Blackjack House Edge Calculator
May 25th, 2017 at 9:06:41 AM
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I'm curious about your setup for basic strategy with cut card. I assume this is based on a simulator after a gazillion hands (millions is not enough). Where do you have the cut card for a double deck game and how many players at the table? Our simulator is in the ballpark but a little different than yours. Thanks in advance.
May 27th, 2017 at 9:08:59 AM
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still crickets?
We've only run 7 billion hands so far, but we're finding something interesting I didn't expect.
Double deck, Basic Strategy, DAS allowed, Dlr hits S17, no surrender, 1 card on split aces, cut card 45 from end:
4 players at table: EV=-.428%
1 player at table: EV=-.443%
Based on the t-test, 95% confidence the difference is real. The difference is only 1 bet every 7,000 hands but I'm having trouble believing playing with others at the table makes any difference. Has anyone else run a similar analysis?
p.s. Do not trust Microsoft random number generator! It is not good enough for things like this.
We've only run 7 billion hands so far, but we're finding something interesting I didn't expect.
Double deck, Basic Strategy, DAS allowed, Dlr hits S17, no surrender, 1 card on split aces, cut card 45 from end:
4 players at table: EV=-.428%
1 player at table: EV=-.443%
Based on the t-test, 95% confidence the difference is real. The difference is only 1 bet every 7,000 hands but I'm having trouble believing playing with others at the table makes any difference. Has anyone else run a similar analysis?
p.s. Do not trust Microsoft random number generator! It is not good enough for things like this.
May 27th, 2017 at 10:46:35 AM
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Could the increased EoR (and plays based on Optimal Strategy given known cards) on the last hands of each pair of decks account for the difference? Is your program designed to make decisions based on EoR?
https://wizardofvegas.com/forum/off-topic/gripes/11182-pet-peeves/120/#post815219
May 27th, 2017 at 11:28:34 AM
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The version we are running right now stays with double deck BS to the end. I'm not sure I'm interpreting your "Effect of Removal" comment correctly, but it would be interesting to look at the difference if we start playing single deck BS at the end.
We also see a slight sensitivity to deck penetration. One thought I have is that when the cut card comes out, there is deeper penetration on that last hand with more players in the game and that makes an iota of a difference. Sorry if that is restating your comment in different words.
We were hoping to match the WoO house edge calculator before we turn on more advanced features.
We also see a slight sensitivity to deck penetration. One thought I have is that when the cut card comes out, there is deeper penetration on that last hand with more players in the game and that makes an iota of a difference. Sorry if that is restating your comment in different words.
We were hoping to match the WoO house edge calculator before we turn on more advanced features.
May 27th, 2017 at 11:42:35 AM
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I ran a quick 20 billion rounds for each using your specs:
1 player: -0.4567
4 players: -0.4436
As a comparison:
Mike’s online calculator: -.45688
BJTF online calculator: -.456
1 player: -0.4567
4 players: -0.4436
As a comparison:
Mike’s online calculator: -.45688
BJTF online calculator: -.456
"It is impossible to begin to learn that which one thinks one already knows." -Epictetus
May 27th, 2017 at 11:47:26 AM
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Lots of lousy PRNGs. They've caused problems for some scientific studies.Quote: LouisTrezp.s. Do not trust Microsoft random number generator! It is not good enough for things like this.
May 27th, 2017 at 3:46:03 PM
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Thanks QFIT!! A quick 20 billion. Love it. Is that a proprietary program you're using?
May 27th, 2017 at 3:50:59 PM
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Quote: LouisTrezThanks QFIT!! A quick 20 billion. Love it. Is that a proprietary program you're using?
I try to avoid mentioning my software. CVData. A billion rounds for normal counting takes 30 seconds on my PC.
"It is impossible to begin to learn that which one thinks one already knows." -Epictetus
May 27th, 2017 at 6:15:18 PM
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Quote: QFITA billion rounds for normal counting takes 30 seconds on my PC.
