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Other Casino Games - FAQ

I know. I know: Casino War Casino War can seem like a simple game. Yet, at Casino Niagara, the game has special rules. In case of a tie, players enter a war where they must make a second bet equal to their initial one. If they win, they get paid at a rate of 2-1. Furthermore, if players tie with the dealer after the second round, they win at 3-1. I believe these rules significantly reduce the casino's advantage. Is that correct?

Tibby from St. Catharines, Canada

Thank you for shedding light on this variant. The way Casino Niagara describes the game of war has its own unique terminology. However, they overlook the point that the original bet is lost if a tie occurs.

What actually happens is that they provide a payout of double the Ante for winning after a tie and triple the Ante for a tie following a tie. The conventional rules still give double the Ante for a tie after a tie. This adjustment lowers the casino edge from 2.88% to 2.33%.

I found your insights into various side bets such as Streak and Pair Square quite captivating. Do you have any knowledge on how these new games are conceived and put into practice? Are professionals like yourself hired by casinos to calculate the odds? If so, do these games receive copyright protection?

Bob P. from Lake Charles, Louisiana

I could discuss this subject endlessly. Analyzing such games is a part of my livelihood. Gaming regulatory bodies necessitate this type of analysis prior to a game being approved for play. Typically, these games are conceived by individuals. In Nevada, after a game receives licensing, it must undergo a trial period of 30 days. If the trial is successful, the owner can then apply for a permanent license. The entire procedure is notably prolonged, and convincing a casino to host a trial is quite challenging since they tend to be risk-averse. Yes, game designers usually pursue copyright protections to prevent their concepts from being appropriated.

For more extensive information about the marketing of casino table games, visit my Game Inventors Corner .

Hello Wizard, I love your website. I was curious to know the house odds for a game named 'Catch A Wave' that is played at Foxwoods in Connecticut.

Ken L. from Boston, USA

Ask me, and you shall receive. Please have a look at my page on Catch a Wave .

How can one make money playing solitaire in Las Vegas?

Pattie from Arlington, USA

In my experience, I have never seen solitaire played for real money in Vegas. I believe that back in the early days of Las Vegas, people placed bets on the traditional Klondike version of solitaire, although I don't have any more details about that.

Last November in Las Vegas, I stumbled upon a table game known as '3 Way', where players go head-to-head against the dealer in high card, blackjack, and five-card poker using the same set of cards. Have you encountered this game? I would appreciate any insights on the odds or strategies. Keep up the great work on your site!

Billy O. from Vancouver, USA

I came across this at the World Gaming Expo but haven’t had the chance to analyze it thoroughly. Once I relocate to Las Vegas in February, I aim to better cover new games like this one.

I have a question regarding the house edge and risk factors for Casino War under Casino Niagara’s rules (where there's a 3-1 payout on a raise while losing the initial wager). How did you determine these figures? I'm currently trying to calculate them myself but am facing some difficulties. Thank you for your assistance.

Mark from Vancouver, Canada

Let’s denote d as the number of decks. The probability of a tie occurring in the initial round is (4*d-1)/(52*d-1)= 0.073955. In the second round, it is given by 12*4*d/(52*d-2)*(4*d-1)/(52*d-3)+(4*d-2)/(52*d-2)*(4*d-3)/(52*d-3) = 0.073974. Let's refer to p' as the probability of a tie in the first round and p' as the probability in the second round. Thus, the player's return becomes p’/2*(1-2)= -0.023301. When you multiply this by -1, you arrive at the house edge of 2.33%. I hope I haven’t rushed through this explanation.1Which casinos feature the game Super Fun 21? Could you provide me with a list?2I've noticed it at the Regent, New York, New York, and Palace Station. I’ve also heard it’s available at Sunset Station and Santa Fe Station.1*(2*p2+(1-p2First off, thanks for the amazing site. Are you planning to review 'Draw Caribbean Stud' anytime soon? I will be visiting Dubuque this weekend, and they have the game there. I tried it briefly during my last trip, but since I wasn't familiar with the optimal strategy, I only played a few hands and ended up winning ten dollars.

