3/23/2022
18
  1. What Is Better Quad Aces Or Royal Flush
  2. Does Four Aces Beat A Royal Flush
In the 2008 World Series of Poker Motoyuki Mabuchi's quad aces were beaten by Justin Phillip's Royal flush. I have a simple question about the odds of this occurring. ESPN and others quoted it as 1 in approximately 2.7 billion. It appears to me that they simply took the published odds of quads occurring, and multiplied them by the odds of a royal flush occurring. Is this the correct method of calculation?

An ace high straight flush, such as Ad Kd Qd Jd 10d is called a royal flush, and is the highest ranked hand in standard poker, without wild cards. Four of a kind Also known as quads, four of a kind is a hand like 7h 7s 7c 7d 2s, that has four cards of the same rank, and one other card. Autoplay is paused. You're signed out. Videos you watch may be added to the TV's watch history and influence TV recommendations. To avoid this, cancel and sign in to YouTube on your. If playback doesn't begin shortly, try restarting your device. You're signed out. Videos you watch may be added to the TV's watch history and influence TV. Instead, game designers turned to four-ace hands, and also ramped up the paybacks on other fours-of-a-kind. In Double Bonus Poker, four aces come up about once per 4,406 hands, and four 2s, 3s or 4s about once per 1,896. The aces pay 800 coins for a five-coin bet, and the 2s, 3s or 4s pay 400.

I disagree with the 1 in 2.7 billion figure too. As you said, they seemed to calculate the probabilities independently for each player, for just the case where both players use both hole cards, and multiplied. Using this method I get a probability of 0.000000000341101, or about in 1 in 2.9 billion. Maybe the one in 2.7 billion also involves compounding a rounding error on both player probabilities. They also evidently forgot to multiply the probability by 2, for reasons I explain later.

There are three ways four aces could lose to a royal flush, as follows.

Case 1: One player has two to a royal flush, the other has two aces, and the board contains the other two aces, the other two cards to the royal, and any other card.

Example:

Player 1:
Player 2:
Board:

In most poker rooms, to qualify for a bad-beat jackpot, both winning and losing player must make use of both hole cards. This was also the type of bad beat in the video; in fact, these were the exact cards.

Case 2: One player has two to a royal flush (T-K), the other has one ace and a 'blank' card, and the board contains the other three aces and the other two cards to the royal.

Example:

Player 1:
Player 2:
Board:

Flush

Case 3: One player has one to a royal flush (T-K) and a blank card, the other has two aces, and the board contains the other two aces and the other three cards to the royal flush.

Example:

Player 1:
Player 2:
Board:

The following table shows the number of combinations for each case for both players and the board. The lower right cell shows the total number of combinations is 16,896.

Bad Beat Combinations

CasePlayer 1Player 2BoardProduct
1243443,168
22413213,168
3704312,112
Total8,448

However, we could reverse the cards of the two players, and still have a bad beat. So, we should multiply the number of combinations by 2. Adjusting for that, the total qualifying combinations is 2 × 8,448 = 16,896.

The total number of all combinations in two-player Texas Hold ’Em is combin(52,2) × combin(50,2) × combin(48,5) = 2,781,381,002,400. So, the probability of a four aces losing to a royal flush is 8,448/2,781,381,002,400 = 0.0000000060747, or about 1 in 165 million. The probability of just a case 1 bad beat is 1 in 439 million. The simple reason the odds are not as long as reported in that video is that the two hands overlap, with the shared ace. In other words, the two events are positively correlated.

It is my understanding that the 'racinos' at Monticello and Yonkers, New York, are known as 'Video Lottery Terminals.' I read that they are not true slot/video poker machines, because they do not use a random number generator, but are connected to a central computer in Albany, that controls the outcome of the game. For example, in video poker if you are initially dealt a four of a kind and you discard them all, it will reappear as a winner, since the central computer was programmed for your machine to get a four of a kind. Therefore, any strategy is useless. Is this correct?

You are absolutely right, according to the paper Telling the Truth about New York Video Poker. The player’s outcome is indeed predestined. Regardless of what cards the player keeps, he can not avoid his fate. If the player tries to deliberately avoid his fate, the game will make use of a guardian angel feature to correct the player's mistake. I completely agree with the author that such games should warn the player that they are not playing real video poker, and the pay table is a meaningless measure of the player's actual odds. It also also be noted these kinds of fake video poker machines are not confined to New York.

I use your great site quite often, thanks! I found a new pay table at the Borgata in Atlantic City, for the Three Card Bonus bet in Let It Ride. They implemented these very recently, to the point the dealers were struggling to remember the new odds. Here is the new pay table:

Mini Royal: 50 to 1
Straight flush: 40 to 1
Three of a kind: 30 to 1
Straight: 6 to 1
Flush: 4 to 1
Pair: 1 to 1

I am curious how it impacts the overall house edge.