Very impressive QFIT. Do you care to share how you are generating your random numbers?
May 27th, 2017 at 6:19:18 PM
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Quote: LouisTrezVery impressive QFIT. Do you care to share how you are generating your random numbers?
A customized version of MarZam II. The MarZam II PRNG has a period so long, that if you started a PC generating numbers as fast as it could at the beginning of the Universe, it will not yet have repeated, and it passes the Diehard tests.
"It is impossible to begin to learn that which one thinks one already knows." -Epictetus
May 27th, 2017 at 7:28:09 PM
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Quote: LouisTrezI'm curious about your setup for basic strategy with cut card. I assume this is based on a simulator after a gazillion hands (millions is not enough). Where do you have the cut card for a double deck game and how many players at the table? Our simulator is in the ballpark but a little different than yours. Thanks in advance.
I think I put it at 75% for two or more decks. 50% for one. Strangely, I find I find no correlation between cut card placement and house edge as long as it isn't so shallow that the number of hands per decks is almost always the same. To be honest, I have never understood why this is. Perhaps QFIT can shed some light.
"For with much wisdom comes much sorrow." -- Ecclesiastes 1:18 (NIV)
May 27th, 2017 at 7:42:25 PM
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Mike and I both came to the conclusion ages ago that once you pass the early part of the shoe, it doesn't matter. I never really looked into it. If you look at:
https://www.blackjackincolor.com/blackjackeffects1.htm
you will see that the effect occurs in the final rounds. I assume what's important is not simply the penetration, or number of players; both of which would alter the ratio of normal rounds versus affected rounds. Indeed, if there are multiple players, it doesn't matter which seat you choose. What likely matters is the happenstance of the variation of numbers of rounds. That depends on number of players and how they play and wouldn't be linear. That's just a guess. It would take a few trillion rounds to examine -- and wouldn't provide any useful AP info. Which is a long way of saying: "I don't know". :)
https://www.blackjackincolor.com/blackjackeffects1.htm
you will see that the effect occurs in the final rounds. I assume what's important is not simply the penetration, or number of players; both of which would alter the ratio of normal rounds versus affected rounds. Indeed, if there are multiple players, it doesn't matter which seat you choose. What likely matters is the happenstance of the variation of numbers of rounds. That depends on number of players and how they play and wouldn't be linear. That's just a guess. It would take a few trillion rounds to examine -- and wouldn't provide any useful AP info. Which is a long way of saying: "I don't know". :)
"It is impossible to begin to learn that which one thinks one already knows." -Epictetus
May 28th, 2017 at 7:54:59 AM
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Quote: QFITA customized version of MarZam II. The MarZam II PRNG has a period so long, that if you started a PC generating numbers as fast as it could at the beginning of the Universe, it will not yet have repeated, and it passes the Diehard tests.
QFIT it appears you are a respected expert in BJ simulation. We think our project is suffering RNG blues. Will need to dig further to find MarZam II but what do you think about KISS? Also have you ever tried a TRNG service like random.org?
May 28th, 2017 at 8:03:26 AM
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I wouldn't think a service would be fast enough. Mersenne Twister should probably be adequate.
"It is impossible to begin to learn that which one thinks one already knows." -Epictetus
May 28th, 2017 at 6:48:09 PM
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Custom code your own. I compared a bunch of them for speed compiling with gcc - you can easily get 5x the speed of Mersenne Twister with some of these.Quote: LouisTrezWe think our project is suffering RNG blues.
https://en.wikipedia.org/wiki/List_of_random_number_generators
The Big Crush tests are far more strenuous than the Diehard tests, but Diehard is good enough. In particular, the xorshifts are easy to code, pass nearly every Big Crush test and are very fast.
"A naive C implementation of a xorshift+ generator that passes all tests from the BigCrush suite (with an order of magnitude fewer failures than Mersenne Twister or WELL) typically takes fewer than 10 clock cycles on x86 to generate a random number ..."
