Question 1

From your Let it Ride section, you do not list a low pair as a good hand to "let it ride" on. Just how bad of a bet would it be to go contrary to your advice?

Accepted Answer

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.

Question 2

I had the good fortune of hitting four of a kind at a local casino, and was subsequently invited to play in a Let it Ride tournament, where approximately 300 players will compete for quite substantial prize money. My question is, what do you think would be the optimal strategy? Each player is to be given $5,000 in play chips, and the minimum bet will be $25 a hand. There will be "heats", with the first round having all but 100 eliminated, second all but 25, third will have 6 left, and then the final round.

Accepted Answer

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.

Question 3

Recently, I visited one of the Indian casinos in our state (had an out-of-towner visiting.) They have Let It Ride. However, the payoff is only 500 to 1 on the Royal Flush. I would like to know what that does to the house edge on the game?

Accepted Answer

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

Question 4

I would like to know what the players edge would be in Let It Ride if he can see can see both the community cards and then if he can only see one of them? I was told that you could figure it out.

Accepted Answer

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.

Question 5

Has anyone done work on the optimal betting strategies in "Let It Ride" w/ additional information? I know the casinos say players may not look at other players hands, but in practice, it seems that most players know what at least two other players are holding. I may want to go for an inside straight if I know that at least six of the cards on the table are NOT what I need to pull.

Accepted Answer

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.

Question 6

I was wondering why you recommend folding a 2-3-4 straight flush hand in let it ride? I understand folding A-2-3 as there is only "one side" to match. However, 2-3-4 seems the same as any other outside straight?

Accepted Answer

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).

Question 7

I will be visiting Reno in the near future and have frequented your site in regards to Let It Ride and craps. I seem to have more luck at LIR than Craps. What effect does the number of players at LIR have on the probability of winning, if any?

Accepted Answer

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

Question 8

I understand the calculations made to determine the house advantage for the various games. My question is most applicable to the games with a large payout (for example, a royal flush in Let It Ride). Would it not be more reasonable to calculate the "house advantage" with the royal flush excluded? While hitting the royal is possible, it is extremely unlikely for the average player. Would this modified house advantage be more applicable to the average player? Thanks for the great site.

Accepted Answer

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.

Question 9

I was playing &rsquo;let it ride&rsquo; on a video machine last week. Someone told me I would have better odds if I played at a table with 6 players because more cards are out (20 instead of 5). Is he correct?

Accepted Answer

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

Question 10

Wizard, I have just read an article on another site that was talking about Three Card Poker. The author called the "Pair Plus " bet a sucker bet ,compared to the "ante" bet. Of the two bets , I thought the "ante" bet was more of a sucker bet because of its higher house edge. Also, what is the element of risk in Three Card Poker , compared to Let it Ride , assuming the player is starting with $5 bets in the three betting circles for Let It Ride, and $5 in the Pair plus and ante bet in Three Card Poker?

Accepted Answer

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.

Question 11

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)

Accepted Answer

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

Question 12

This past weekend I played Let it Ride at El Dorado in Reno. Side Bet payout was 20000 (Royal), 2000 (Straight Flsh), 200 Four, 75 Full, 50 Flush, 25 Straight, 5 Three, 4 Two pair, 1 High pair. Did not see this covered on House edge what would edge be?

Accepted Answer

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.

Question 13

I know that mathematically anything is possible, but the other night at the casino I think that I witnessed something that would be a billion to 1 shot, not that those don?t ever happen. Here is what happened: In the course of 40 hands (40 single 3 card deals about 8 rounds with 5 players) at a let it ride table 3 four of a kinds were dealt. With a four of a kind being about 4100 to 1 what would be the odds of three of them being dealt within 40 deals? Please answer as this is killing me. Long time fan

Accepted Answer

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.

Question 14

I was wondering what happens to the house advantage if you could view all 7 player&rsquo;s hands. Would this result in a negative house advantage?

Accepted Answer

In "Mastering the Game of Let it Ride" Stanley Ko addresses this topic. Ko says, most of the value in seeing other player&rsquo;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&rsquo;t help you should cause you to "let it ride." Ko doesn&rsquo;t indicate that this can result in a negative house edge, and I doubt this chips away at the house edge much at all.

Question 15

I trust you Let it Ride advice is correct but I still like raising on a low pair with three cards. Often I have seen these turn into paying hands. So how much is it costing me to raise on low pairs?

Accepted Answer

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.

Question 16

What is the probability of getting two four of a kinds in a two hour period playing Let it Ride?

Accepted Answer

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.

Question 17

Hi I’ve been playing the Java Let It Ride Game on your website and it’s really fun. Thanks for putting it out on your website. I was wondering, is it fairly accurate as to how a game in a live casino would be played? And does it use a virtual new shuffled deck for each new hand that is dealt?

Accepted Answer

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.

Question 18

I am going to Las Vegas next weekend and like to play $5 blackjack & Let It Ride on the tables. Will I be able to find an open $5 table on a weekend or should I plan on bringing more funds than usual with me? If $5 tables are few and far between, where might I find them?

Accepted Answer

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.

Question 19

I would like to know the decisions per hour in particular for the poker games: Three Card Poker, Caribbean Stud, and Let It Ride. Thank you.

Accepted Answer

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

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%

Question 20

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!

Accepted Answer

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&rsquo;t want to, lest it give you more bargaining power if you did make a big scene over it.

Question 21

I was killing time in the Harrah’s in New Orleans the other day, and sat at a Let It Ride table for the first time in years. I noticed that the disclaimer stated that the aggregate payout one round was $25,000. This was generally at $75,000 when the game was first introduced. Since this was a $10 minimum table, this meant that in the unlikely event of a Royal Flush, even a minimum bet would not be fully paid out. How can they set it so that a minimum bet can’t be paid off? To me, this is like to a slot machine having a big sign saying "$1,000,000 jackpot" with fine print saying "Payout limited to $100,000". I understand that the aggregate payout amount is pretty much what the traffic will bear, but are there any guidelines that require a certain minimum level for the aggregate limit?

Accepted Answer

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.

Question 22

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.

Accepted Answer

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

Question 23

This pertains to the aggregate payout in Let in Ride and how the $1 side bet is affected. When a table posts an aggregate payout of say $50,000, is this just for the standard three bets that you make to start the game OR does this actually include the $1 side bet as well? Over the years I have heard conflicting info.

Accepted Answer

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.

Question 24

I was playing Let It Ride at Cache Creek Casino in northern California. A woman two seats from me hit a straight flush. The payoff for the bonus bet was $2000. When she left an hour later, my girlfriend sat next to me to play. Within 30 minutes, she also hit a straight flush. So, two straight flushes were dealt at the same table within 1.5 hours. Can you calculate the odds of such an occurrence?

Accepted Answer

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.

Question 25

More of just an update than a question, but as of a few weeks ago, Aria started dealing Let It Ride face up. I see you already addressed the issue of having more information, but it certainly appears that the extra info, especially at a full table, could be an advantage over a standard game. According to the dealer, it was to stop the cards from being bent by players, but by playing for an hour it becomes apparent that they can push a lot more hands out by not having to wait.

Accepted Answer

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.

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