Bradford Wiley from Winthrop Harbor, U.S.

Moe from Philadelphia, USA

Thanks for your kind words. I just encountered this game at the California casino here in Las Vegas, but it wasn’t active yet. I managed to grab the rule card and will delve into it as soon as I can.

When visiting Treasure Island in Las Vegas last week, I came across a game titled Triple Shot, which incorporated hands of War, Blackjack, and Poker (6 card stud). It appeared quite fascinating, yet I would like to grasp all the rules and payout structures. Can you assist me? Additionally, are there other casinos on the Vegas Strip that have this game?

I’ve seen it there as well and thankfully documented some notes. It resembles a game that was once found at the Las Vegas Club. In Triple Shot, players can place any combination of three bets. The first is a standard blackjack wager. The second involves a poker hand, while the third is a war bet. I'm unsure whether the poker wager is based on the player's or dealer's hand, but the best five out of six cards are utilized. If the blackjack hand consists of fewer than six cards, additional cards are drawn to complete the hand. According to the odds table for the poker bet, the house edge is set at 3.20%.

Lastly, for the war game, the player compares their first card against the dealer's up card, with the highest card emerging victorious. In the event of a tie, the player loses half of their bet. The house edge in the war game stands at 2.94%. I am not aware of any other casinos that offer this game; it may currently only be in its trial phase at Treasure Island.

I am uncertain as well. If you find out, please share. I have a keen interest because

Kara from Castaic, California

casinos have just rolled out two variations of Klondike solitaire. Three Way Action I’m just beginning to learn Baccarat, and since each participant can place bets on either player or banker, rather than competing against one another, I’m curious about the game depicted in the James Bond movies. For instance, in Dr. No, it seems Bond is playing against a woman and winning her money? Am I missing something, or is it a different type of game altogether? Thank you for your response.

Triple Shot

Hand Combinations Probability Pays Return
Royal flush 376 0.000018 100 to 1 0.001847
Straight flush 1468 0.000072 30 to 1 0.002163
Four of a kind 14664 0.000720 15 to 1 0.010804
Full house 165984 0.008153 7 to 1 0.057071
Flush 205792 0.010108 5 to 1 0.050542
Straight 361620 0.017763 4 to 1 0.071050
Three of a kind 732160 0.035963 3 to 1 0.107890
Two pair 2532816 0.124411 2 to 1 0.248821
Pair 2252472 0.110640 1 to 1 0.110640
Nothing 14091168 0.692151 -1 to 1 -0.692151
Total 20358520 1 -0.031321

Fortunately, I am a huge fan of James Bond and own all the Bond films on DVD. I did some research and discovered that he is actually playing Chemin De Fer. The conversation in that scene is in French, which complicates things further. There’s a similar moment in

What is the house edge in solitaire?

anonymous

. In that film, it appears that Bond is engaged in baccarat, serving as the banker, but after the players act, he hesitates, and another character advises Bond that, \"The odds favor standing pat.\" This suggests that Bond has the ability to choose whether or not to take a third card, which is not an option available in standard baccarat. From what I know about gambling history, the American version of baccarat is a more straightforward adaptation of Chemin De Fer, with predetermined drawing rules. Interestingly, according to sources, American baccarat originated at the Capri Casino in Havana, Cuba. Cryptologic Hello! I am curious about the house edge in a game that I believe is exclusive to Portugal. The game is named Banca Francesa (literally, French Bank) and is played with three dice. Players can wager on 'Big' (when the sum of the 3 dice equals 14, 15, or 16), 'Small' (if it equals 5, 6, or 7), or 'Aces' (if the total is 3 or if each die shows one spot). The dealer will keep rolling the dice until one of these outcomes appears. Both Big and Small pay even money, while Aces pay 61 to 1. Thank you for your time.

