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November 11, 2000 Column


[ Click here to Ask the Wizard of Odds a question ]

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. -- Brian of Stafford, Virginia

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.

Hey Wiz, Great Site. I wondered if you knew the House Odds on a game played at Foxwoods in Connecticut, called "Catch A Wave." -- Ken Laird of Boston, USA

Thanks for the compliment. I've been requested to analyze this game quite a few times. However it is generally my policy to wait until a game goes nationwide before I cover it on my site.

Is my boyfriend cheating on me? - Melevinna of IA City, USA

How should I know? However don't make any accusations unless you have sufficient evidence to back them up.

My question revolves around the system Norman Leigh used in the 60s to break the bank in Nice. His team used a reverse Labouchere system, which involves absorbing a number of small losses before hitting a big win (based on the idea that instead of canceling out wins they are added to the sequence and losses are crossed out ensuring that each game can only lose a fixed amount but can potentially win the table limit). Other than Norman's book (and books based on it) I have not seen any analysis of the system. The book states that this approach uses the house edge against them and that in the long run the player will come out ahead. Is this nonsense or is there something in this idea? -- Billy from ?

I admit I don't know much about this incident. However I will say that if indeed they won it was because of luck and not because it was a winning system. As I have said a thousand times before no system based on a negative expectation game wins in the long run.

First, let me congratulate you on your great website. I tell everyone I know that if they are going to gamble to make sure that they visit your site first! My question is on Three Card Poker ante & play. If you know one of the dealer's three cards how should you change your basic strategy and could you obtain an advantage over the house and by how much? -- G.M. from Monmouth County, New Jersey

Are you friends with Brian Widdowson (see above)? In 'Mastering the Game of Three Card Poker' by Stanley Ko a section is devoted to this topic. He explains when to raise and fold on a queen high hand, based on the cards of other players you are able to see. According to Ko if you had perfect knowledge of all cards in a seven-player game and could make perfect use of this information it would cut the house edge from 3.37% to 2.32%. You can find this booklet at that Gambler's Book Club. Thanks for the compliment on my site.

Concerning the 5%vig on buy bets and lays how would the odds change if $1 was charged for $20-$39, $2 for $40-$59, $3 for $60-$79 and $4 for $80-$99 without round up. Your information you give is outstanding. -- Bry of Chesterton, USA

Thanks for the compliment. The formula for the house edge in buy and lay bets is the commission divided by the bet plus commission. In this case the best bet is to bet $39 for the $1 commission. On the buy bet the house edge would be 1/40 = 2.5%. Assuming you can lay $78 to win $39 on the 4 and 10, and still only pay $1, the house edge would be 1/79=1.27%. I'll leave the other situations as an exercise for the reader (I hated it when my math books would say that).

How do you win money playing solitaire in Vegas? -- Pattie from Arlington, USA

I have never seen solitaire played for money in Vegas. I understand in the early days of Vegas people wagered on the standard Klondike variation of solitaire but I don't anything else about it.

Ever wonder why Three Card Poker is not available online? ñ Bob from Houston, Texas

It is still not as popular as Let it Ride and Caribbean Stud. I speculate when the software developers either don't understand it or don't think it is popular enough. However I get asked about Three Card Poker online all the time. The first online casino to offer the game is going to be very glad they did, I predict. (p.s. Since this question was published Three Card Poker has become available at most Internet casinos)

In general, when betting on anything which pays even odds, is there any kind of "system" to help improve chances and or payoffs? -- JJ from Boston, USA

No.

What is the probability of getting three pair in Pai Gow? Are the chances lesser or greater than three of a kind? - Alex of Long Beach, Mississippi

Not counting a three of a kind and two pairs the following are the ways to get a three pair and number of combinations.

No wild card: combin(13,3)*10*63*4 =2471040
Wild card used to compete pair of aces: combin(12,2)*10*62*42 = 380160
Wild card used as singleton ace: combin(12,3)*63 = 47520

The total number of combinations is 2898720. This is less than half of the 7470676 combinations for a three of a kind.

Hi, you have a wonderful page for categorizing the Casinos by the type of software they used. However, Casino-On-Net was not mentioned in the list. Do you know what software is Casino-On-Net using? ñ Andrew from Bangkok, Thailand

Thanks for the compliment. I believe Casino on Net uses their own software. It is my understanding that they are one of the three biggest online casinos. Once a casino starts making tons of money it is more cost effective to develop their own software than keep paying somebody else a percentage of the profit to use theirs.

I've noticed some new video slot machines (Money to burn, High Bid, Money for nothing, Who Dun it, etc) that differ from the normal 3 reel slots in the following ways - first they have 5 reels. You can typically bet on 1 to 9 paylines (even though some have as many as 15 different pay lines), and multiple coins per line; thus, with 9 pay lines and 5 coins played per line, you would have a total bet of 45 coins (even in nickles, this can start to add up!). Most payoffs are multiples of the line bet, even though there are some "bonus" wins that pay multiples of the total amount bet. My question is - Is it best to always pay all possible pay lines, or is there an optimum combination of pay lines to play to achieve the best return. I suspect that getting a winning combination on any particular pay line is the same for all, but wondered if you have any better insight to share. ñ Scott of Leawood, USA

I believe each frame in these video slots are weighted the same way. Assuming this to be true any given line is equally likely to produce any given combination. Thus the return is the same regardless of the number of coins played. However I am not sure of this, slot makers are notoriously secretive about such things.

I wonder if you could comment on the Casino's practice of switching dealers. It always seems to happen that the table is on a winning streak and then the casino switches dealers mid-shoe. All of a sudden everyone starts to lose. Do you think that certain dealers tip the balance more in the casino's favor? ñ Hobbes from Toronto, Canada

The casino switch dealers when it is time for someone to go on a break. Switching dealers does not change the player's odds unless the player is a card counter and the game is single or double deck where a new dealer necessitates a fresh shuffle.

How many numbers does the RNG pick for each spin? Is it 3 numbers (1 for each reel) or is it 1 number that's mapped to a unique combination of symbols for all 3 reels? -- Vincent of Chicago, Illinois

The machine picks one number for each reel.

Great site Mike! Often times I hear the word, "binomial distribution" being used in gambling. Can you explain to me what it means? Thanks in advance. -- Dennis from Toronto, Ontario

Thanks for the compliment. Any introductory probability and statistics book should give good treatment to the binomial distribution. Briefly the binomial distribution is the probability that any given number of events will happen given a specific probability for each event and a specific number of trials. Specifically if the probability of each success is p, the number of success is s, and the number of trials is n then the probability of s successes is ps * (1-p)n-s * combin(n,s). The combin function is explained in my section on probabilities in poker. For example suppose you want to know the probability that in 100 spins of a roulette wheel the number of reds will be exactly 60. According to the binomial distribution the probability is (18/38)60 * (20/38)40 * combin(100,60) = 0.003291.

I just finished reading your section on strategy for craps with great interest. I understand that better the pass line and come bets with full odds is a good strategy. My question is "does the house edge change at all when playing a strategy of pass line with full odds and making a maximum of two come bets with maximum odds?" In other words; how does time (more rolls) and having more money at risk affect these odds if at all? Or should a person stick with just the single bet with full odds? This seems to be a favorite strategy for most knowledgeable players I have met at the dice tables. -- Jim of Yakima, USA

The house edge is the same regardless of how many come bets you make assuming you always take the maximum allowable odds and leave the odds turned on during a come out roll. How many come bets you make should be a matter of personal preference.
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