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Last Updated: June 12, 2017

Raise the Roof

Introduction



Raise the Roof is a blackjack side bet that wins if the dealer busts, according to what the dealer's bust card was. The lower the card, the more it pays. Plus, the player has the opportunity to raise his side bet after seeing the dealer's up card.

As of this writing (June 13, 2017), Raise the Roof can be found at the Tortoise Rock in California and unknown casinos in the Czech Republic.

Rules



  1. The game is based on conventional blackjack rules, which I assume the reader understands.
  2. The only rules affecting the Raise the Roof side bet are the number of decks, whether the dealer hits or stands on a soft 17, and the pay table used.
  3. At the time of making his blackjack wager, the player has the option to make the Raise the Roof side bet.
  4. The dealer shall then deal each player two cards and two to himself -- one up and one down, as usual.
  5. If the dealer has blackjack, the Raise the Roof bet shall lose.
  6. Otherwise, if the dealer doesn't have blackjack, the player may raise his Raise the Roof with an additional amount of 1x to 5x the original Raise the Roof wager.
  7. Next, the players shall play out their blackjack hands, as normal. If the player busts, any Raise the Roof wagers will still remain live.
  8. The dealer will then play out his hand. If the dealer has a total of 17 to 21, then all Raise the Roof wagers, both initial and raises, will lose.
  9. If the dealer busts, and the player did not raise his Raise the Roof bet, then the original Raise the Roof wager shall pay 1 to 1.
  10. If the dealer busts, and the player did raise his Raise the Roof bet, then the original Raise the Roof wager and the Raise bet shall pay according to one of the pay tables below, depending on which one management decides to use.
  11. The wins for a 4-5-6-7 refer to the entire dealer hand. The cards do not have to be in that order but there can not be any additional cards. For example, 4-5-6-A-7 would not qualify because of the ace.



There are six pay tables available to casino management for use on the Raise the Roof side bet, as shown in the table below. Pay tables 1 and 2 are meant for six- and eight-deck games where the dealer hits a soft 17. Pay tables 3 and 4 are meant for six- and eight-deck games where the dealer stands on a soft 17. Pay tables 5 and 6 were meant for two-deck games where the dealer hits a soft 17. All wins are on a "to one" basis.

Raise the Roof Pay Tables

Event Pay Table 1 Pay Table 2 Pay Table 3 Pay Table 4 Pay Table 5 Pay Table 6
4-5-6-7 suited 200 500 200 500 300 500
4-5-6-7 40 50 50 40 30 25
Bust with 6 10 10 10 10 10 10
Bust with 7 5 4 5 5 5 5
Bust with 8 2 2 2 2 2 2
Bust with 9 1 1 1 1 1 1
Bust with 10 1 1 1 1 1 1


Analysis

To analyze this side bet I first had to calculate the probability probability of all possible outcomes of the dealer's hand. The following three tables are more information than you need to know to analyze this side bet, but you never know who will find it useful (including me later on). These tables are "pre-peek," mean before dealer checks for blackjack.

The following table is for the raw dealer probabilities for two decks and the dealer hits a soft 17.

The following table is for the raw dealer probabilities for six decks and the dealer hits a soft 17.

Pre-Peek Dealer Probabilities -- Six Decks -- Dealer Hits on Soft 17Expand

Event Ace up 2 up 3 up 4 up 5 up 6 up 7 up 8 up 9 up 10 up
BJ 0.308682 0 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.077170
17 0.057270 0.130071 0.125900 0.122458 0.118089 0.115064 0.369208 0.128940 0.120310 0.111914
18 0.142822 0.135978 0.131930 0.125405 0.123042 0.114574 0.137931 0.359955 0.117348 0.111669
19 0.142935 0.131607 0.126656 0.122620 0.118216 0.115043 0.078428 0.128723 0.351854 0.111945
20 0.143284 0.125662 0.122185 0.117830 0.112435 0.110177 0.078682 0.069219 0.120368 0.340014
21 0.065858 0.120022 0.116371 0.113217 0.108586 0.105882 0.073816 0.069470 0.060877 0.034817
Bust with 6 0.004560 0.009703 0.009316 0.009107 0.008832 0.027906 0.009886 0.008990 0.008655 0.007784
Bust with 7 0.009240 0.019136 0.018408 0.017929 0.037906 0.039539 0.018290 0.017392 0.016458 0.015506
Bust with 8 0.013899 0.028091 0.027209 0.046992 0.048280 0.048982 0.027217 0.024344 0.024180 0.022424
Bust with 9 0.018560 0.036879 0.056261 0.057145 0.057715 0.058031 0.035189 0.033087 0.029802 0.028862
Bust with 10 0.092890 0.262851 0.265764 0.267297 0.266899 0.264802 0.171355 0.159881 0.150146 0.137895


The following table is for the raw dealer probabilities for six decks and the dealer stands on a soft 17.