Climate Casino: https://climatecasino.net/climate-casino/
May 28th, 2017 at 7:27:08 PM
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Newer Intel chips also have a true RNG. But, it's a royal pain to use.
"It is impossible to begin to learn that which one thinks one already knows." -Epictetus
May 28th, 2017 at 7:34:59 PM
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Maybe there should be an "off the top house edge" and an "overall house edge."
DUHHIIIIIIIII HEARD THAT!
May 29th, 2017 at 4:33:37 AM
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Never really cared that much as I'm generally interested in the counter's edge. Never understood why counters use BS edge, which is defined as off-the-top edge.
"It is impossible to begin to learn that which one thinks one already knows." -Epictetus
May 29th, 2017 at 6:50:47 AM
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We are more interested in the counter's edge too but need to establish a baseline. We wrote our own custom code because we are exploring some non-traditional counting systems designed to be easier for the "Average Joe". I'm a new poster but I must say the knowledge level here is exceptional. Appreciate all the help!
May 29th, 2017 at 7:58:05 AM
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Quote: QFITMersenne Twister should probably be adequate.
Well, we are now using Mersenne Twister and after 4 billion hands we are again converging on EV of -0.443%. I wonder if Swift is already using MT. Anyway, still statistically different than your -0.457%.
QFIT - I understand you don't care too much about BS edge, but we are sticklers for detail. Do you mind if I send you a private message?
May 29th, 2017 at 8:06:52 AM
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E-mail support@qfit.com. I prefer to centralize my correspondence.
"It is impossible to begin to learn that which one thinks one already knows." -Epictetus
May 29th, 2017 at 2:28:34 PM
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Quote: QFITE-mail support@qfit.com. I prefer to centralize my correspondence.
how long before this pops up down the block at the Losers Lounge?
The older I get, the better I recall things that never happened
May 29th, 2017 at 5:48:18 PM
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Don't think I know what Loser's Lounge is. But, my e-mail has been public for 24 years. Pretty much every AP knows it. After all those years, I have only one e-mail troll.
"It is impossible to begin to learn that which one thinks one already knows." -Epictetus
May 29th, 2017 at 5:55:10 PM
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Quote: QFITBut, my e-mail has been public for 24 years. Pretty much every AP knows it. After all those years, I have only one e-mail troll.
I wonder who that could be.
"For with much wisdom comes much sorrow." -- Ecclesiastes 1:18 (NIV)
May 29th, 2017 at 6:03:58 PM
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Gotye had a succinct response.
"It is impossible to begin to learn that which one thinks one already knows." -Epictetus
May 29th, 2017 at 6:39:55 PM
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Quote: LouisTrezp.s. Do not trust Microsoft random number generator! It is not good enough for things like this.
Here is my C# code that uses cryptographically strong pseudo random numbers to shuffle a deck:
public static void Shuffle<T>(this IList<T> list)
{
RNGCryptoServiceProvider provider = new RNGCryptoServiceProvider();
int n = list.Count;
while (n > 1)
{
byte[] box = new byte[1];
do provider.GetBytes(box);
while (!(box[0] < n * (Byte.MaxValue / n)));
int k = (box[0] % n);
n--;
T value = list[k];
list[k] = list[n];
list[n] = value;
}
}
May 30th, 2017 at 6:29:19 AM
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Quote: gamerfreakHere is my C# code that uses cryptographically strong pseudo random numbers to shuffle a deck:
Thanks gamerfreak. So what EV does your simulator converge on for 1 player and 4 players with rules as above?
May 30th, 2017 at 7:07:30 AM
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Quote: LouisTrezThanks gamerfreak. So what EV does your simulator converge on for 1 player and 4 players with rules as above?
Still need to flesh out my program more, I have a solid card/deck objects created, and most of a blackjack game.
I still need to implement Splitting/Surrendering and a strategy class, then I should be able to run accurate simulations.