That is not bad for a side bet. I show the house edge is 2.14%.

Hi Wizard, I came across a new online casino, and decided to give it a try. I was playing at their craps table and noticed that on 20 rolls of the dice, the field bet lost 16 times, and won only 4 times. The sequence went like this: L6,W1,L1,W1,L1,W1,L2,W1,L6. I realize this is a small sample, but is it enough to pass some sort of assessment as to whether this new casino is legit or not?

The probability of an event with probability p happening x times, out of a possible n, is combin(n,x) × px × (1-p)(n-x). In this case, p=4/9, x=4, and n=20. Here is the probability for all possible number of number of field rolls out of 20:

Bad Beat Combinations

WinsProbability
00.000008
10.000126
20.000954
30.004579
40.015567
50.039851
60.079703
70.127524
80.165782
90.176834
100.155614
110.113174
120.067904
130.033430
140.013372
150.004279
160.001070
170.000201
180.000027
190.000002
200.000000
Total1.000000

Taking the sum for 0 to 4, the probability is 2.12%. So, this could have easily happened in a fair game.

Thank you for your entertaining collection of math puzzles. My girlfriend and I came up with this variation on the pirate puzzle. What if all the pirates are of equal rank, and in each round the proposer of the division is chosen by lot? In this variation, assume that each pirate’s highest priority is to maximize his expected amount of coins received. I have what I think is the solution, but perhaps you’d like to try your hand at it first. Thanks again.

You’re welcome. If there are only two pirates left, then the one chosen to make a suggestion has no hope, because the other pirate will vote no. The one drawn will get zero, and the other all 1000. So, before the draw, the expected value with two pirates left is 500 coins.

At the three pirate stage, the drawn pirate should suggest giving one of the other pirates 501, and 499 to himself. The one getting 501 will vote yes, because it is more than the expected value of 500 by voting no. Before the draw, with three pirates left, you have a 1/3 chance each of getting 0, 499, or 501 coins, for an average of 333.33.

Flush

At the four pirate stage the drawn pirate should choose to give 334 to any two of the other pirates, and 332 to himself. That will get him two ’yes’ votes from the pirates getting 334 coins, because they would rather have 334 than 333.33. Including your own vote, you will have 3 out of 4 votes. Before the draw, the expected value for each pirate is the average of 0, 334, 334, and 332, or 1000/4=250.

By the same logic, at the five pirate stage, the drawn pirate should choose to give 251 to any two pirates, and 498 to himself. Unlike the original problem, it isn’t necessary to work backwards. Just divide the number of coins by the number of pirates, not including yourself. Then give half of them (rounding down) that average, plus one more coin.

Royal Aces Poker video poker is a 5 coin game that players can win up to 4000 coins. The 4000 coin jackpot is triggered when you make either a royal flush or 4 aces.

The game also pays off on traditional poker hands with higher payouts for hands with 4 of a kind.

How to Play Royal Aces Bonus Poker Video Poker

As with most video poker games, Royal aces Bonus Poker video poker is based on 5 card draw poker. The game deals you 5 cards and you must decide which to keep and which to discard in order to make the best hand. Except for the few cases that we will explain later in this article, the ranking of the hands are essentially the same as a standard poker hand.

In this game, aces can be high or low. The goal is to get 4 of them for the big payout. However, getting quads or 4 of a kind, is to your benefit.

Also, unless you have a pair of aces, single pairs are useless as a final hand, they can be great as a starting point to get your quads, however.

While the standards poker hand ranking technically do apply to Royal Aces Bonus Poker video poker, looking at it from a payout standpoint (which we will go over in our odds and pay tables section) the following ranking should be used as a best to worse scenario:

  • 4 Aces: All four aces in the deck.
  • Royal Flush: ace, King, Queen, Jack, 10 all of the same suit
  • Straight Flush: 5 cards in consecutive order all of the same suit. For example 6, 7, 8, 9, and 10 all of clubs
  • 4 of a Kind (2s, 3s, or 4s): 4 matching rank cards of either 2s, 3s, or 4s.
  • 4 of a Kind (5s through Kings): 4 matching rank cards of 5s, 6s, 7s, 8s, 9s, 10s, Jacks, Queens or Kings
  • Full House: 2 cards of matching rank along with 3 matching cards of a different match rank. For example 2 9s and 3 Jacks.
  • Flush: 5 cards of any rank with a matching suit.
  • Straight: 5 cards in consecutive order with different suits, i.e. 4, 5, 6, 7, and 8 with mixed suits.
  • 3 of a Kind: 3 cards of the same rank. For example: 3 9s.
  • 2 Pair: a set of 2 cards of matching rank along with a second set of 2 cards with a different matching rank. For example 2 3s and 2 Queens.
  • 1 Pair: In this game, the only pair that wins is a pair of aces.

