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Last Updated: January 13, 2023

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Big City 4s

Introduction

 

 

Big City 4s is a video poker variant that awards a bonus if the player gets a four of a kind on the draw. Three of a kinds and full houses on the draw vest credits into the bonus round.

Rules

  1. The game is based on standard multi-play video poker, which I assume the reader is familiar with.
  2. As usual, the game can be played in 3-, 5-, or 10-play mode.
  3. The player may play normally with 1 to 5 credits bet per play.
  4. If the player bets 6 credits per play, then he will invoke the bonus feature. This extra credit bet per play is a fee. Any wins in the base game are based on a 5-credit bet per play.
  5. All following rules apply only if the feature is activated.
  6. If the player gets certain hands, then credits will be added to the top two levels of the jackpots in the bonus round. The hands and average contribution vary by game.
  7. If the player gets a four of a kind on the draw, then he will play the Bonus game.
  8. In each level of the bonus game, the player will choose from among three cards of different ranks. The object is to pick the card highest in rank.
  9. The player starts on level 1.
  10. If the player picks the highest card in rank, then he will advance a level, up to a highest level of 4.
  11. If the player makes it to Level 4, then he automatically wins the Big City 4's Jackpot.
  12. If the player picks the middle card in rank, then that level will be replayed, until the player either advances or picks the lowest card.
  13. If the player picks the lowest card in rank, then the bonus shall be over. The player shall win according to the level of the bonus he achieve, as follows:
    • Level 4: Big City 4's Jackpot
    • Level 3: Level 3 Jackpot
    • Level 2: 300 credits
    • Level 1: 150 credits
  14. If the player gets a four of a kind and either three of a kind or full house in the same game, then the contribution to the jackpots shall be made before the bonus is played.
  15. The reset value for the Level 3 jackpot is 500 credits.
  16. The reset value for the Big City 4s jackpot is 800 credits.
  17. If the player gets two or more four of a kinds in the same game, then he shall play the bonus round once for each four of a kind.

If my explanation was not clear, here are the rule screens directly from the game.

Example

Big City 4s Example 1

In the image above, I got two three of a kinds on the draw.  One earned 1 credit and the other 2 credits towards the Big City 4s jackpot, as indicated in the lower left corner of the two winning hands.

big city 4s example 2

In the screen above, I got a three of a kind, which contributed 3 credits to the Big City 4s jackpot.  I also got a four of a kind, which triggered the bonus, after the contribution for three of a kind was made. 

big city 4s example 3

The bonus starts with Round 1, in which the player tries to advance to level 2.  You can see my Bonus Win is already 150, which is the least I can win.

big city 4s example 4

After two pushes, I correctly pick the highest card in the middle, advancing me to Level 2, with the goal to reach Level 3.  Note my bonus win is now at 300, for at least reaching level 2.

big city 4s example 5

In the next level, I correctly pick the highest card on the right, advancing me to Level 3, with the goal to reach Level 4.  Note my bonus win is now at 585, for at least reaching level 3./p>

big city 4s example 6  

In the next level, I incorrectly pick the lowest card.  Having failed to reach level 4, I collect the level 3 jackpot of 585, which I did earn by passing two levels, to level 3.   The Level 3 jackpot reset to 500 after that game.

Analysis

The way I analyzed Big City 4's is to assume the player plays an infinite period of time. Thus, any credits won towards the jackpots are just as valuable as if they were awarded immediately. The value of a bonus I count as 312.5 for wins based on five credits per play. That comes to 62.5 credits per credit bet per play (not counting the credit bet to invoke the feature). You can see in the tables below how I do it. The totals in the combinations column are based on an optimal strategy for the total wins shown.

The following table is for 9-5 Jacks or Better. For a max bet, the game awards average bonus contributions as follows:

  • Three of a kind — 2.00
  • Full house — 9.25

All wins in the table are relative to each credit bet per play, assuming a max bet. The lower right cell shows a return to player of 98.66%. This was calculated as the product of the total win, probability, and 5/6. The reason for multiplying by 5/6, is the player must pay 1/6 of his total bet as a fee to invoke the feature.

