Draftkings 420s blackjack

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December 23rd, 2021 at 8:28:56 PM permalink

Initial review: S17, split to four hands, no resplit aces, split aces one card only, double any initial hand.

8 Decks, shuffled every round.

The wager on each hand and the four 20s sidebet must be identical. If you bet $5, $1 goes on each spot.

I didn't see anything egregious in their suggested strategy (under settings/paytable on the demo), but I didn't do a close review.

I didn't play enough rounds to get a good feel for the sidebet spinner weighting. Based on the graphics, my guess is that the spinner offers 6 fair stops, of push - 1x - push - 2x - push - 3x.

May the cards fall in your favor.

Dieter
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December 23rd, 2021 at 8:39:45 PM permalink

Quote: GBAM
One thing I like is even though it’s $25 per hand (a lot for me, especially when it’s just on a couch at home) you only need to win 3/5 spots to come out ahead and you don’t lose all 5 spots too often

link to original post

At least in the web demo version, the $5 table minimum is satisfied by a $1 bet on each spot, for $5 total per round.

May the cards fall in your favor.

GBAM

GBAM

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December 23rd, 2021 at 8:59:03 PM permalink

Quote: Dieter
Quote: GBAM
One thing I like is even though it’s $25 per hand (a lot for me, especially when it’s just on a couch at home) you only need to win 3/5 spots to come out ahead and you don’t lose all 5 spots too often

link to original post

At least in the web demo version, the $5 table minimum is satisfied by a $1 bet on each spot, for $5 total per round.
link to original post

It is for the real money draft kings app too but I wanna win $2k lol

Anyone got the math on getting dealt 4 20s

ksdjdj

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December 23rd, 2021 at 9:29:34 PM permalink

Quote: GBAM
Quote: Dieter
Quote: GBAM
One thing I like is even though it’s $25 per hand (a lot for me, especially when it’s just on a couch at home) you only need to win 3/5 spots to come out ahead and you don’t lose all 5 spots too often

link to original post

At least in the web demo version, the $5 table minimum is satisfied by a $1 bet on each spot, for $5 total per round.
link to original post

It is for the real money draft kings app too but I wanna win $2k lol

Anyone got the math on getting dealt 4 20s
link to original post

To get dealt 4 20's, the chance is about 1/7.8k, for infinite*** decks (if I worked it out right).

***: The game is played with 8 decks (going by posts above)
Note : I have played it in demo mode before, but I don't know the value for getting 1 20

----
Update (About 10pm, Pac Time):

Quote: Dieter
(snip)
I didn't play enough rounds to get a good feel for the sidebet spinner weighting. Based on the graphics, my guess is that the spinner offers 6 fair stops, of push - 1x - push - 2x - push - 3x.
link to original post

At the infinite deck level, I get a player edge of 2.43% for the bonus game (see figures below)

Chance / Odds / EV:
0 x 20 = 63.7325023584590000% / blank / - 63.73%
1 x 20 = 30.3890077470798000% / 1 to 1^^^ / +30.39%
2 x 20 = 5.4337960872262000% / 4 to 1 / +21.74%
3 x 20 = 0.4318248546140020% / 20 to 1 / +8.64%
4 x 20 = 0.0128689526209471% / 420 to 1 / +5.40%

Total EV = -63.73% + 30.39% + 21.74% + 8.64% + 5.4% = 2.43%

^^^: Assuming that the "spinner offers 6 fair stops, of push - 1x - push - 2x - push - 3x.". as stated in the "snipped quote", above.
Note: Again this is for infinite decks,

Last edited by: ksdjdj on Dec 23, 2021

Dieter
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December 23rd, 2021 at 9:29:39 PM permalink

I estimate about 1 in 14500. This is not exact, it's an estimation.

edit: I am notoriously bad at math.

