- Appendices
- Miscellaneous
- External Links
Version 1
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 |
How to Play 21/Blackjack: The goal of 21 is to amount your card values as near to 21 as possible without exceeding or 'busting' it. Moreover, you have to beat whatever hand both the dealer and other players have drawn; if they have 20 and you have 19, you lose the hand. Get a casino quality Blackjack experience right on your iPhone, iPad, or iPod Touch! Download Blackjack 21+ and double down for intense gambling action with up to three hands at once. Play and feel like a. 21+3 Blackjack strategy. In most online blackjack games that offer a side bet the goal is to lower the odds for the player. The overall percentage in 21+3 blackjack is 99.70% which means that the casino returns a shade over 0.99 cents on each dollar wagered. By enticing players to make the three-card side bet the online casino lowers that number.
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.
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
Casino 21 Card Game Rules
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%
Written by: Michael Shackleford
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