Jacks or Better — 9-5

Hand Base
Win
Feature
Win
Total
Win
Combinations Probability Return
Royal flush 800 0.00 800.00 41,307,396 0.000025 0.016578
Straight flush 50 0.00 50.00 163,203,492 0.000098 0.004094
Four of a kind 25 62.50 87.50 3,966,846,449 0.002388 0.174131
Full house 9 1.86 10.86 19,279,674,081 0.011607 0.105020
Flush 5 0.00 5.00 15,699,926,967 0.009452 0.039381
Straight 4 0.00 4.00 18,394,513,604 0.011074 0.036912
Three of a Kind 3 0.40 3.40 125,388,137,363 0.075485 0.213874
Two pair 2 0.00 2.00 217,109,715,255 0.130702 0.217837
Jacks or better 1 0.00 1.00 356,416,518,270 0.214566 0.178805
Nothing 0 0.00 0.00 904,642,700,223 0.544604 0.000000
Total       1,661,102,543,100 1.000000 0.986632

The following table is for 8-5 Bonus Poker. For a max bet, the game awards average bonus contributions as follows:

  • Three of a kind — 2.00
  • Full house — 10.00

All wins in the table are relative to each credit bet per play, assuming a max bet. The lower right cell shows a return to player of 99.41%. This was calculated as the product of the total win, probability, and 5/6. The reason for multiplying by 5/6, is the player must pay 1/6 of his total bet as a fee to invoke the feature.

Bonus Poker — 8-5

Hand Base
Win
Feature
Win
Total
Win
Combinations Probability Return
Royal flush 800 0.00 800.00 41,492,554 0.000025 0.016653
Straight flush 50 0.00 50.00 160,798,760 0.000097 0.004033
Four aces 80 62.50 142.50 342,047,929 0.000206 0.024453
Four 2s - 4s 40 62.50 102.50 889,848,106 0.000536 0.045757
Four 5s-Ks 25 62.50 87.50 2,746,864,166 0.001654 0.120578
Full house 8 2.00 10.00 19,318,576,869 0.011630 0.096916
Flush 5 0.00 5.00 15,543,677,781 0.009357 0.038989
Straight 4 0.00 4.00 18,201,198,418 0.010957 0.036524
Three of a Kind 3 0.40 3.40 125,818,742,158 0.075744 0.214608
Two pair 2 0.00 2.00 217,615,222,008 0.131006 0.218344
Jacks or better 1 0.00 1.00 353,377,226,154 0.212737 0.177280
Nothing 0 0.00 0.00 907,046,848,197 0.546051 0.000000
Total       1,661,102,543,100 1.000000 0.994137

The following table is for 8-5 Bonus Poker Deluxe. For a max bet, the game awards average bonus contributions as follows:

  • Three of a kind — 2.00
  • Full house — 8.75

All wins in the table are relative to each credit bet per play, assuming a max bet. The lower right cell shows a return to player of 98.56%. This was calculated as the product of the total win, probability, and 5/6. The reason for multiplying by 5/6, is the player must pay 1/6 of his total bet as a fee to invoke the feature.

Bonus Poker Deluxe — 8-5

Hand Base
Win
Feature
Win
Total
Win
Combinations Probability Return
Royal flush 800 0.00 800.00 41,307,396 0.000025 0.016578
Straight flush 50 0.00 50.00 163,203,492 0.000098 0.004094
Four of a kind 25 62.50 87.50 3,966,846,449 0.002388 0.174131
Full house 9 1.75 10.75 19,279,674,081 0.011607 0.103975
Flush 5 0.00 5.00 15,699,926,967 0.009452 0.039381
Straight 4 0.00 4.00 18,394,513,604 0.011074 0.036912
Three of a Kind 3 0.40 3.40 125,388,137,363 0.075485 0.213874
Two pair 2 0.00 2.00 217,109,715,255 0.130702 0.217837
Jacks or better 1 0.00 1.00 356,416,518,270 0.214566 0.178805
Nothing 0 0.00 0.00 904,642,700,223 0.544604 0.000000
Total       1,661,102,543,100 1.000000 0.985588

The following table is for 9-6-4 Double Bonus Poker. For a max bet, the game awards average bonus contributions as follows:

  • Three of a kind — 2.00
  • Full house — 9.29

All wins in the table are relative to each credit bet per play, assuming a max bet. The lower right cell shows a return to player of 96.99%. This was calculated as the product of the total win, probability, and 5/6. The reason for multiplying by 5/6, is the player must pay 1/6 of his total bet as a fee to invoke the feature.