June 8th, 2017 at 2:24:57 PM
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Quote: gamerfreakI still need to implement Splitting/Surrendering and a strategy class, then I should be able to run accurate simulations.
What say you gamerfreak? Are you getting the same number as qfit? I'm seeing numbers all over the map out there.
June 13th, 2017 at 9:41:21 AM
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The more I look at this, I see other numbers out there for double deck, DAS allowed, H17, no surrender:
qfit, I found this one from your site calculator
If I calculate for the above rules I get EV=-.38% (please check me)
and from Arnold Snyder's blackjackforumonline
EV=-.31 - .20 (H17) + .14 (DAS) = -.37%
These are more in line with what our new simulator is converging to. As you can see, I'm kind of obsessed with finding the "right answer". What if those who came before us left us with pi=3-1/8 or e (natural log base)=2.7 or Avogadro's constant = 6x10^23. We would be screwed!!
I cannot sleep until we have put this to rest. What say all you smart people?
p.s. How do you post links here??
qfit, I found this one from your site calculator
If I calculate for the above rules I get EV=-.38% (please check me)
and from Arnold Snyder's blackjackforumonline
EV=-.31 - .20 (H17) + .14 (DAS) = -.37%
These are more in line with what our new simulator is converging to. As you can see, I'm kind of obsessed with finding the "right answer". What if those who came before us left us with pi=3-1/8 or e (natural log base)=2.7 or Avogadro's constant = 6x10^23. We would be screwed!!
I cannot sleep until we have put this to rest. What say all you smart people?
p.s. How do you post links here??
June 13th, 2017 at 9:54:38 AM
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The calculator at the QFIT site does not take into account the cut card effect. I'll replace it with my newer calculator at: https://www.blackjacktheforum.com/resourcespage.php?do=edgepage
Arnold's calculations are based on numbers from 1983, do not take into account the CCE, and ignore interactions between rules. You cannot simply add rule effects since they interact with each other.
Update: I just replaced the QFIT calculator with the newer one.
Arnold's calculations are based on numbers from 1983, do not take into account the CCE, and ignore interactions between rules. You cannot simply add rule effects since they interact with each other.
Update: I just replaced the QFIT calculator with the newer one.
"It is impossible to begin to learn that which one thinks one already knows." -Epictetus
June 13th, 2017 at 11:39:11 AM
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qfit, you are the man with the answers!
How about this one. I am running an analysis of 4-card 16 vs. 10 to see which has the better EV: Hit, Stand, or "Rule of 45". I usually use the WoO Hand Calculator for each permutation, but it seems to crash on all combinations with 2 aces. I have seen another Hand Calculator somewhere but can't find it now. Do you know another one?
How about this one. I am running an analysis of 4-card 16 vs. 10 to see which has the better EV: Hit, Stand, or "Rule of 45". I usually use the WoO Hand Calculator for each permutation, but it seems to crash on all combinations with 2 aces. I have seen another Hand Calculator somewhere but can't find it now. Do you know another one?
June 13th, 2017 at 12:17:19 PM
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There was one long way back; but it's gone. I don't know of any other online BJ combinatorial analyzers.
"It is impossible to begin to learn that which one thinks one already knows." -Epictetus
June 13th, 2017 at 2:25:32 PM
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What say you Mr. Wizard? Any chance you could take a look at your Hand Calculator and see why it crashes on 4-card hands that contain 2 Aces? The result comes back as STAND -1.000000. Thanks
June 13th, 2017 at 2:36:47 PM
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I did the programming on that, so I'll investigate.
June 14th, 2017 at 7:25:30 AM
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Fixed. The problem was with hands with multiple aces, the hand total wasn't always being correctly calculated. For example, if you entered A/3/A/A, it was incorrectly being treated as a busted total of 26, hence the only option it saw was to "stand" with an EV of -1.