May the cards fall in your favor.

ksdjdj

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December 23rd, 2021 at 9:42:44 PM permalink

Quote: Dieter
I estimate about 1 in 14500. This is not exact, it's an estimation.

edit: I am notoriously bad at math.
link to original post

I originally got that, but then I remembered that A-9 and 9-A, also count as a 20 for the "bonus".

Note: I played it about a week or two ago, so they may have changed the rules?

Dieter
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December 23rd, 2021 at 9:54:31 PM permalink

Quote: ksdjdj
Quote: Dieter
I estimate about 1 in 14500. This is not exact, it's an estimation.

edit: I am notoriously bad at math.
link to original post

I originally got that, but then I remembered that A-9 and 9-A, also count as a 20 for the "bonus".

Note: I played it about a week or two ago, so they may have changed the rules?
link to original post

Well, I only played about 5 deals, and forgot entirely about soft 20.

I think that the odds are likely to favor the house. ;)

May the cards fall in your favor.

ksdjdj

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December 23rd, 2021 at 10:01:33 PM permalink

Quote: Dieter
Quote: ksdjdj
Quote: Dieter
I estimate about 1 in 14500. This is not exact, it's an estimation.

edit: I am notoriously bad at math.
link to original post

I originally got that, but then I remembered that A-9 and 9-A, also count as a 20 for the "bonus".

Note: I played it about a week or two ago, so they may have changed the rules?
link to original post

Well, I only played about 5 deals, and forgot entirely about soft 20.

I think that the odds are likely to favor the house. ;)
link to original post

Probably, but I get a small player edge at infinite decks, if all pays are " to 1" for the bonus.
Note: I may be able to work out a more accurate chance and EV, but I am slower at doing it the "correct way for 8 decks" (compared to the infinite deck "short-cut estimate")

ksdjdj

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December 23rd, 2021 at 10:41:46 PM permalink

Quote: ksdjdj
(snip)
4 x 20 = 0.0128689526209471% / 420 to 1 / +5.40%
(snip)
link to original post

For 8 decks, I get about 0.0114...% as the chance*** for "4 x 20".

***: I took some more short-cuts in getting this "8-deck" figure, because I didn't want to manually work out all the "16 ways you can get 4 x 20".

---
Important Update (about 10:45 pm, Pac time):

Reminder, the "2.43% player edge" that I mentioned in previous replies, was for infinite deck only, the "8- deck edge" will almost surely be in the houses favor.

ksdjdj

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December 23rd, 2021 at 11:54:40 PM permalink

Quote: Dieter
(snip)
I didn't play enough rounds to get a good feel for the sidebet spinner weighting (snip)
link to original post

Here are my results after making it to "20 x rounds of the sidebet spinner": .

Totals:
0 x 20 = ?
1 x 20 = 20***
2 x 20 = 2
3 x 20 = 0
4 x 20 = 0

***: Below is the break-downs for the "sidebet spinner"

Odds (to 1) / No. of times it occurred

Push / five
1 / nine
2 / three
3 / three

Note: The sample size is probably too small to work out a good estimate of the "sidebet spinner" weighting, but anyone can add my figures to their testing, if they choose to do so.

DogHand

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December 24th, 2021 at 1:41:49 AM permalink

Quote: Dieter
I estimate about 1 in 14500. This is not exact, it's an estimation.

edit: I am notoriously bad at math.
link to original post

I worked out the probability for four pat 20's off-the-top of an 8D shoe to be 7.967005 x 10^(-5), or about 1 in 12,550 rounds.

Hope this helps!

Dog Hand

Edit: fixed the mantissa to say 7.967005 rather than 0.7967005.

Last edited by: DogHand on Dec 24, 2021

ksdjdj

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December 24th, 2021 at 2:48:49 AM permalink

Here are my results after making it to "40 x rounds of the sidebet spinner":

Totals:
0 x 20 = ?
1 x 20 = 40***
2 x 20 = 4
3 x 20 = 0
4 x 20 = 0

***: Below is the break-downs for the "sidebet spinner"

Odds (to 1) / No. of times it occurred

Push / eleven
1 / seventeen
2 / eight
3 / four

Note: The sample size is still probably too small to work out a good estimate of the "sidebet spinner" weighting, but anyone can add my figures to their testing, if they choose to do so.

