs A9, for -3, or KK vs JQ, for -4). Therefore, the average count on Round 2 (when you get to play it) will be negative, and so your IBA on these Round 2's will be even worse than the -0.18% that you face on Round 1. This means that, over all the rounds, your IBA will be worse than the reported value of -0.18%.

With this terrible penetration, you'd actually be better off playing 2 spots against the dealer (or playing with at least one other player), so she'll have to shuffle every round: then your IBA will be a steady -0.18% on every hand. Naturally, you could improve your edge even further by instead not playing this game at all ;-)

Although I used a SD game with awful pen as the example, the CCE is present any time a CC is used, though the overall effect is lessened with increasing pen and number of decks. When I run CVData sims of 6 and 8 deck shoe games that use CC's, the output shows that the average true count on every round after the first is negative: typically -0.1. However, the average true count on the last few rounds becomes increasingly negative. On the other hand, sims with a fixed number of rounds between shuffles show the average true count as 0 on every round.

Hope this helps!

Dog Hand

Thanks for the above, it's interesting to see (although possibly within margin of error) running 10 million shoes of 6 deck UK Blackjack got the following results with a cutcard at various penetrations.

Penetration	House Edge	Average Count	Hands
16%	-.472 630%	-.077 302	95 978 495
66%	-.479 635%	-.083 957	370 930 867
83%	-.488 044%	-.083 794	462 584 768

Quote: charliepatrick

Thanks for the above, it's interesting to see (although possibly within margin of error) running 10 million shoes of 6 deck UK Blackjack got the following results with a cutcard at various penetrations.

Penetration	House Edge	Average Count	Hands
16%	-.472 630%	-.077 302	95 978 495
66%	-.479 635%	-.083 957	370 930 867
83%	-.488 044%	-.083 794	462 584 768

charliepatrick,

I assume these "House Edge" values are instead IBA values, since they're all negative.

Are these results for heads-up, one spot, flat-betting, and using only B.S.? And is the count the HiLo true count?

Dog Hand

^ Yes simply one spot flat betting and sticking to infinte deck strategy - each hand is recorded using the count, HiLo divided by the number of decks left, rounded to 0.1, keeping a tally of wins, losses etc.

I'm not sure what "IBA" is but the "House Edge" represents the profit, (Wins-Losses)/Hands played, the player has (so is usually negative).

Thanks to all for the comments. I will make some time to get some game sim data I see and post the info but can't go into the details of the game atm. I will run the same deck penetration so we have comparable data, in a sense :-)

Interesting calc, thanks CP.

There is a well-known effect that card consumption is higher with hands that make the count go positive (i.e., hands with many small cards) so that one ultimately gets dealt fewer hands with a positive count than with a negative count.. Could that be accounting for your results?

Sounds like it, here are the figures for the same 10m shoes...

Penetration	Hands -ve	Hands 0	Hands +ve
16%	42.449 386%	19.739 665%	37.810 949%
66%	46.594 948%	9.182 004%	44.223 048%
83%	46.746 182%	8.544 526%	44.709 293%

Quote: charliepatrick

Sounds like it, here are the figures for the same 10m shoes...

Penetration	Hands -ve	Hands 0	Hands +ve
16%	42.449 386%	19.739 665%	37.810 949%
66%	46.594 948%	9.182 004%	44.223 048%
83%	46.746 182%	8.544 526%	44.709 293%

Intuitively, I would think the above results are not drivin solely by the cut card effect but also by the effect mentioned by Gordon above, which is partially independent of the cut card (but exacerbated by the cut card). Would be interested in seeing the above where the shoe is cut off after a set number of rounds that approximate the penetrations above.

Folks,

How can I post an image from my computer?

I have an example that demonstrates the Cut Card Effect, but I cannot seem to get it posted here.

I tried uploading it to this URL:

https://ibb.co/SwWmSv9

but I'm still unable to get the picture to appear here.

Thanks!

Dog Hand

Here is your image, although its easier to read by going to the link site.



It looks like you only studied penetrations up to one deck in a 6-deck shoe, is that right?

Quote: gordonm888

Here is your image, although its easier to read by going to the link site.



It looks like you only studied penetrations up to one deck in a 6-deck shoe, is that right?

gordonm888,

Thanks for posting the image!

Yes, this is to compare with the 16% pen 6D UK-rules data from earlier in the thread.

The left side is using a Cut Card; the right side is for a fixed number of rounds. As you can see, for the fixed rounds data the average RC and TC are both zero (no Cut Card Effect), while the CC data show a marked drop in the RC and TC as the CC is approached.

Hope this helps!

Dog Hand

Thanks all for your time and effort in discussing this question. I am wondering if your data comes from a purely mathematical model or does it come from simulated game play, and if so do you use a dealer strategy or a basic BJ strategy?

I have a game simulator that can use either strategy plus I can enable/disable the new game feature and the data I get back regarding the HE can vary from -2.95% in favour of the house to 1.47% in favour of the player when running as std BJ with a virtual CC 49 cards deep which basically emulates the effect of a CSM as the used cards are reshuffled into the available cards once 49 (16%) cards are exposed. I can mimic a shoe by upping the CC to 259 (83%).

Obviously I am questioning myself as to whether I have a bug in the game sim due to the results!

1 player, basic strategy, 100,000 games(101,754 hands dealt includes splits) results in HE of 1.52% Player advantage

1 player, basic strategy, 500,000 games(508,901 hands dealt includes splits) results in HE of 1.50% Player advantage

5 players, basic strategy, 100,000 games(511,305 hands dealt includes splits) results in HE of -1.08% House advantage

5 players, basic strategy, 20,000 games(102,303 hands dealt includes splits) results in HE of 1.34% Player advantage

CC in all cases at 49 so emulating a CSM deal with 6 decks

Dealer Strategy results are;

1 player, 100,000 (100,930) -3.51% House
1 player 500,000 (504,504) -2.82% House
5 players, 100,000 (505,736) -2.87% House
5 players, 20,000 (101,166) -3.13% House

One other thing to note is that this is European style BJ paying insurance at 1-1 on dealer Ace showing (one card dealt)

Any thoughts? other than, go check my code :-) or should that be :-(

I can't remember how wide the results were for such small numbers, but you can try it out by seeing how wide your range of results begin to converge as you ramp up the number of shoes/hands. I ssupect 100k hands is too variable and you need over 10 million hands before you get some consistency.

If you've still got a problem you need to check the code using other methods, such as using the random numbers to play roulette or craps (where you know the expected EV). Also you need to check the cards are being shuffled correctly when you come to the end of a shoe - I forget how I found a bug in my code but it was some simple game I had devised.