Pre-Peek Dealer Probabilities -- Six Decks -- Dealer Stands on Soft 17Expand

Event Ace up 2 up 3 up 4 up 5 up 6 up 7 up 8 up 9 up 10 up
BJ 0.308682 0 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.077170
17 0.130017 0.139656 0.134296 0.130556 0.121843 0.165707 0.369208 0.128940 0.120310 0.111914
18 0.130822 0.134389 0.130539 0.124062 0.122437 0.106194 0.137931 0.359955 0.117348 0.111669
19 0.130594 0.13002 0.125226 0.121272 0.117575 0.106431 0.078428 0.128723 0.351854 0.111945
20 0.130910 0.124019 0.120817 0.116441 0.111793 0.101551 0.078682 0.069219 0.120368 0.340014
21 0.053504 0.118413 0.114928 0.111866 0.107945 0.097276 0.073816 0.069470 0.060877 0.034817
Bust with 6 0.003693 0.009585 0.009213 0.009007 0.008786 0.027311 0.009886 0.008990 0.008655 0.007784
Bust with 7 0.007518 0.018907 0.018208 0.017736 0.037817 0.038342 0.018290 0.017392 0.016458 0.015506
Bust with 8 0.011431 0.027764 0.026923 0.046716 0.048152 0.047267 0.027217 0.024344 0.024180 0.022424
Bust with 9 0.015391 0.036456 0.055890 0.056788 0.057550 0.055836 0.035189 0.033087 0.029802 0.028862
Bust with 10 0.077441 0.260791 0.263960 0.265558 0.266101 0.254086 0.171355 0.159881 0.150146 0.137895


The next table is for two decks and the dealer hits a soft 17.

Post-Peek Dealer Probabilities -- Two Decks -- Dealer Hits on Soft 17Expand

Event Ace up 2 up 3 up 4 up 5 up 6 up 7 up 8 up 9 up 10 up
BJ 0.310680 0 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.077670
17 0.056818 0.129949 0.124999 0.122575 0.117533 0.115500 0.370478 0.129697 0.120940 0.112904
18 0.142065 0.134838 0.131904 0.121499 0.123331 0.114155 0.138195 0.361182 0.112016 0.112156
19 0.142376 0.132234 0.125913 0.122342 0.117920 0.115451 0.078013 0.129025 0.354051 0.113008
20 0.143456 0.12565 0.122970 0.117798 0.109627 0.109956 0.078781 0.068857 0.121118 0.335608
21 0.064980 0.120801 0.116754 0.114458 0.107921 0.106185 0.073390 0.069610 0.060977 0.035463
Bust with 6 0.004592 0.009714 0.009137 0.009144 0.008948 0.025844 0.009971 0.008589 0.008826 0.007423
Bust with 7 0.009385 0.019249 0.018250 0.018071 0.038449 0.040067 0.016878 0.016732 0.016310 0.015827
Bust with 8 0.014016 0.02796 0.027153 0.047560 0.048937 0.049135 0.026692 0.021816 0.024714 0.022857
Bust with 9 0.018620 0.036848 0.056631 0.057382 0.058072 0.058417 0.034853 0.033301 0.027776 0.029432
Bust with 10 0.093013 0.262756 0.266290 0.269172 0.269262 0.265292 0.172749 0.161192 0.153273 0.137653


The next three post-peek tables refine the ones above to just the pertinent events for the Raise the Raise side bet and assuming the dealer has already checked for blackjack. These probabilities are important to calculating the expected value of whether to make a small raise (1x), big raise (5x), or no raise.

The next table is for six decks and the dealer hits a soft 17.

