In a game of Texas Holdem, how often will you be dealt a Royal Flush (10, Jack, Queen, King and Ace all in the same suit) We’ve all done it. We’re in the casino, sitting at the poker table, and we have a reasonable hand but it’s just one card short of a great hand.

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Letting it ride on a low pair (9's or less) is definitely a bad bet. The house edge on a low pair with three cards is 6.37%. With four cards the house edge jumps to 45.83%. So don't be tempted to let it ride on low pairs.

Table game tournament strategy is very complicated. However, briefly, I would bide by time in the early hands of each round. Sometimes your opponents will all burn themselves out and you can advance without any effort. When it gets down to about five hands to go you'll need to make your move on any players way ahead of you. This is the time when you want to pull into first or go bust trying. It is also good to wait to save your big bets for when you act AFTER your biggest competitors.

This increases the house edge from 3.506% to 3.737%.

If you could see both the community cards, then your edge would be 42.06%. I don't know the advantage for one card, I'm afraid, but I am sure it would be high, especially if the second one were exposed.

Yes! In Mastering the Game of Let It Ride by Stanley Ko a section is devoted to this topic. Ko explains how the odds change if you have a 4-card straight or flush and can see extra cards. He does not indicate such adjustments at the three-card stage of the game. You can find this booklet at that Gambler's Book Club.

There are 2 directions to complete a 2-3-4 straight (A-2-3-4-5, 2-3-4-5-6), yet 3 directions to complete a 3-4-5 straight (A-2-3-4-5, 2-3-4-5-6, 3-4-5-6-7).

Assuming you are not peeking at any other player's cards, it doesn't make any difference. Have a good time in Reno.

You make a good point. In terms of what to expect in the short run then you should ignore the highest hands. I know video poker players sometimes disregard royal flushes when determining their short-term expectations. However, as a mathematical purist, I can't help but consider every possible outcome, regardless of how unlikely.

No. Unless you can actually see the other player’s cards and use that information correctly in your strategy then the number of other plays makes no difference.

Good question. In full play Three Card Poker the house edge on Pairplus is 2.32% and on Ante & Play is 3.37%. However the element of risk on Pairplus is still 2.32% while in Ante & Play it is 2.01%. I believe if comparing one game to another the element of risk is more appropriate. In other words comparing the expected loss to the total amount bet. In this case Ante & Play has the lower element of risk and is thus the better bet. So I would disagree with the writer of the article you mention. According to my house edge index the element of risk in Let it Ride is 2.85%, higher than that of Ante & Play.

What is the increased house advantage for letting the following hands 'ride' on Let it Ride?

1) three unsuited cards (A-K-Q and K-Q-J for example)
2) low connected straight flush cards (3-4-5)
3) something like J-10-7 of diamonds, spread of 5.

Thanks Mike, great site as usual (I’ll say it every time)

Thanks for the compliment. First, you’re supposed to 'let it ride' with suited 3-4-5 (three consecutive suited cards) and suited 7-10-J (three to a straight flush with 2 high cards and 2 gaps). My own strategy states this. Here is the effect on your expected return for each of the other hands, measured in units. For example if you bet three units of $1 raising on unsuited A-K-Q would cost you 18.62 cents.

Unsuited A-K-Q: -0.186224
Unsuited K-Q-J: -0.104592

This pay table has a house edge of 13.07%, the lowest I have heard of for Let it Ride. Still a sucker bet though.

For the sake of simplicity let’s assume each hand is dealt from a fresh deck. The probability of a four of a kind is 13*48/combin(52,5) = 624/2598960. The probability of exactly 3 out of 40 four of a kinds is combin(40,3)*p³*(1-p)³⁷ = 1 in 7378135, where p = 624/2598960. So that is more like a 1 in 7 million shot.

In 'Mastering the Game of Let it Ride' Stanley Ko addresses this topic. Ko says, most of the value in seeing other player’s cards is when you have a borderline hand of 4 to an outside straight with no high cards or JQKA. Viewing a single card should not encourage you to 'let it ride' but seeing a card that won’t help you should cause you to 'let it ride.' Ko doesn’t indicate that this can result in a negative house edge, and I doubt this chips away at the house edge much at all.

With a low pair your expected value on the initial bet is -7.40%. So if your original bet was $10 then letting it ride with a low pair will cost you an extra 74 cents.

The probability of a four of a kind in any given hand is 13*48/combin(52,5) = 0.0002401. Let’s assume in two hours you can play 120 hands. The probability of exactly two four of a kinds would be combin(120,2) × 0.0002401² × (1-0.0002401)¹¹⁸ = 0.000400095 = 1 in 2499.41.

It plays just like the real thing. The casinos use a shuffling machine, which I understand to be very good. My program shuffles the deck after every hand too.

It will be difficult finding $5 blackjack on the Strip on a weekend. You’ll probably have to settle for a low-roller casino like the Riviera, Sahara, Frontier, or Circus Circus. It will be a lot easier downtown. Let It Ride is slowly fading away, but if you find it the minimum unit is usually $5.

Please see the following table. This table also shows the house edge assumed for player rating purposes. My source is an executive with a major Strip casino here in Vegas, who wishes to remain anonymous.

