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777 Bets Free Bet

Posted on 4/11/2022 by admin

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Version 1

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Version 1 of 21+3 I noticed at the Las Vegas Hilton in April, 2001. The side bet pays based on the player's first two cards and the dealer's up card. If the three cards equal a flush, straight, straight flush, or three of a kind the side bet pays 9 to 1. The following table shows the probability of each hand in a six-deck game,as played at the Hilton.

21+3 — 6 decks

Hand	Combinations	Probability	Pays	Return
Straight flush	10368	0.002068	9 to 1	0.018613
Three of a kind	26312	0.005248	9 to 1	0.047236
Straight	155520	0.031021	9 to 1	0.279192
Flush	236736	0.047221	9 to 1	0.424993
Pair+flush	56160	0.011202	9 to 1	0.100819
Pair (no flush)	977184	0.194918	Loss	-0.194918
Nothing	3551040	0.708321	Loss	-0.708321
Total	5013320	1	-0.032386

Following is the house edge for 4, 6, and 8 decks.

4 decks — 4.24%
6 decks — 3.24%
8 decks — 2.74%

Version 2

At the Regent (now known as the Rampart) in Las Vegas all hands listed above, plus a pair, pay 5 to 2. I'll call this version 2. Two decks are used in this version. The following table shows a house edge under these rules of 2.78%.

21+3 — 2 decks

Hand	Combinations	Probability	Pays	Return
Straight flush	384	0.002109	2.5 to 1	0.005272
Three of a kind	728	0.003998	2.5 to 1	0.009994
Straight	5760	0.03163	2.5 to 1	0.079076
Flush	8768	0.048148	2.5 to 1	0.120371
Pair	34944	0.19189	2.5 to 1	0.479726
Nothing	131520	0.722225	Loss	-0.722225
Total	182104	1	-0.027786

Version 3

I have an unconfirmed report that Internet casinos using Wagerworks software use the following pay table, which I will call 'Version 3.'

21+3 — Version 3 — Six Decks

Hand	Pays	Combinations	Probability	Return
Suited three of a kind	100	1040	0.000207	0.020745
Three of a kind	33	25272	0.005041	0.166352
Straight flush	35	10368	0.002068	0.072383
Straight	10	155520	0.031021	0.310214
Flush	5	292896	0.058424	0.292118
Loss	-1	4528224	0.903239	-0.903239
Total	5013320	1	-0.041427

Although Wager Works only uses six decks in their blackjack game, as far as I know, here is the house edge for 3 to 8 decks.

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21+3 — Version 3 — 3-8 Decks

Decks	House Edge
3	7.76%
4	5.99%
5	4.89%
6	4.14%
7	3.60%
8	3.18%

Version 4

This version, with a 30-20-10-5 pay table, is known as '21+3 Xtreme.' The following return table shows the house edge for six decks is 13.39% (ouch!).

21+3 — Version 4 — Six Decks

Hand	Pays	Combinations	Probability	Return
Straight flush	30	10,368	0.002068	0.062043
Three of a kind	20	26,312	0.005248	0.104968
Straight	10	155,520	0.031021	0.310214
Flush	5	292,896	0.058424	0.292118
Loser	-1	4,528,224	0.903239	-0.903239
Total	5,013,320	1.000000	-0.133896

If you happen to see it with other than six decks, here is the expected value for various number of decks.

21+3 — Version 4 -- 1 to 8 Deck Summary

Decks	Expected Value
1	-0.227330
2	-0.172736
4	-0.143780
5	-0.137863
6	-0.133896
8	-0.128912

The Caesars Entertainment Blog mentions that the xtreme version of 21+3 can be found in the Party Pit at the Paris casino in Las Vegas. I had to chuckle at their sense of humor with this remark,

'We would calculate the odds of hitting these side bets, but being in Vegas isn't about math, it's about having fun. And just never-you-mind that this is the blog of a casino company. Check out the new Ooh La La Party Pit at Paris Las Vegas the next time you’re in the neighborhood.