Dieter
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December 24th, 2021 at 3:23:59 AM permalink

Quote: DogHand
Quote: Dieter
I estimate about 1 in 14500. This is not exact, it's an estimation.

edit: I am notoriously bad at math.
link to original post

I worked out the probability for four pat 20's off-the-top of an 8D shoe to be 0.7967005 x 10^(-5), or about 1 in 12,550 rounds.

Hope this helps!

Dog Hand
link to original post

I saw a number like that too, but I didn't like it.
When I punch 1/(7.97*10^-6) into my calculator, I get an extra zero.

Care to smarten me up?

May the cards fall in your favor.

Dieter
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December 24th, 2021 at 4:10:21 AM permalink

Subjective aesthetic notes:

The paytables all state payouts as "to 1", but the software seems to display game results as "for 1". I understand why they do it, but it annoys me.

Turning off animations in the web version does speed the game, but not enough to make it engaging for me.
The side bet resolution really slows down the game.
If you think video poker on turbo "could be faster", you'll probably notice.

I'm glad the music can be disabled.

Objective notes:
Double after split is allowed. I had missed that.
No action allowed on hands totalling 21.

May the cards fall in your favor.

DogHand

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December 24th, 2021 at 7:52:35 AM permalink

Quote: Dieter
Quote: DogHand
Quote: Dieter
I estimate about 1 in 14500. This is not exact, it's an estimation.

edit: I am notoriously bad at math.
link to original post

I worked out the probability for four pat 20's off-the-top of an 8D shoe to be 0.7967005 x 10^(-5), or about 1 in 12,550 rounds.

Hope this helps!

Dog Hand
link to original post

I saw a number like that too, but I didn't like it.
When I punch 1/(7.97*10^-6) into my calculator, I get an extra zero.

Care to smarten me up?
link to original post

Dieter,

Oops... I mistyped the mantissa. I should have typed 7.967005 x 10^(-5).

I shall edit my original post.

Dog Hand

Dieter
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December 24th, 2021 at 8:32:26 AM permalink

Quote: DogHand
Oops... I mistyped the mantissa. I should have typed 7.967005 x 10^(-5).

link to original post

If catching a minor flub on a decimal place is the worst thing that happens until next year, I think things are pretty ok.

Does the 1/12550 approximation include soft hands?

May the cards fall in your favor.

DogHand

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December 24th, 2021 at 12:01:22 PM permalink

Quote: Dieter
Quote: DogHand
Oops... I mistyped the mantissa. I should have typed 7.967005 x 10^(-5).

link to original post

If catching a minor flub on a decimal place is the worst thing that happens until next year, I think things are pretty ok.

Does the 1/12550 approximation include soft hands?
link to original post

Dieter,

Yes, I counted both hard and soft 20's. These are the probabilities for 4 H and 0 S, 3 H and 1 S, 2 H and 2 S, 1 H and 3 S, 0 H and 4 S, and their Sum, respectively:

6.87746E-05 9.54142E-06 1.20237E-06 1.37414E-07 1.42182E-08 7.967005E-05

Dog Hand

ksdjdj

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December 24th, 2021 at 2:17:00 PM permalink

Quote: DogHand
Quote: Dieter
Quote: DogHand
Oops... I mistyped the mantissa. I should have typed 7.967005 x 10^(-5).

link to original post

If catching a minor flub on a decimal place is the worst thing that happens until next year, I think things are pretty ok.