Post-Peek Dealer Probabilities -- Six Decks -- Dealer Hits on Soft 17Expand

Event Ace up 2 up 3 up 4 up 5 up 6 up 7 up 8 up 9 up 10 up
No bust 0.798719 0.643340 0.623042 0.601530 0.580368 0.560740 0.738065 0.756307 0.770757 0.769761
Bust with 6 0.006596 0.009703 0.009316 0.007780 0.007505 0.026579 0.008559 0.008990 0.008655 0.008435
Bust with 7 0.013366 0.019136 0.018408 0.016602 0.036579 0.038212 0.016963 0.017392 0.016458 0.016803
Bust with 8 0.020105 0.028091 0.027209 0.046992 0.048280 0.048982 0.027217 0.024344 0.024180 0.024299
Bust with 9 0.026847 0.036879 0.056261 0.057145 0.057715 0.058031 0.035189 0.033087 0.029802 0.031276
Bust with 10 0.134367 0.262851 0.265764 0.267297 0.266899 0.264802 0.171355 0.159881 0.150146 0.149426
4-5-6-7 suited 0.000000 0.000000 0.000000 0.000029 0.000029 0.000015 0.000015 0.000000 0.000000 0.000000
4-5-6-7 0.000000 0.000000 0.000000 0.001827 0.001827 0.000914 0.000914 0.000000 0.000000 0.000000


The next table is for six decks and the dealer stands on a soft 17.

Post-Peek Dealer Probabilities -- Six Decks -- Dealer Stands on Soft 17Expand

Event Ace up 2 up 3 up 4 up 5 up 6 up 7 up 8 up 9 up 10 up
No bust 0.832970 0.646497 0.625806 0.604197 0.581593 0.577159 0.738065 0.756307 0.770757 0.769761
Bust with 6 0.005342 0.009585 0.009213 0.007680 0.007459 0.025984 0.008559 0.008990 0.008655 0.008435
Bust with 7 0.010875 0.018907 0.018208 0.016409 0.036490 0.037015 0.016963 0.017392 0.016458 0.016803
Bust with 8 0.016535 0.027764 0.026923 0.046716 0.048152 0.047267 0.027217 0.024344 0.024180 0.024299
Bust with 9 0.022263 0.036456 0.055890 0.056788 0.057550 0.055836 0.035189 0.033087 0.029802 0.031276
Bust with 10 0.112019 0.260791 0.263960 0.265558 0.266101 0.254086 0.171355 0.159881 0.150146 0.149426
4-5-6-7 suited 0.000000 0.000000 0.000000 0.000029 0.000029 0.000015 0.000015 0.000000 0.000000 0.000000
4-5-6-7 0.000000 0.000000 0.000000 0.001827 0.001827 0.000914 0.000914 0.000000 0.000000 0.000000


The next table is for two decks and the dealer hits on a soft 17.

Post-Peek Dealer Probabilities -- Two Decks -- Dealer Hits on Soft 17Expand

Event Ace up 2 up 3 up 4 up 5 up 6 up 7 up 8 up 9 up 10 up
No bust 0.797445 0.643472 0.622540 0.598672 0.576332 0.561247 0.738857 0.758371 0.769102 0.768856
Bust with 6 0.006662 0.009714 0.009137 0.007764 0.007568 0.024464 0.008591 0.008589 0.008826 0.008048
Bust with 7 0.013615 0.019249 0.018250 0.016691 0.037069 0.038687 0.015498 0.016732 0.016310 0.017160
Bust with 8 0.020333 0.027960 0.027153 0.047560 0.048937 0.049135 0.026692 0.021816 0.024714 0.024782
Bust with 9 0.027012 0.036848 0.056631 0.057382 0.058072 0.058417 0.034853 0.033301 0.027776 0.031910
Bust with 10 0.134934 0.262756 0.266290 0.269172 0.269262 0.265292 0.172749 0.161192 0.153273 0.149245
4-5-6-7 suited 0.000000 0.000000 0.000000 0.000030 0.000030 0.000015 0.000015 0.000000 0.000000 0.000000
4-5-6-7 0.000000 0.000000 0.000000 0.001900 0.001900 0.000950 0.000950 0.000000 0.000000 0.000000


The next six tables show the expected return for each viable action by dealer up card for the six pay tables above. The only viable plays are:

  • S = Stand
  • 1x = Make raise bet equal to 1x the Raise the Roof wager.
  • 5x = Make raise bet equal to 5x the Raise the Roof wager.