Double Bonus Poker — 9-6-4

Hand Base
Win
Feature
Win
Total
Win
Combinations Probability Return
Royal flush 800 0.00 800.00 39,817,188 0.000024 0.015980
Straight flush 50 0.00 50.00 180,863,592 0.000109 0.004537
Four aces 160 62.50 222.50 390,745,214 0.000235 0.043616
Four 2s - 4s 80 62.50 142.50 877,279,249 0.000528 0.062716
Four 5s-Ks 50 62.50 112.50 2,719,606,509 0.001637 0.153490
Full house 9 1.86 10.86 18,103,714,596 0.010899 0.098614
Flush 6 0.00 6.00 18,722,346,270 0.011271 0.056355
Straight 4 0.00 4.00 18,791,279,764 0.011313 0.037708
Three of a Kind 3 0.40 3.40 125,858,880,981 0.075768 0.214677
Two pair 1 0.00 1.00 206,090,004,807 0.124068 0.103390
Jacks or better 1 0.00 1.00 356,399,785,938 0.214556 0.178797
Nothing 0 0.00 0.00 912,928,218,992 0.549592 0.000000
Total       1,661,102,543,100 1.000000 0.969880

The following table is for 9-6 Double Double Bonus Poker. For a max bet, the game awards average bonus contributions as follows:

  • Three of a kind — 2.00
  • Full house — 9.29

All wins in the table are relative to each credit bet per play, assuming a max bet. The lower right cell shows a return to player of 99.18%. This was calculated as the product of the total win, probability, and 5/6. The reason for multiplying by 5/6, is the player must pay 1/6 of his total bet as a fee to invoke the feature.

Double Double Bonus Poker — 9-6

Hand Base
Win
Feature
Win
Total
Win
Combinations Probability Return
Royal flush 800 0.00 800.00 39,803,944 0.000024 0.015975
Straight flush 50 0.00 50.00 179,657,528 0.000108 0.004506
Four aces + 2-4 400 62.50 462.50 102,861,693 0.000062 0.023866
Four 2s - 4s + A-4 160 62.50 222.50 238,155,401 0.000143 0.026584
Four aces + 5-K 160 62.50 222.50 290,089,593 0.000175 0.032381
Four 2s-4s + 5-K 80 62.50 142.50 639,230,488 0.000385 0.045698
Four 5s-Ks 50 62.50 112.50 2,718,894,429 0.001637 0.153450
Full house 9 1.86 10.86 18,109,095,444 0.010902 0.098644
Flush 6 0.00 6.00 18,709,467,168 0.011263 0.056316
Straight 4 0.00 4.00 18,694,423,984 0.011254 0.037514
Three of a Kind 3 0.40 3.40 125,918,402,355 0.075804 0.214778
Two pair 1 0.00 1.00 206,162,927,217 0.124112 0.103427
Jacks or better 1 0.00 1.00 356,116,144,092 0.214385 0.178655
Nothing 0 0.00 0.00 913,183,389,764 0.549745 0.000000
Total       1,661,102,543,100 1.000000 0.991793

The following table is for 8-5 Super Double Double Bonus Poker. For a max bet, the game awards average bonus contributions as follows:

  • Three of a kind — 2.00
  • Full house — 9.69

All wins in the table are relative to each credit bet per play, assuming a max bet. The lower right cell shows a return to player of 99.85%. This was calculated as the product of the total win, probability, and 5/6. The reason for multiplying by 5/6, is the player must pay 1/6 of his total bet as a fee to invoke the feature.

Super Double Double Bonus Poker — 8-5

Hand Base
Win
Feature
Win
Total
Win
Combinations Probability Return
Royal flush 800 0.00 800.00 41,140,255 0.000025 0.016511
Straight flush 50 0.00 50.00 159,467,523 0.000096 0.004000
Four aces + 2-4 400 62.50 462.50 101,231,520 0.000061 0.023488
Four aces + J-K 320 62.50 382.50 106,359,309 0.000064 0.020409
Four 2s - 4s + A-4 160 62.50 222.50 247,268,692 0.000149 0.027601
Four Js-Ks + J-A 160 62.50 222.50 283,428,433 0.000171 0.031637
Four aces + 5-K 160 62.50 222.50 186,848,257 0.000112 0.020856
Four 2s-4s + 5-K 80 62.50 142.50 666,543,873 0.000401 0.047650
Four 5s-Ks 50 62.50 112.50 2,445,082,559 0.001472 0.137997
Full house 8 1.94 9.94 17,690,369,055 0.010650 0.088198
Flush 5 0.00 5.00 16,453,342,652 0.009905 0.041271
Straight 4 0.00 4.00 18,039,964,586 0.010860 0.036201
Three of a Kind 3 0.40 3.40 127,520,508,137 0.076769 0.217511
Two pair 1 0.00 1.00 207,899,626,869 0.125158 0.104298
Jacks or better 1 0.00 1.00 360,590,565,207 0.217079 0.180899
Nothing 0 0.00 0.00 908,670,796,173 0.547029 0.000000
Total       1,661,102,543,100 1.000000 0.998528