And while it’s a separate game, the game play works the same as Super Aces Bonus Poker video poker. The differences between the 2 games lie in the fact that Royal aces Bonus Poker video poker has higher payouts.

Both International Gaming Technologies (IGT) and Action Gaming offer Royal Aces Bonus Poker video Poker games. Some sites offer it as part of a progressive jackpot (which is won only on Royal Flushes, despite the quad aces bonus).

A progressive jackpot, for those who are new to the game, is a jackpot that is networked with other sites and casinos. It may include both brick and mortar as well as online games. The progressive jackpot only comes into play when you place the maximum bet of 5 coins and get a Royal Flush.

Both IGT and Action Gaming allow you to play 50 or 100 hands at one time. When a game offers these options, 1 hand is dealt. When you discard and receive new cards, each of the 50 or 100 hands will get different replacement cards.

The multiple play feature can be overwhelming for novice players. If you are new to these types of games, it’s recommended that you learn some advanced strategies before playing these types of games.

Depending on the version of Royal aces Bonus Poker video poker you are playing and the video poker site you are playing on, the return on your bets could be as high as 99.2%.

Aces

Here is a list of common variations and their expected return rates:

  • 10-5 Royal Aces Bonus Poker 99.2%
  • 9-5 Royal Aces Bonus Poker 98.1%
  • 8-5 Royal Aces Bonus Poker 97.05%
  • 7-5 Royal Aces Bonus Poker 95.99%
  • 6-5 Royal Aces Bonus Poker 94.93%

The information above was culled from Michael Shackleford’s Wizard of Odds site, which is a great resource for poker odds and return rates. His site is an encyclopedia of this type of information.

From the variations listed above, the most common of the 5 is the 9-5 Royal Aces Bonus Poker version. Here is the pay table for 9-5 Royal Aces Bonus Poker Video poker:

Quad aces loses to royal flush
1 Coin Play2 Coin Play3 Coin Play4 Coin Play5 Coin Play
Royal Flush25050075010004000
Straight Flush100200300400500
4 Aces8001600240032004000
4 of a Kind (2s, 3s or 4s)80160240320400
4 of a Kind (5s through Ks)50100150200250
Full House918273645
Flush510152025
Straight48121620
3 of a Kind3691215
2 Pair12345
Pair of Aces12345

This list now shows you why in that last section we ranked the winning hands as we did as the best pay offs come from having 4 aces then a royal flush, where in normal poker, 4 of a kind would rank 2 levels below a Royal Flush.

If you are more accustomed to “traditional” poker strategies and try to employ them in Royal Aces Bonus Poker, you may find yourself substantially lighter in the wallet when leaving the game than when you started. Royal Aces has specific techniques that you should start to employ from the get-go to minimize any losses that you may incur. Keep in mind that while the big 4000 coin payout is enticing, statistically 70% of your hands will not make you money, and that can increase if you don’t carefully craft your strategies and tactics.

One of the first strategies we can recommend is if you get a pair of aces and can make a straight flush by discarding the ace, don’t do it. Go for the 4 aces. A straight flush will pay off 8 times less than 4 aces on all levels of play. If you can make a royal flush, the call is yours on a 5 coin bet, but if you bet less than 5 coins, go for the quad aces.

In cases where you have a pair of anything other than an ace, for example a pair of 3s, it’s best to shoot for a 4 of a kind. Since pairs have no payoff value by themselves, you really have nothing to lose. An exception would be if you only needs one card for a royal flush or straight flush and had a pair, it would be a wise choice to break up the pair and go for the royal flush or straight flush as those will pay out more than the 2 4 of a kind payouts.

If you have a full house and 2 or 3 of the cards are aces, try for the 4th ace as the payout is a little less than 90 times more. If you have a full house and you don’t have aces, try for the quad. The lower ranked cards pay out almost 9 times more and the higher ranked cards pay out almost 6 times more than a full house.

What Is Better Quad Aces Or Royal Flush

As a rule of thumb, or as a beginner’s strategy, the best payouts are for 4 aces and 4 of a kind, so when in doubt, go for the quad.

Royal Aces Bonus Poker video poker is the definition the adage “the bigger the risk, the greater the reward”. You can walk away a winner with 45 coins for a full house or make 90 times the winnings for drawing the 4th ace.

Does Four Aces Beat A Royal Flush

Learn the strategies and tactics of the game. Learn the variations and the odds. Once you feel comfortable, try playing on a site that offers free play. While it may differ from a real money game, it can give you the feel of the game. It will also allow you to test the strategies and see what works best for you. After you have mastered the free play, they try your hand at a real money video poker site.