Does the 1/12550 approximation include soft hands?
link to original post

Dieter,

Yes, I counted both hard and soft 20's. These are the probabilities for 4 H and 0 S, 3 H and 1 S, 2 H and 2 S, 1 H and 3 S, 0 H and 4 S, and their Sum, respectively:

6.87746E-05 9.54142E-06 1.20237E-06 1.37414E-07 1.42182E-08 7.967005E-05

Dog Hand
link to original post

I got the same starting figures as you, but I did this (to get my estimate):

(6.87746E-05 x 1) + (9.54142E-06 x 4) + (1.20237E-06 x 6) + (1.37414E-07 x 4) + (1.42182E-08 x 1) = ~ 0.0001147...

Note: I don't know if the above step is needed for this kind of problem, but it is similar to what I do when I want to work out my "sports multi " estimated chances (see "three leg" example below):

Example: Say I bet on team A (50% chance of winning), B (60% chance of winning), and C (80% chance of winning) in a three leg multi and for whatever reason I wanted to know what the chances for winning 0 legs to all 3 legs is:
w = "chance of winning", l = "chance of losing"

0 legs = A l x B l x C l = 0.5 x 0.4 x 0.2 = 0.04
1 leg = (A l x B l x C w) + (A l x B w x C l) + (A w x B l x C l) = ... = 0.26
2 legs = (A l x B w x C w) + (A w x B l x C w) + (A w x B w x C l) = ... = 0.46
3 legs = A w x B w x C w = 0.5 x 0.6 x 0.8 = 0.24

4% + 26% + 46% + 24% = 100%

Note: The main reason I needed to know the above for sports, was because I used to get money back for "missing the multi by x legs" (where "x" can be any number, but it was usually between 1 and 3).

Thanks for your help.

Wizard
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December 24th, 2021 at 3:40:36 PM permalink

Here are my combinations for 0 to 4 20's. Please excuse the leading zeros at the end of the totals. I hope there is a spreadsheet in heaven that does not have any cap on the number of significant digits. C++ compiler too. I had to play some tricks to deal with numbers this big.

20's	Total	Probability
4	96,154,845,853,132,800	0.000115
3	3,423,358,427,452,540,000	0.004084
2	44,788,356,273,817,700,000	0.053435
1	255,238,297,847,250,000,000	0.304514
0	534,635,239,424,785,000,000	0.637851
Total	838,181,406,819,158,000,000	1.000000

"For with much wisdom comes much sorrow." -- Ecclesiastes 1:18 (NIV)

ksdjdj

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December 24th, 2021 at 5:14:59 PM permalink

Here are my results after making it to "60 x rounds of the sidebet spinner":

Totals:
0 x 20 = ?
1 x 20 = 60***
2 x 20 = 11
3 x 20 = 0
4 x 20 = 0

***: Below is the break-downs for the "sidebet spinner"

Odds (to 1) / No. of times it occurred

Push / 20
1 / 23
2 / 13
3 / 4 (no change from last test)

Note 1: To make it easier, I am now writing the "No. of times it occurred" in numerals (previously it was written in words).
Note 2: Sample size still probably too small.
Note 3: Anyone can add my figures to their testing, if they like.

Wizard
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December 24th, 2021 at 7:45:25 PM permalink

I just played through 30 spins with the following results:

3x: 0
2x: 4
1x: 16
Push: 10

Adding my results to those of ksdjdj, I get the following totals:

Multiplier	Wiz 12-24-21	ksdjdj	Total
0	10	20	30
1	16	23	39
2	4	13	17
3	0	4	4
Total	30	60	90

This leads to an average spin result of 1.944444444. Remember, if it lands on a line, it is a push and all other wins are on a "to one" basis.

Putting this average multiplier into the overall return, I get the following table. The lower right cell shows a return of 93.57%.

Twenties	Pays	Probability	Return
4	420	0.000115	0.048182
3	20	0.004084	0.081685
2	4	0.053435	0.213741
1	1.94	0.304514	0.592111
0	0	0.637851	0.000000
Total		1.000000	0.935719

To play for free, try this link.

