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Reason #4 why the Wizard likes Bovada:
One-Stop Shopping
Bovada offers the triple crown of gambling: casino, poker, and sports. Many other casinos have tacked on poker as an afterthought, and many poker rooms have tacked on a casino as an afterthought, and the lack of attention shows, sometimes painfully. And very few of these sites let you make sports wagers.
But Bovada doesn’t just offer all three, they do each one well, and everything’s integrated. It’s easy to play all three off one deposit, off just one account.
Another nice thing about Bovada is that you don’t need a separate account to play casino games with fake money. In fact you do not even need an account for that at all, you can just click over there and play. Finally, Bovada usernames are only six or seven characters long making them possible to remember. By contrast some competitors’ usernames are extremely long and cumbersome.
Crazy 4 Poker
Last Update: June 24, 2004
Introduction
Crazy 4 Poker is a new poker variation invented by Roger Snow and is marketed by Shufflemaster. The game bears some similarities to Three Card Poker but as the name says, is based on four cards. With proper strategy the element of risk is only 1.09%, which is comparitively good for the new generation of casino games.
Normally I do all the game analysis on this site but this game is an exception. The math was done by Stanley Ko of and provided to me with permission to publish on this site by Shufflemaster.
Rules
- Three initial bets are available: The Ante, Super Bonus, and the Queens Up. The player must bet equal amounts on the Ante and Super Bonus. The Queens Up may be any amount.
- All players and dealer get five cards each.
- Players making the Ante and Super Bonus bets must decide to fold or raise.
- If the player folds he forfeits all bets.
- If player raises he must raise at least the amount of the ante. With a pair of aces or better the player may raise up to three times the Ante amount. With less than a pair of aces the player must raise exactly the amount of the ante.
- Players then keep their best four cards and discard one.
- Following is the ranking of hands from lowest to highest: high card, pair, two pair, straight, flush, three of a kind, straight flush, four of a kind.
- After all decisions have been made the dealer will turn over his cards and select the best four out of five.
- The player's hand shall be compared to the dealer's hand, the higher hand winning.
- The dealer must have a king high or better to qualify. If the dealer does not qualify the player shall win even money on the Raise and the Ante shall push.
- If the dealer's hand is higher the player shall lose the Ante and Raise.
- If the two hands are equal the Ante and Raise shall push.
- If the player's hand is higher the Ante and Raise shall pay one to one.
- The Super Bonus bet shall pay if the player has a straight or higher, regardless of the value of the dealer's hand. The Super Bonus Pay Table below shows what each hand pays.
- If the player (1) folds or (2) has less than a straight and loses to the dealer then the Super Bonus shall lose.
- If (1) the player has less than a straight and (2) the dealer doesn't qualify or the player beats the dealer then the Super Bonus shall push.
- Another bet is available (similar to the Pairplus in Three Card Poker) based only on the player's four card hand called the Queens Up. Four pay tables are available as indicated below.
|
Super Bonus Pay Table |
|
|
Hand |
Pays |
| Four aces | 200 to 1 |
| Four 2-K | 30 to 1 |
| Straight flush | 15 to 1 |
| Three of a kind | 2 to 1 |
| Flush | 1.5 to 1 |
| Straight | 1 to 1 |
|
Queens Up Pay Table |
||||
|
Hand |
Table 1 | Table 2 | Table 3 | Table 4 |
| Four of a kind | 50 to 1 | 50 to 1 | 50 to 1 | 50 to 1 |
| Straight flush | 30 to 1 | 40 to 1 | 30 to 1 | 40 to 1 |
| Three of a kind | 9 to 1 | 8 to 1 | 8 to 1 | 7 to 1 |
| Flush | 4 to 1 | 4 to 1 | 4 to 1 | 4 to 1 |
| Straight | 3 to 1 | 3 to 1 | 3 to 1 | 3 to 1 |
| Two pair | 2 to 1 | 2 to 1 | 2 to 1 | 2 to 1 |
| Pair of queens or better | 1 to 1 | 1 to 1 | 1 to 1 | 1 to 1 |
Strategy
Stanley Ko's "simplified strategy" is as follows.