Hey, it is about the math everywhere, even in the Party Pit!

Version 5

I saw this version at an Internet casino using live dealers from Evolution Gaming. Following is the return table, based on eight decks.

21+3 — Version 5 — 8 Decks

Event	Pays	Combinations	Probability	Return
Suited three of a kind	100	2,912	0.000244	0.024446
Straight flush	40	24,576	0.002063	0.082524
Three of a kind	25	61,568	0.005169	0.129213
Straight	10	368,640	0.030947	0.309465
Flush	5	700,928	0.058841	0.294207
Loser	-1	10,753,536	0.902736	-0.902736
Total	11,912,160	1.000000	-0.062882

Following is the house edge for this pay table for various numbers of decks.

4 decks: 8.78%
5 decks: 7.81%
6 decks: 7.14%
7 decks: 6.29%

Version 6

I have an unconfirmed report that the Ameristar in Kansas City is using the following pay table with two decks.

21+3 — Version 6 — 2 Decks

Event	Pays	Combinations	Probability	Return
Straight flush	7	384	0.002109	0.014761
Three of a kind	7	728	0.003998	0.027984
Straight	7	5,760	0.031630	0.221412
Flush	7	10,016	0.055002	0.385011
Pair	0	33,696	0.185037	0.000000
Loser	-1	131,520	0.722225	-0.722225
Total	182,104	1.000000	-0.073057

The next table shows the house edge of the Version 6 pay table by number of decks.

21+3 — Version 6

Version 7

This pay table I hear is used by live dealer casinos by Evolution Gaming, which use eight decks.

21+3 — Version 7 — 8 Decks

Event	Pays	Combinations	Probability	Return
Suited three of a kind	100	2,912	0.000244	0.024446
Straight flush	40	24,576	0.002063	0.082524
Three of a kind	30	61,568	0.005169	0.155055
Straight	10	368,640	0.030947	0.309465
Flush	5	700,928	0.058841	0.294207
Loser	-1	10,753,536	0.902736	-0.902736
Total	11,912,160	1.000000	-0.037039

Here is the house edge for four and six decks.

Four decks: 6.39%
Six decks: 3.70%

Version 8

I think I saw this version at the Global Gaming Expo, but I'm not sure. This version is noteworthy because it pays a progressive jackpot for three suited aces. Here is the full pay table. Pays are on a 'to one' basis.

Version 8 Pay Table

Event	Pays
Suited three aces	Jackpot
Suited three of a kind	125
Straight flush	25
Three of a kind	20
Straight	7
Flush	3

The following table shows my analysis based on a six-deck game.

Version 8 Return Table — Six Decks

Event	Pays	Combinations	Probability	Return
Suited three aces	?	80	0.000016	?
Suited three of a kind	125	960	0.000191	0.023936
Straight flush	25	10,368	0.002068	0.051702
Three of a kind	20	25,272	0.005041	0.100819
Straight	7	155,520	0.031021	0.217150
Flush	3	292,896	0.058424	0.175271
Loser	-1	4,528,224	0.903239	-0.903239
Total	5,013,320	1.000000	-0.334360

The lower right cell shows that a house edge of 33.44%, before considering the value of the jackpot. If the minimum bet is $1, then each $1,000 in the meter decreases the house edge by 1.60%. If the minimum bet is $5, then each $10,000 in the meter decreases the house edge by 3.19%.

The breakeven points, where the house edge is zero, is $27,016.90 for a $1 bet and $135,084.50 for a $5 bet, based on six decks.

Version 9

I saw this version at the Rampart casino in Las Vegas on January 29, 2021 . This version is similar to version 8, except a suited three of a kind in queens to aces is required to hit the jackpot and it is a $1 'red light' bet, meaning pays are on a 'for one' basis. Following is the pay table.

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Version 9 Pay Table

Event	Pays
Suited three of a kind (Q's-A's)	Jackpot
Suited three of a kind (2's-J's)	$125
Straight flush	$25
Three of a kind	$20
Straight	$6
Flush	$2