Pay Table 1 Return — Six Decks — Dealer Hits on Soft 17Expand

Ace up No Raise 1x Raise 5x Raise Max EV Strategy Prob. Return
A -0.597439 -0.929011 -2.787033 -0.597439 S 0.053178 -0.031771
2 -0.286680 -0.189436 -0.568308 -0.189436 1x 0.076923 -0.014572
3 -0.246084 -0.122798 -0.368394 -0.122798 1x 0.076923 -0.009446
4 -0.203060 0.125153 0.375458 0.375458 5x 0.076923 0.028881
5 -0.160736 0.367243 1.101728 1.101728 5x 0.076923 0.084748
6 -0.121480 0.738589 2.215768 2.215768 5x 0.076923 0.170444
7 -0.476128 -0.508589 -1.525766 -0.476128 S 0.076923 -0.036625
8 -0.512613 -0.675582 -2.026746 -0.512613 S 0.076923 -0.039432
9 -0.541516 -0.747218 -2.241654 -0.541516 S 0.076923 -0.041655
10 -0.539523 -0.744198 -2.232593 -0.539523 S 0.283948 -0.153196
Blackjack -1.000000 0.047489 -0.047489
Total 1.000000 -0.090113


Pay Table 2 Return — Six Decks — Dealer Hits on Soft 17Expand

Ace up No Raise 1x Raise 5x Raise Max EV Strategy Prob. Return
A -0.597439 -0.955743 -2.867228 -0.597439 S 0.053178 -0.031771
2 -0.286680 -0.227708 -0.683124 -0.227708 1x 0.076923 -0.017516
3 -0.246084 -0.159614 -0.478842 -0.159614 1x 0.076923 -0.012278
4 -0.203060 0.145095 0.435285 0.435285 5x 0.076923 0.033483
5 -0.160736 0.347231 1.041693 1.041693 5x 0.076923 0.080130
6 -0.121480 0.687412 2.062235 2.062235 5x 0.076923 0.158633
7 -0.476128 -0.517268 -1.551805 -0.476128 S 0.076923 -0.036625
8 -0.512613 -0.710366 -2.131098 -0.512613 S 0.076923 -0.039432
9 -0.541516 -0.780134 -2.340402 -0.541516 S 0.076923 -0.041655
10 -0.539523 -0.777803 -2.333409 -0.539523 S 0.283948 -0.153196
Blackjack -1.000000 0.047489 -0.047489
Total 1.000000 -0.107715


Pay Table 3 Return — Six Decks — Dealer Stands on Soft 17Expand

Ace up No Raise 1x Raise 5x Raise Max EV Strategy Prob. Return
A -0.665935 -1.115646 -3.346937 -0.665935 S 0.053178 -0.035413
2 -0.292994 -0.206674 -0.620022 -0.206674 1x 0.076923 -0.015898
3 -0.251612 -0.137880 -0.413640 -0.137880 1x 0.076923 -0.010606
4 -0.208392 0.147135 0.441406 0.441406 5x 0.076923 0.033954
5 -0.163187 0.397087 1.191262 1.191262 5x 0.076923 0.091636
6 -0.154317 0.667471 2.002412 2.002412 5x 0.076923 0.154032
7 -0.476128 -0.490317 -1.470952 -0.476128 S 0.076923 -0.036625
8 -0.512613 -0.675582 -2.026746 -0.512613 S 0.076923 -0.039432
9 -0.541516 -0.747218 -2.241654 -0.541516 S 0.076923 -0.041655
10 -0.539523 -0.744198 -2.232593 -0.539523 S 0.283948 -0.153196
Blackjack -1.000000 0.047489 -0.047489
Total 1.000000 -0.100694