"For with much wisdom comes much sorrow." -- Ecclesiastes 1:18 (NIV)

ksdjdj

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December 24th, 2021 at 9:01:05 PM permalink

I just did 10 more spins, so now the combined total is 100 (results below inc. Wiz's results from his previous post):

0 (Push) / 32
1x / 43
2x / 20
3x / 5

Quote: Wizard
(snip)
Putting this average multiplier into the overall return, I get the following table. The lower right cell shows a return of 93.57%.

Twenties Pays Probability Return
4 420 0.000115 0.048182
3 20 0.004084 0.081685
2 4 0.053435 0.213741
1 1.94 0.304514 0.592111
0 0 0.637851 0.000000
Total 1.000000 0.935719

(snip)
link to original post

In the above table, are all the figures under the heading "Pays" correct ?
I think you need to change it from:
"420", "20" and "4" to "421", "21" and "5" ?

Wizard
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December 24th, 2021 at 9:29:21 PM permalink

Quote: ksdjdj
I just did 10 more spins, so now the combined total is 100 (results below inc. Wiz's results from his previous post):

0 (Push) / 32
1x / 43
2x / 20
3x / 5

First, you're right, I should have adjusted everything to a "for one" basis. When I do that, based on the 90 spins of data, I get the following return.

Twenties	Pays	Probability	Return
4	421	0.000000	0.048296
3	21	0.066667	0.085770
2	5	0.283333	0.267176
1	1.94	0.650000	0.592111
0	0	1.000000	0.000000
Total		0.000000	0.993353

Here is my updated table of spins. I would prefer if you gather more data, let me know just the new data.

Multiplier	Wiz	ksdjdj	Total
0	10	22	32
1	16	27	43
2	4	16	20
3	0	5	5
Total	30	70	100

With your windfall of 2x multipliers, here is my new return table for the side bet.

Twenties	Pays	Probability	Return
4	421	0.000000	0.048296
3	21	0.073529	0.085770
2	5	0.294118	0.267176
1	1.98	0.632353	0.602938
0	0	1.000000	0.000000
Total		0.000000	1.004180

"For with much wisdom comes much sorrow." -- Ecclesiastes 1:18 (NIV)

Wizard
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December 25th, 2021 at 1:31:52 AM permalink

The game help file claims a return of 99.58%, which I presume to be a weighted blend of the base game and side bet. My house edge calculator gives a house edge of the game game of 0.5744%. That means the side bet would have a player advantage of 0.1976%.

"For with much wisdom comes much sorrow." -- Ecclesiastes 1:18 (NIV)

ksdjdj

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December 25th, 2021 at 2:37:12 AM permalink

Merry Christmas WoV Members

Quote: Wizard
(snip)I would prefer if you gather more data, let me know just the new data.
(snip)
link to original post

Just did another 10 spins, here are the results:

Push / 2
1 / 7
2 / 0
3 / 1

Quote: Wizard
The game help file claims a return of 99.58%, which I presume to be a weighted blend of the base game and side bet. My house edge calculator gives a house edge of the game game of 0.5744%. That means the side bet would have a player advantage of 0.1976%.
link to original post

It is also double after split, so the house edge is 0.43286% for each of the 4 boxes in the main game ?

Wizard
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December 25th, 2021 at 8:58:00 AM permalink

Quote: ksdjdj
It is also double after split, so the house edge is 0.43286% for each of the 4 boxes in the main game ?
link to original post

You're right, I see it is double after a split. I did a few more spins. Here is my new table showing our combined data.

Multiplier	Wiz	ksdjdj	Total	Probability	Expected
0	11	24	35	0.307018	0.307018
1	17	34	51	0.447368	0.894737
2	6	16	22	0.192982	0.578947
3	0	6	6	0.052632	0.210526
Total	34	80	114	1.000000	1.991228

I suspect our results are exceeding expectations.

