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Last Updated: August 4, 2021

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Big Rollover Poker

Introduction

Big Rollover Poker is a variant of Ultimate Texas Hold 'Em by PureRNG, a software company that provides games to Internet casinos. The rules are the same as Ultimate, except the large raise may be made for 3x the Ante only, as opposed to up to 4x. This rule changes increases the house edge from 2.18% to 9.86%.

Big Rollover Poker

Rules

  1. The game is played with a single ordinary 52-card deck.
  2. The player must make an equal bet on both the Ante and Blind, and can also make an optional Trips bet.
  3. Two cards are dealt face down to the player and dealer. The player may look at his own cards.
  4. The player can check or make a Play bet equal to three times the Ante.
  5. The dealer turns over three community cards.
  6. If the player previously checked, then he may make a Play bet equal to two times his Ante. If the player already made a Play bet, then he may not bet further.
  7. Two final community cards are turned over.
  8. If the player previously checked twice, then he must either make a Play bet equal to exactly his Ante, or fold, losing both his Ante and Blind bets. If the player already raised he may not bet further.
  9. The player and dealer will both make the best possible hand using any combination of their own two cards and the five community cards.*
  10. The dealer will need at least a pair to open.
  11. The following table shows how the Blind, Ante, and Play bets are scored, according to who wins, and whether the dealer opens.

    Scoring Rules

    Winner Dealer Opens Blind Ante Play
    Player Yes Win Win Win
    Player No Win Push Win
    Dealer Yes Lose Lose Lose
    Dealer No Lose Push Lose
    Tie Yes or No Push Push Push
  12. Winning Ante and Play bets pay 1 to 1. Winning Blind bets pay according to the following pay table.

    Blind Bet Pay Table

    Player Hand Pays
    Royal flush 500 to 1
    Straight flush 50 to 1
    Four of a kind 10 to 1
    Full house 3 to 1
    Flush 3 to 2
    Straight 1 to 1
    All other Push
  13. The Trips bet will pay according to the poker value of the player's hand regardless of the value of the dealer's hand, according to one of the Trips bet pay tables below.

Analysis

There are 52 possible outcomes of each hand. The table below shows the probability of each and the contribution to the total return, assuming optimal strategy. A 3X raise is referred to as a "large raise," a 2X raise as "medium," and 1x as "small."

Return TableExpand

Raise Dealer
Qualifies
Player Hand Winner Pays Combinations Probability Return
Large Yes Less than straight Player 4 3,671,050,165,880 0.131987 0.527946
Large Yes Straight Player 5 246,174,692,160 0.008851 0.044254
Large Yes Flush Player 5.5 241,047,929,080 0.008666 0.047666
Large Yes Full house Player 7 295,405,180,920 0.010621 0.074346
Large Yes Four of a kind Player 14 23,008,208,760 0.000827 0.011581
Large Yes Straight flush Player 54 1,818,135,760 0.000065 0.003530
Large Yes Royal flush Player 504 596,356,920 0.000021 0.010806
Large No Less than straight Player 3 1,556,797,035,840 0.055972 0.167916
Large No Straight Player 4 81,416,649,960 0.002927 0.011709
Large No Flush Player 4.5 50,874,988,680 0.001829 0.008231
Large No Full house Player 6 0 0.000000 0.000000
Large No Four of a kind Player 13 0 0.000000 0.000000
Large No Straight flush Player 53 229,686,840 0.000008 0.000438
Large No Royal flush Player 503 90,386,280 0.000003 0.001635
Large 0   Push 0 285,142,270,600 0.010252 0.000000
Large Yes   Dealer -5 3,931,554,359,920 0.141353 -0.706763
Large No   Dealer -4 102,655,952,400 0.003691 -0.014763
Medium Yes Less than straight Player 3 2,114,839,654,764 0.076036 0.228107
Medium Yes Straight Player 4 133,100,158,992 0.004785 0.019142
Medium Yes Flush Player 4.5 152,618,008,784 0.005487 0.024692
Medium Yes Full house Player 6 289,401,836,880 0.010405 0.062430
Medium Yes Four of a kind Player 13 18,537,793,620 0.000666 0.008664
Medium Yes Straight flush Player 53 2,704,129,504 0.000097 0.005153
Medium Yes Royal flush Player 503 112,333,500 0.000004 0.002031
Medium No Less than straight Player 2 1,083,763,469,592 0.038965 0.077930
Medium No Straight Player 3 45,053,788,356 0.001620 0.004860
Medium No Flush Player 3.5 38,820,798,396 0.001396 0.004885
Medium No Full house Player 5 0 0.000000 0.000000
Medium No Four of a kind Player 12 0 0.000000 0.000000
Medium No Straight flush Player 52 358,131,456 0.000013 0.000670
Medium No Royal flush Player 502 8,830,620 0.000000 0.000159
Medium     Push 0 191,611,691,060 0.006889 0.000000
Medium Yes   Dealer -4 1,841,155,221,088 0.066196 -0.264783
Medium No   Dealer -3 7,978,353,108 0.000287 -0.000861
Small Yes Less than straight Player 2 1,375,033,295,072 0.049437 0.098874
Small Yes Straight Player 3 395,087,247,768 0.014205 0.042614
Small Yes Flush Player 3.5 190,959,227,136 0.006866 0.024030
Small Yes Full house Player 5 43,297,986,840 0.001557 0.007784
Small Yes Four of a kind Player 12 859,737,984 0.000031 0.000371
Small Yes Straight flush Player 52 1,962,591,576 0.000071 0.003669
Small Yes Royal flush Player 502 42,135,660 0.000002 0.000760
Small No Less than straight Player 1 720,579,458,748 0.025907 0.025907
Small No Straight Player 2 136,018,223,484 0.004890 0.009781
Small No Flush Player 2.5 40,911,000,804 0.001471 0.003677
Small No Full house Player 4 0 0.000000 0.000000
Small No Four of a kind Player 11 0 0.000000 0.000000
Small No Straight flush Player 51 269,696,304 0.000010 0.000495
Small No Royal flush Player 501 6,109,020 0.000000 0.000110
Small     Push 0 418,339,128,088 0.015041 0.000000
Small Yes   Dealer -3 2,700,150,685,692 0.097079 -0.291238
Small No   Dealer -2 47,223,220,344 0.001698 -0.003396
Fold -2 5,335,144,079,760 0.191816 -0.383633
Total   27,813,810,024,000 1.000000 -0.098585