Pay Table 4 Return — Six Decks — Dealer Stands on Soft 17Expand

Ace up No Raise 1x Raise 5x Raise Max EV Strategy Prob. Return
A -0.665935 -1.115646 -3.346937 -0.665935 S 0.053178 -0.035413
2 -0.292994 -0.206674 -0.620022 -0.206674 1x 0.076923 -0.015898
3 -0.251612 -0.137880 -0.413640 -0.137880 1x 0.076923 -0.010606
4 -0.208392 0.127994 0.383982 0.383982 5x 0.076923 0.029537
5 -0.163187 0.377946 1.133838 1.133838 5x 0.076923 0.087218
6 -0.154317 0.657900 1.973700 1.973700 5x 0.076923 0.151823
7 -0.476128 -0.499888 -1.499664 -0.476128 S 0.076923 -0.036625
8 -0.512613 -0.675582 -2.026746 -0.512613 S 0.076923 -0.039432
9 -0.541516 -0.747218 -2.241654 -0.541516 S 0.076923 -0.041655
10 -0.539523 -0.744198 -2.232593 -0.539523 S 0.283948 -0.153196
Blackjack -1.000000 0.047489 -0.047489
Total 1.000000 -0.111737


Pay Table 5 Return — Two Decks — Dealer Hits on Soft 17Expand

Ace up No Raise 1x Raise 5x Raise Max EV Strategy Prob. Return
A -0.594889 -0.920284 -2.760851 -0.594889 S 0.053025 -0.031544
2 -0.286945 -0.189126 -0.567378 -0.189126 1x 0.076923 -0.014548
3 -0.245079 -0.125386 -0.376158 -0.125386 1x 0.076923 -0.009645
4 -0.197343 0.112732 0.338195 0.338195 5x 0.076923 0.026015
5 -0.152664 0.364340 1.093019 1.093019 5x 0.076923 0.084078
6 -0.122492 0.690583 2.071749 2.071749 5x 0.076923 0.159365
7 -0.477714 -0.535973 -1.607919 -0.477714 S 0.076923 -0.036747
8 -0.516741 -0.701392 -2.104176 -0.516741 S 0.076923 -0.039749
9 -0.538203 -0.737630 -2.212890 -0.538203 S 0.076923 -0.041400
10 -0.537711 -0.743714 -2.231143 -0.537711 S 0.283794 -0.152599
Blackjack -1.000000 0.047797 -0.047797
Total 1.000000 -0.104571


Pay Table 6 Return — Two Decks — Dealer Hits on Soft 17Expand

Ace up No Raise 1x Raise 5x Raise Max EV Strategy Prob. Return
A -0.594889 -0.920284 -2.760851 -0.594889 S 0.053025 -0.031544
2 -0.286945 -0.189126 -0.567378 -0.189126 1x 0.076923 -0.014548
3 -0.245079 -0.125386 -0.376158 -0.125386 1x 0.076923 -0.009645
4 -0.197343 0.105796 0.317387 0.317387 5x 0.076923 0.024414
5 -0.152664 0.357404 1.072211 1.072211 5x 0.076923 0.082478
6 -0.122492 0.687115 2.061344 2.061344 5x 0.076923 0.158565
7 -0.477714 -0.539441 -1.618324 -0.477714 S 0.076923 -0.036747
8 -0.516741 -0.701392 -2.104176 -0.516741 S 0.076923 -0.039749
9 -0.538203 -0.737630 -2.212890 -0.538203 S 0.076923 -0.041400
10 -0.537711 -0.743714 -2.231143 -0.537711 S 0.283794 -0.152599
Blackjack -1.000000 0.047797 -0.047797
Total 1.000000 -0.108573


The next table summarizes the house edge and Element of Risk under all six sets of rules. As a reminder, the house edge is the ratio of the expected player loss to initial bet and the Element of Risk is the ratio of the expected player loss to the total average bet (including raises).

House Edge Summary

Decks Soft 17 Pay Table House Edge Element of Risk
6 Hit 1-1-2-5-10-40-200 9.01% 3.90%
6 Hit 1-1-2-4-10-50-500 10.77% 4.67%
6 Stand 1-1-2-5-10-50-200 10.07% 4.36%
6 Stand 1-1-2-5-10-40-500 11.17% 4.84%
2 Hit 1-1-2-5-10-30-300 10.46% 4.53%
2 Hit 1-1-2-5-10-25-500 10.86% 4.70%


Strategy



The strategy nicely works out the same for all pay tables and sets of rules. The following table shows the mathematically best action for every dealer up card. Here, again, are the abbreviations for the strategy: S=Stand, 1x= 1x Raise, 5x=5x raise.

Strategy

Up Card Best Action
A S
2 1x
3 1x
4 5x
5 5x
6 5x
7 S
8 S
9 S
10 S



Written by: Michael Shackleford

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