June 14th, 2017 at 9:33:16 AM
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Aha. Figured it was something like that. Thanks JB!! You guys are good.
fyi, here's the results I get now for 4-card 16 vs. 10 including the permutations with 2 aces (double deck, 1st hand after shuffle):
STAND -54.26%
HIT -54.99%
"Rule of 45" -54.20%
So if my math is correct, the "Rule of 45" edges out STAND but the difference is only about 1 bet in 1,741 hands so it's value is more in a trivia contest than real life.
fyi, here's the results I get now for 4-card 16 vs. 10 including the permutations with 2 aces (double deck, 1st hand after shuffle):
STAND -54.26%
HIT -54.99%
"Rule of 45" -54.20%
So if my math is correct, the "Rule of 45" edges out STAND but the difference is only about 1 bet in 1,741 hands so it's value is more in a trivia contest than real life.
June 14th, 2017 at 11:52:51 AM
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Quote: JBBy the way, i]here is another good blackjack calculator.
Yes, that's the other one I was looking for! Thanks JB
June 16th, 2017 at 9:43:59 AM
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Quote: gamerfreakHere is my C# code that uses cryptographically strong pseudo random numbers to shuffle a deck:
I would say that your routine, as other people's before it, randomizes the deck(s) rather than “shuffles” it (them). With this routine there is a chance that the top card of the deck before the randomization could appear on the bottom of the deck after the randomization. This doesn’t happen after one riffle shuffle (or even two or three).
Technically this routine could completely reverse the deck’s order which is not possible in a riffle shuffle, a wash, or via continuous shufflers. (Yeah, someone’s going to try to prove me wrong on this point.)
I would like to see a routine that models:
- washing cards
- a riffle shuffle with n decks
- various continuous shufflers
I’d have a go at it but I haven’t programmed in 17 years, don’t have a need for one, and have too many programming projects that I am already not creating.
Steven
June 16th, 2017 at 10:29:11 AM
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Interesting and I would agree with you on that. I think the non-randomness results in more severe streaks than a random deck also. I would think the 10's tend to get grouped together in the discard rack and may not be randomly split apart in the shuffle. It seems like when a deck gets sour it can stay sour for a long time and vice versa but hard to prove any of that. One thing I've always wanted to track in real life is how often the dealer busts showing an Ace. Theoretically the dealer busts only about 20% of the time showing an Ace, but it seems he busts at a higher rate, drawing a 10-10 more often than he should.
If anybody knows of a true shuffle routine, we would be interested.
If anybody knows of a true shuffle routine, we would be interested.
June 16th, 2017 at 10:32:16 AM
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My experimentation and that of others shows otherwise. My configurable real shuffle routines provide the same results as random shuffles.
"It is impossible to begin to learn that which one thinks one already knows." -Epictetus
June 16th, 2017 at 11:04:04 AM
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Quote: QFITMy experimentation and that of others shows otherwise. My configurable real shuffle routines provide the same results as random shuffles.
I can see how that would all come out in the wash after 20 billion cycles. But have you ever seen/performed a "small sample size" study? Just thinking out loud here, maybe compare a billion 3-shoe results, random vs. shuffled and see if the shuffled have a higher standard deviation. Wouldn't that indicate "streakier" results? Or am I crazy on that?
June 16th, 2017 at 11:09:42 AM
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Yes. The results are the same. Unless the shuffle is seriously flawed.
Now, if you're a shuffle-tracker, that's a different story. You are essentially manipulating the result of the shuffle by cutting in a prescribed spot and adjusting the counts accordingly.
Now, if you're a shuffle-tracker, that's a different story. You are essentially manipulating the result of the shuffle by cutting in a prescribed spot and adjusting the counts accordingly.
"It is impossible to begin to learn that which one thinks one already knows." -Epictetus
October 21st, 2017 at 9:33:28 PM
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Quote: JBBy the way, here is another good blackjack calculator.
Instead of online calculator : https://wizardofodds.com/games/blackjack/hand-calculator/, is it possible to download?(or buy it) this BJ calculator and run it without internet connection ?
I need a BJ hand calculator that can analyze BJ hands WITHOUT internet connection.