"For with much wisdom comes much sorrow." -- Ecclesiastes 1:18 (NIV)

Dieter
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December 25th, 2021 at 9:13:57 AM permalink

One of the concerns I had was that the sidebet would lose to a dealer blackjack.

Limited testing, but the sidebet did appear to be resolved before insurance was offered.

May the cards fall in your favor.

TwelveOr21

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December 25th, 2021 at 2:32:35 PM permalink

Yep, side bet resolved before Insurance.

gordonm888
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December 25th, 2021 at 4:28:47 PM permalink

So we calculate that the basic BJ game should have an expectation of 99.57% which is very close to the value of 99.58% posted on the game's Help/Info page? Is this making sense?

So many better men, a few of them friends, are dead. And a thousand thousand slimy things live on, and so do I.

ksdjdj

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December 26th, 2021 at 2:49:14 AM permalink

Quote: gordonm888
So we calculate that the basic BJ game should have an expectation of 99.57% which is very close to the value of 99.58% posted on the game's Help/Info page? Is this making sense?
link to original post

Sort of, I am used to side bets with a separate RTP figure, but if the 99.58% RTP "combined figure ^^^ " is correct then the side bet should also be about 99.58%.

^^^: Since it is a "forced side bet", it is probably safe to say that it is a blended figure?

----
Anyone can answer this, but how many tests of the "side bet spinner " do you think would be enough, to get a good feel for it?

There may be at least two answers for the above question:
(i) One answer would be for, when you have "no idea" what the spinner should pay

(ii) The other answer would be for, when you think the average odds could be ~$1.95 (~0.95/1) for the spinner.

----
Update (320 am, Pac Time):

Just did another 16 spins, here are the results:

Push / 4
1 / 10
2 / 2
3 / 0

Last edited by: ksdjdj on Dec 26, 2021

Wizard
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December 26th, 2021 at 7:22:13 AM permalink

I would like to announce my new page on Four 20's Blackjack. As always, I welcome all comments, questions, and corrections.

"For with much wisdom comes much sorrow." -- Ecclesiastes 1:18 (NIV)

ksdjdj

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December 26th, 2021 at 1:47:15 PM permalink

Quote: Wizard
I would like to announce my new page on Four 20's Blackjack. As always, I welcome all comments, questions, and corrections.
link to original post

Looks good to me.

Also, my early estimated chances for the "One 20 Wheel" were:

3 - 5%
2 - 20%
1 - 40%
Push - 35%

Mewtwo

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December 27th, 2021 at 7:54:13 PM permalink

Wow, this looks like one of the most fair side bets I've ever seen offered on a game.

I don't like that they disallow surrender but everything else is spot on for good blackjack. (In PA, surrender is if DraftKings offers this game on their PA platform, wouldn't they be required to modify it to allow that option?)

Dieter
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December 27th, 2021 at 8:57:23 PM permalink

The PA rules I skimmed also seemed to require a dealer, a certain design of table, a discard rack, and playing cards.

I am assuming electronic blackjack falls under a different set of rules. Hopefully someone more familiar with PA rules can educate me.

May the cards fall in your favor.

mwalz9

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December 28th, 2021 at 6:50:31 AM permalink

I played quite a few hands on the demo version just to try it out. It seems to me the wheel has an abnormally large amount of pushes when you make 1 20, but I do realize Im looking at a very small sample size to form a solid opinion.

gordonm888
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January 2nd, 2022 at 1:12:47 PM permalink

Quote: ksdjdj
Quote: Wizard

Also, my early estimated chances for the "One 20 Wheel" were:

3 - 5%
2 - 20%
1 - 40%
Push - 35%
link to original post

Here's data on an additional 20 spins on the One 20 Wheel:
3: 2
2: 2
1: 10
Push: 6
So many better men, a few of them friends, are dead. And a thousand thousand slimy things live on, and so do I.

Wizard
Administrator