## Introduction

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. 4-Deck to 8-Deck Blackjack Strategy Introduction. To use the basic strategy, look up your hand along the left vertical edge and the dealer's up card along the top.

To use the basic strategy, look up your hand along the left vertical edge and the dealer's up card along the top. In both cases an A stands for ace. From top to bottom are the hard totals, soft totals, and splittable hands. There are two charts depending on whether the dealer hits or stands on soft 17.

Other basic strategy rules.

• Never take insurance or 'even money.'
• If there is no row for splitting (fives and tens), then look up your hand as a hard total (10 or 20).
• If you can't split because of a limit on re-splitting, then look up your hand as a hard total, except aces. In the extremely unlikely event you have a pair of aces you can't re-split and drawing to split aces is allowed, then double against a 6, otherwise hit.

If you play a mixture of six-deck games, some where the dealer hits a soft 17, and some where he stands, and you only wish to memorize one strategy, I would recommend you memorize the one where the dealer stands on soft 17. The cost in errors due to playing the wrong strategy is 2.3 times higher playing a stand on soft 17 game, with the hit on 17 strategy, than vise versa.

## Basic Strategy in Text

For the benefit of my blind readers, here is the above strategy in text form, when the dealer stands on soft 17 and surrender is allowed. To use the strategy, start at the top, and follow the first rule that applies.

## Surrender

• Surrender hard 16 (but not a pair of 8s) vs. dealer 9, 10, or A, and hard 15 vs. dealer 10.

## Split

• Always split aces and 8s.
• Never split 5s and 10s.
• Split 2s and 3s against a dealer 4-7, and against a 2 or 3 if DAS is allowed.
• Split 4s only if DAS is allowed and the dealer shows a 5 or 6.
• Split 6s against a dealer 3-6, and against a 2 if DAS is allowed.
• Split 7s against a dealer 2-7.
• Split 9s against a dealer 2-6 or 8-9.

## Double

• Double hard 9 vs. dealer 3-6.
• Double hard 10 except against a dealer 10 or A.
• Double hard 11 except against a dealer A.
• Double soft 13 or 14 vs. dealer 5-6.
• Double soft 15 or 16 vs. dealer 4-6.
• Double soft 17 or 18 vs. dealer 3-6.

## Hit or Stand

• Always hit hard 11 or less.
• Stand on hard 12 against a dealer 4-6, otherwise hit.
• Stand on hard 13-16 against a dealer 2-6, otherwise hit.
• Always stand on hard 17 or more.
• Always hit soft 17 or less.
• Stand on soft 18 except hit against a dealer 9, 10, or A.
• Always stand on soft 19 or more.

As I've said many times, the above strategy will be fine under any set of rules. However, for you perfectionists out there, here are the modifications to make if the dealer hits a soft 17.

• Surrender 15, a pair of 8s, and 17 vs. dealer A.
• Double 11 vs. dealer A.
• Double soft 18 vs. dealer 2.
• Double soft 19 vs. dealer 6.

My thanks to Kelly for putting together the above text strategy.

Written by:Michael Shackleford
• Appendices
• Miscellaneous

## 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

HandCombinationsProbabilityPaysReturn
Straight flush103680.0020689 to 10.018613
Three of a kind263120.0052489 to 10.047236
Straight1555200.0310219 to 10.279192
Flush2367360.0472219 to 10.424993
Pair+flush561600.0112029 to 10.100819
Pair (no flush)9771840.194918Loss-0.194918
Nothing35510400.708321Loss-0.708321
Total50133201-0.032386

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

HandCombinationsProbabilityPaysReturn
Straight flush3840.0021092.5 to 10.005272
Three of a kind7280.0039982.5 to 10.009994
Straight57600.031632.5 to 10.079076
Flush87680.0481482.5 to 10.120371
Pair349440.191892.5 to 10.479726
Nothing1315200.722225Loss-0.722225
Total1821041-0.027786

## 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

HandPaysCombinationsProbabilityReturn
Suited three of a kind10010400.0002070.020745
Three of a kind33252720.0050410.166352
Straight flush35103680.0020680.072383
Straight101555200.0310210.310214
Flush52928960.0584240.292118
Loss-145282240.903239-0.903239
Total50133201-0.041427

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.

DecksHouse Edge
37.76%
45.99%
54.89%
64.14%
73.60%
83.18%

## 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

HandPaysCombinationsProbabilityReturn
Straight flush3010,3680.0020680.062043
Three of a kind2026,3120.0052480.104968
Straight10155,5200.0310210.310214
Flush5292,8960.0584240.292118
Loser-14,528,2240.903239-0.903239
Total5,013,3201.000000-0.133896

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

DecksExpected
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

EventPaysCombinationsProbabilityReturn
Suited three of a kind1002,9120.0002440.024446
Straight flush4024,5760.0020630.082524
Three of a kind2561,5680.0051690.129213
Straight10368,6400.0309470.309465
Flush5700,9280.0588410.294207
Loser-110,753,5360.902736-0.902736
Total11,912,1601.000000-0.062882

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

EventPaysCombinationsProbabilityReturn
Straight flush73840.0021090.014761
Three of a kind77280.0039980.027984
Straight75,7600.0316300.221412
Flush710,0160.0550020.385011
Pair033,6960.1850370.000000
Loser-1131,5200.722225-0.722225
Total182,1041.000000-0.073057

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

## 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

EventPaysCombinationsProbabilityReturn
Suited three of a kind1002,9120.0002440.024446
Straight flush4024,5760.0020630.082524
Three of a kind3061,5680.0051690.155055
Straight10368,6400.0309470.309465
Flush5700,9280.0588410.294207
Loser-110,753,5360.902736-0.902736
Total11,912,1601.000000-0.037039

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

EventPays
Suited three acesJackpot
Suited three of a kind125
Straight flush25
Three of a kind20
Straight7
Flush3

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

### Version 8 Return Table — Six Decks

EventPaysCombinationsProbabilityReturn
Suited three aces?800.000016?
Suited three of a kind1259600.0001910.023936
Straight flush2510,3680.0020680.051702
Three of a kind2025,2720.0050410.100819
Straight7155,5200.0310210.217150
Flush3292,8960.0584240.175271
Loser-14,528,2240.903239-0.903239
Total5,013,3201.000000-0.334360

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.

### Version 9 Pay Table

EventPays
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

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

## Are Side Bets In Blackjack Worth It

### Version 9 Return Table — Six Decks

EventPaysCombinationsProbabilityReturn
Suited three of a kind (Q's-A's)Jackpot2400.000048?
Suited three of a kind (2's-J's)\$125.008000.0001600.019947
Straight flush\$25.0010,3680.0020680.051702
Three of a kind\$20.0025,2720.0050410.100819
Straight\$6.00155,5200.0310210.186128
Flush\$2.00292,8960.0584240.116847
Loser\$-4,528,2240.9032390.000000
Total5,013,3201.0000000.475444 + ?

## Side Bets Blackjack Rules Card Game

The lower right cell an expected return of 47.54%, before considering the value of the jackpot. Each \$1,000 in the jackpot increases the return by 4.79%. For example, at the time I saw this side bet the jackpot was at \$3,886.15, for an expected return of 66.15%.

The breakeven point, with no house edge, is at a jackpot of \$10,957.37. Horse racing cards drinking game board.

## Side Bets Blackjack Rules Printable

Written by: Michael Shackleford