The following table is for 8-5 Super Double Bonus Poker. For a max bet, the game awards average bonus contributions as follows:

  • Three of a kind — 2.00
  • Full house — 8.75

All wins in the table are relative to each credit bet per play, assuming a max bet. The lower right cell shows a return to player of 99.85%. This was calculated as the product of the total win, probability, and 5/6. The reason for multiplying by 5/6, is the player must pay 1/6 of his total bet as a fee to invoke the feature.

Super Double Bonus Poker — 8-5

Hand Base
Win
Feature
Win
Total
Win
Combinations Probability Return
Royal flush 800 0.00 800.00 41,140,556 0.000025 0.016511
Straight flush 80 0.00 80.00 185,457,798 0.000112 0.007443
Four aces 160 62.50 222.50 380,518,438 0.000229 0.042474
Four Js-Ks 120 62.50 182.50 1,087,042,494 0.000654 0.099525
Four 2s-4s 80 62.50 142.50 887,406,566 0.000534 0.063440
Four 5s-10s 50 62.50 112.50 1,757,600,963 0.001058 0.099196
Full house 8 1.75 9.75 15,380,404,497 0.009259 0.075231
Flush 5 0.00 5.00 17,272,847,746 0.010398 0.043327
Straight 4 0.00 4.00 18,634,725,622 0.011218 0.037394
Three of a Kind 3 0.40 3.40 130,552,617,404 0.078594 0.222683
Two pair 1 0.00 1.00 184,286,171,322 0.110942 0.092452
Jacks or better 1 0.00 1.00 379,142,907,123 0.228248 0.190206
Nothing 0 0.00 0.00 911,493,702,571 0.548728 0.000000
Total       1,661,102,543,100 1.000000 0.989882

The following table is for 9-6 Triple Double Bonus Poker. For a max bet, the game awards average bonus contributions as follows:

  • Three of a kind — 2.00
  • Full house — 8.75

All wins in the table are relative to each credit bet per play, assuming a max bet. The lower right cell shows a return to player of 98.38%. This was calculated as the product of the total win, probability, and 5/6. The reason for multiplying by 5/6, is the player must pay 1/6 of his total bet as a fee to invoke the feature.

Triple Double Bonus Poker — 9-6

Hand Base
Win
Feature
Win
Total
Win
Combinations Probability Return
Royal flush 800 0.00 800.00 39,661,855 0.000024 0.015918
Straight flush 50 0.00 50.00 177,578,086 0.000107 0.004454
Four aces + 2-4 800 62.50 862.50 117,128,451 0.000071 0.050681
Four 2s - 4s + A-4 400 62.50 462.50 287,437,500 0.000173 0.066693
Four aces + 5-K 160 62.50 222.50 248,547,376 0.000150 0.027744
Four 2s-4s + 5-K 80 62.50 142.50 534,210,327 0.000322 0.038190
Four 5s-Ks 50 62.50 112.50 2,714,134,028 0.001634 0.153181
Full house 9 2.14 11.14 17,575,595,046 0.010581 0.098242
Flush 6 0.00 6.00 18,463,806,574 0.011115 0.055577
Straight 4 0.00 4.00 20,867,991,643 0.012563 0.041876
Three of a Kind 2 0.40 2.40 126,085,271,079 0.075905 0.151809
Two pair 1 0.00 1.00 205,077,698,721 0.123459 0.102882
Jacks or better 1 0.00 1.00 351,859,979,496 0.211823 0.176519
Nothing 0 0.00 0.00 917,053,502,918 0.552075 0.000000
Total       1,661,102,543,100 1.000000 0.983766

The following table is for 9-5 Triple Triple Bonus Poker. For a max bet, the game awards average bonus contributions as follows:

  • Three of a kind — 2.00
  • Full house — 11.25

All wins in the table are relative to each credit bet per play, assuming a max bet. The lower right cell shows a return to player of 98.86%. This was calculated as the product of the total win, probability, and 5/6. The reason for multiplying by 5/6, is the player must pay 1/6 of his total bet as a fee to invoke the feature.