The lower right cell shows a house edge of 9.86% per ante bet. What this means, for example, is if you bet $1 and both the Ante and Blind initially, then you can expect to lose 9.86 cents on average. However for comparison to other games I believe the Element of Risk is more appropriate to look at. The average total amount bet by the end of the hand is 3.775177658 times the ante bet. So the element of risk would be 9.86%/3.775177658 = 2.61%.

Wizard Strategy

The following is my "Wizard Strategy" for Big Rollover Poker, which is the same as for Ultimate Texas Hold 'Em®.

Large Raise: The following table shows when to make the 3X raise.

Medium Raise: Make the 2X raise with any of the following:

  • Two pair or better.
  • Hidden pair*, except pocket deuces.
  • Four to a flush including a hidden 10 or better to that flush
 

* Hidden pair = Any pair with at least one card in your hole cards (thus the pair is hidden to the dealer).

Small Raise: Make the 1X raise with any of the following, otherwise fold:

  • Hidden pair or better.
  • Less than 21 dealer outs beat you.

Example

What I mean by an "out" is a dealer hole card that will cause you to lose. Let's look at this situation as an example.

In the example above, there 15 cards that will pair the dealer and beat you (three suits each of K, 7, 2, A, and 10). Then there are the two ranks (jacks and queens) which will out-kick the player. All four jacks and queens remain in the decks, so that is 2×4=8 more cards that will beat you. So, we're up to 15+8=23. We don't count the other three nines because those will result in a push. So, because there are only 23 outs (21 or more), we fold.

BTW, using my Ultimate Texas Hold 'Em® calculator, we see that the expected value of raising this hand is -2.136364, which is less than the -2 of folding.

I get asked a lot about combinations of cards that will beat the player. For example, any two dealer spades that would give the dealer a flush in the example above. The answer is no. It would really make things complicated if the strategy accounted for double-card combinations that would beat the player.

Side Bet

The following side bet is offered, which pays based on the poker-value of the player's hand only. The lower right cell shows a house edge of 6.18%.

Side Bet Pay Table

Player Hand Combinations Pays Probability Return
Royal flush 4324 50 0.000032 0.001616
Straight flush 37260 40 0.000279 0.01114
Four of a kind 224848 20 0.001681 0.033613
Full house 3473184 7 0.025961 0.181727
Flush 4047644 6 0.030255 0.18153
Straight 6180020 5 0.046194 0.230969
Three of a kind 6461620 3 0.048299 0.144896
All other 113355660 -1 0.8473 -0.8473
Total 133784560   1 -0.061808

Conclusion

Please do not play this game. As mentioned in the introduction, limiting the large raise to 3x increases the house edge from 2.18% to 9.86%. This is unforgivable and merits the Wizard's finger wagging of shame.


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