Hands per Hour and Average House Edge

10 Person Poker Table Dimensions

Games	Hands/Hour	House Edge
Baccarat	72	1.2%
Blackjack	70	0.75%
Big Six	10	15.53%
Craps	48	1.58%
Car. Stud	50	1.46%
Let It Ride	52	2.4%
Mini-Baccarat	72	1.2%
Midi-Baccarat	72	1.2%
Pai Gow	30	1.65%
Pai Pow Poker	34	1.96%
Roulette	38	5.26%
Single 0 Roulette	35	2.59%
Casino War	65	2.87%
Spanish 21	75	2.2%
Sic Bo	45	8%
3 Way Action	70	2.2%

I had an interesting occurrence at a major high-end strip property and I was wondering how I should have handled the situation. A friend and I were the only players at a Let It Ride table. After playing for a while, the blue deck started getting stuck in the shuffler. After a while, the dealer asked the floor manager to replace the deck. Before replacing the deck, the dealer counted the cards, only 51 cards! Several recounts, looking all around, calling in another supervisor etc failed to produce the missing card.

My friend was down about $300 and I was up around $150 when all this happened. Since we are both ’full comp’ at the property, I did not raise a stink about this. The dealer seemed very worried about her job and we did not joke around at all. The supervisors and floor person did not say anything to us or offer any compensation. More or less, after a while, they replaced the deck and continued the game.

Personally, I figured that the odds say the missing card was a low card and it probably helped our odds of winning. My friend (who was down) thinks differently, that he should have been compensated. In the end, we did not raise the issue with the floor person. Was that correct? Should we have been aggressive given the situation? And, I am curious, assuming it was a random card, likely a low card, wouldn’t that actually have helped out odds during the time it was gone missing? Regards!

If you take a single card out of the deck randomly, the odds of Let it Ride do not change. This would be true of any casino game I can think of, where the cards are shuffled between hands. Without knowing the missing card, the effects of removal of bad cards and good cards exactly cancel one another out. So, complaining is not mathematically justified. Even if they found that it was a high card that got lost, it was still accidental. It could have just as easily been a low card that got lost. If it happened to me, I would have let it slide. I think an apology from somebody would be called for, but they probably didn’t want to, lest it give you more bargaining power if you did make a big scene over it.

For the benefit of other readers, in Let it Ride the player starts with three bets, and may pull back two of them if his cards don’t look good. If the minimum were $10, he would start with $30 in bets. If the player has a possible royal flush, proper strategy says to always stay in the game. A royal flush pays 1000 to 1. With a royal flush, the player would win 1000 to 1 on three bets of $10, or a total of $30,000 on bets of $10. However, the maximum aggregate payout is $25,000, so the 1000 to 1 is impossible to achieve, unless the player deviates from proper strategy, and doesn’t raise with hopes of royal.

I completely agree with your point. In my opinion it is false advertising to offer a win that is impossible to get under proper strategy. So, to Harrah’s I say “shame on you.” They can afford to pay a $25,000 jackpot.

Here in Nevada, an aggregate payout rule must be in plain view, and it cannot apply to wins less than 50 to 1 (Nevada Revised Statute 5.190). So, unless there is another statute I don’t know about, this would be legal here too. However, I am not aware of the same kind of impossible jackpot here. The maximum payout is also usually $25,000, but some of the classier casinos have higher maximum payouts. For example, the Wynn is at $75,000. The minimum bet here is usually $5, so as long as you stay at bets of $8 or less, the win for a royal will stay under $25,000. With a $1 side bet, the win would be exactly $25,000, so they would be allowed to deduct any wins of other players against you. My advice is to never bet so much that the aggregate payout rule might apply, on principle alone.

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%.

I asked two Las Vegas casino executives about this. The first one said their policy on all games with a jackpot-based side bet is to first pay the primary bets (i.e. not the side bets) to the full odds. The aggregate cap only applies to the side bets. In the event the side bet wins exceed the aggregate maximum, then winners are paid on a pro-rata basis, according to their win. For example, if the aggregate is $50,000, player 1 won $50,000, player 2 won $10,000, and player 3 won $100, then each player would get paid $50,000/($50,000+$10,000+$100)=83.19% of what he would get without the limit. The second casino executive, with another company, said the same thing except they pay the side bets in full and pro-rate the primary bets.

Let's assume 60 hands per hour, and a total of four players at the table. So, in 90 minutes that would be 1.5×60×4=360 hands. The probability of a straight flush is 4×9/combin(52,5) = 36/2,598,960 = 0.000013852. The probability of exactly two straight flushes in 360 hands is combin(360,2)* 0.000013852²×(1-0.000013852)³⁵⁸ = 1 in 81,055. Stranger things have happened.

Royal Flush Poker Hand

Video Poker Royal Flush

According to Beyond Counting (Exhibit CAA) by James Grosjean, if you can see every player card in a 7-player game, and make perfect use of the information, the house edge drops, but not more than the 3.51% house edge. As I state in my Let It Ride page, I would eyeball the table for the cards you need in the two borderline plays, four to an outside straight with no high cards, and four to an inside straight with four high cards. That would be of very marginal help.