Triple Triple Bonus Poker — 9-5

Hand Base
Win
Feature
Win
Total
Win
Combinations Probability Return
Royal flush 800 0.00 800.00 41,491,049 0.000025 0.016652
Straight flush 50 0.00 50.00 167,002,155 0.000101 0.004189
Four aces + 2-4 800 62.50 862.50 118,201,642 0.000071 0.051145
Four 2s - 4s + A 800 62.50 862.50 139,730,980 0.000084 0.060461
Four 2s - 4s + 2-4 400 62.50 462.50 134,327,056 0.000081 0.031167
Four aces + 5-K 160 62.50 222.50 251,988,282 0.000152 0.028128
Four 2s-4s + 5-K 80 62.50 142.50 535,954,292 0.000323 0.038315
Four 5s-Ks 50 62.50 112.50 2,722,196,227 0.001639 0.153636
Full house 9 2.25 11.25 17,614,730,679 0.010604 0.099415
Flush 5 0.00 5.00 17,029,580,836 0.010252 0.042717
Straight 3 0.00 3.00 16,844,625,732 0.010141 0.025352
Three of a Kind 2 0.40 2.40 126,084,344,859 0.075904 0.151808
Two pair 1 0.00 1.00 208,556,865,099 0.125553 0.104628
Jacks or better 1 0.00 1.00 360,710,934,075 0.217152 0.180960
Nothing 0 0.00 0.00 910,150,570,137 0.547920 0.000000
Total       1,661,102,543,100 1.000000 0.988571

There are also deuces wild and joker poker games available for Big City 4s. For purposes of progressive contributions and triggering the bonus, deuces and the joker are not wild. I have no analyzed these games yet, so you're on your own there.

To create a strategy for any game without wild cards, first go to my Video Poker Strategy Maker. Then, add to the full 5-coin wins whatever the average contribution is for a three of a kind and full house. For all four of a kind wins, add 312.5. That will generate the approriate strategy for that game.

Return Summary

The following table shows the games available at VideoPoker.com, average progressive contributions, and return. These are most likely the most liberal pay tables available for Big City 4s.

Summary

Game Pay Table Three of a Kind
Contribution
Full House
Contribution
Return
Jacks or Better 9-5 2.00 9.29 98.66%
Bonus Poker 8-5 2.00 10.00 99.41%
Bonus Poker Deluxe 8-5 2.00 8.75 98.56%
Double Bonus 9-6 2.00 9.29 96.99%
Double Double Bonus 9-6 2.00 9.29 99.18%
Super Double Double 8-5 2.00 9.69 99.85%
Super Double Bonus 8-5 2.00 8.75 98.99%
Triple Double Bonus 9-6 2.00 10.71 98.38%
Triple Triple Bonus 9-5 2.00 11.25 98.86%
Deuces Wild 25-15-9-4-4-3-2 2.00 2.50 ?
Deuces Wild Bonus 25-13-9-4-3-3 1.00 1.00 ?
Joker Poker (kings or better) 16-7-5-3-2 1.50 8.00 ?
Joker Poker (two pair or better) 16-8-5-4-2 1.50 8.00 ?

Vulturing

Any game with a progressive turns positive at some point, including this game (shut up, Wiz!). To find the breakeven point, the sum of the top two jackpots, for any game that doesn't involve wild cards, can be easily approximated as, 21300 - 20000r, where r = the return to player. For every 100 credits above that point, combined between the two jackpots, the return goes up by 0.5%.

The following table shows the breakeven point for the non-wild-card games shown in this page.

Breakeven Points

Game Pay Table Return Breakeven
Point
Jacks or Better 9-5 98.66% 1569
Bonus Poker 8-5 99.41% 1417
Bonus Poker Deluxe 8-5 98.56% 1590
Double Bonus 9-6 96.99% 1902
Double Double Bonus 9-6 99.18% 1464
Super Double Double 8-5 99.85% 1329
Super Double Bonus 8-5 98.99% 1496
Triple Double Bonus 9-6 98.38% 1632
Triple Triple Bonus 9-5 98.86% 1534

External Links

 

  • VideoPoker.com — Play Big City 4s for fun. A Gold level membership is required for this game.
  • Discussion about Big City 4s in my forum at Wizard of Vegas.

 


Written by: 

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