- Fold if the highest 4-card hand is less than K-Q-8-4.
- Raise 1 unit if the highest 4-card hand is K-Q-8-4 to a pair of kings.
- Raise 3 units with pair of aces or higher.
The cost of using the simplified strategy compared to optimal strategy is only 0.0002% of the total wager.
Analysis
The next table shows the probability of each hand and the return under pay table 3 of the Queens Up side bet. I chose table 3 because that is the one I noticed at a casino here in Las Vegas. The lower right cell shows a house edge of 5.32%.
|
Return for Queens Up Pay Table 3 |
||||
|
Hand |
Combinations | Probability | Pays | Return |
| Four of a kind | 624 | 0.00024 | 50 | 0.012005 |
| Straight flush | 2072 | 0.000797 | 30 | 0.023917 |
| Three of a kind | 58656 | 0.022569 | 8 | 0.180552 |
| Flush | 114616 | 0.044101 | 4 | 0.176403 |
| Straight | 101808 | 0.039173 | 3 | 0.117518 |
| Two pair | 123552 | 0.047539 | 2 | 0.095078 |
| Pair of queens or better | 242916 | 0.093467 | 1 | 0.093467 |
| Nothing | 1954716 | 0.752115 | -1 | -0.752115 |
| Total | 2598960 | 1 | -0.053175 | |
The next table shows the house edge according to all four Queens Up pay tables.
|
Queens Up House Edge |
|
|
Pay Table |
House Edge |
| 1 | 3.06% |
| 2 | 4.52% |
| 3 | 5.32% |
| 4 | 6.78% |
The next table shows the return of the Ante bet under optimal player strategy.
|
Return for Ante bet |
||||
| Event | Probability | Pays | Return | |
| Player folds | 0.235073 | -1 | -0.235073 | |
| Player raises 1 unit and wins | 0.215511 | 2 | 0.431022 | |
| Player raises 1 unit and ties | 0.000206 | 0 | 0 | |
| Player raises 1 unit and loses | 0.274169 | -2 | -0.548338 | |
| Player raises 1 unit and dealer doesn't qualify | 0.08942 | 1 | 0.08942 | |
| Player raises 3 units and wins | 0.139517 | 4 | 0.558067 | |
| Player raises 3 units and ties | 0.000073 | 0 | 0 | |
| Player raises 3 units and loses | 0.017084 | -4 | -0.068335 | |
| Player raises 3 units and dealer doesn't qualify | 0.028948 | 3 | 0.086844 | |
| Total | 1 | 0.313607 | ||
The next table shows the return of the Super Bonus bet under optimal player strategy.
|
Return for Super Bonus bet |
||||
| Event | Probability | Pays | Return | |
| Four aces | 0.000018 | 200 | 0.003694 | |
| Four 2-K | 0.000222 | 30 | 0.006649 | |
| Straight flush | 0.000797 | 15 | 0.011959 | |
| Three of a kind | 0.022569 | 2 | 0.045138 | |
| Flush | 0.044101 | 1.5 | 0.066151 | |
| Straight | 0.039173 | 1 | 0.039173 | |
| Player loses with less than straight or folds | 0.520558 | -1 | -0.520558 | |
| Other | 0.372562 | 0 | 0 | |
| Total | 1 | -0.347795 | ||
So, the player has an expected return of 0.313607 on the Ante bet and -0.347795 on the Super Bonus. The net player expected return on these two bets is 0.313607-0.347795 = -0.034189. If we were to define the house edge as the expected player loss to either one of the Ante or Super Bonus bets then the answer would be 3.42%. For example if the player bet $1 on the Ante and $1 on the Super Bonus then he could expect to lose 3.42 cents overall. If we were to define the house edge as the expected loss of the sum of both wagers then we would divide by 3.42% by 2 to get 1.71%. The overall average wager is 3.136171 units, thus the element of risk (expected loss divided by total wager) is 1.09%.
Note: There is also a similar game called Four Card Poker.
Links
Shufflemaster's official web site for Crazy 4 Poker 
.