We find that the probability of rolling a total of 5 or 16 is 6/216, for 6 or 15 it’s 10/216, and for 7 or 14 it’s 15/216; while for a total of 3, it’s 1/216. Therefore, on any single roll, both 'big' and 'small' each have a winning probability of 31/216, and 'aces' has a probability of 1/216. The ways these outcomes can occur total 2*31+1=63. Thus, whenever one of these events occurs, the probability that it was 'big' is 31/63, for 'small' it's 31/63, and for 'aces', it’s 1/63. The house edge for all three betting options is calculated to be 1.59%.

anonymous

I've recently started playing 3-card guts online for fun (they do have live versions), and I have a question. Where can I find a guide detailing what constitutes a medium starting hand in games with different player counts, like 10-handed, 9-handed, or 8-handed? The hand rankings are the same as those in three-card poker. I have discovered the probabilities for three-card poker on your site but am unsure how to delve deeper to identify the medium expected hand. Can you offer assistance? Dr. No Below is the median high hand based on the number of players. This estimate assumes that the hands are independent of one another, which in reality, is not the case, but this table should still provide a close approximation. For Your Eyes Only I've been trying to find a risk-of-ruin table for full-pay pick ’em poker or related data about its variance. The $1 full-pay machines clearly provide the best returns in the Buffalo-Niagara region, but I'm uncertain about acceptable bankroll sizes. Any guidance would be greatly appreciated. Thank you. www.casino-info.com The standard deviation in Pick ‘em Poker is 3.87. In conventional video poker, the standard deviation typically ranges from 4.4 to 6.4. Unfortunately, I don’t have specific risk-of-ruin tables for Pick ‘em Poker. Hence, my best recommendation is to refer to the jacks or better table on my

What are the odds in Faro?

Tommy from Houston, Texas

Please see my faro page for the answer to that question.

. Jacks or Better has the lowest standard deviation recorded in that appendix at 4.42, which means you could afford to be more aggressive than the table suggests.

Carlos from Lisbon

From my Sic Bo appendix I possess a free betting coupon from Mohegan Sun, usable on baccarat, sic bo, or big six. If I win, I can keep the winnings, but regardless of the outcome, I must surrender the coupon. Which bet would be the most favorable for utilizing it in each of these games?

In general, your best bet is to place it on a long shot. This is due to the fact that you will not retain the coupon on a win, which diminishes its value according to the probability of winning. The lower the likelihood of winning, the less that value diminishes. Below are three tables corresponding to the three games mentioned. You will find that the best betting choices are a tie between the 12, 30, 60, triple, and any triple in sic bo.

Annie from Prior Lake

Other Casino Games - Frequently Asked Questions - Wizard of Odds

Median Hand in Guts

Players Median Hand
1 K,10,2
2 A,Q,8
3 5,5,K
4 9,9,7
5 J,J,Q
6 K,K,5
7 A,A,7
8 8,5,3 flush
9 10,8,6 flush
10 J,10,6 flush

Explore the Top Online Casinos Available in Your Nation

Fred from Buffalo

Calculator for Lottery Jackpot Ticket Sales video poker appendix 1 Engage in Slot Tournaments with Huge Prize Pools

Although it may seem like a simple game, Casino Niagara has its unique set of rules. In cases where players tie, known as going to war, you must place another bet equal to your initial stake. Winning the war pays out at 2-1. If you find yourself tied with the dealer after the second cards are dealt, you'll receive a payout of 3-1. These specific rules likely lessen the house edge significantly. Is that the case?

Mike H. from New Jersey

I appreciate you highlighting this variant for me. They describe the game of Casino War at Casino Niagara with different terminology. One important detail they overlook is that your original stake is lost in case of a tie.

Baccarat

Free Bet Coupon Value in Baccarat

Bet Pays Probability Return
Banker wins 0.95 0.458597 0.481484
Player wins 1 0.446247 0.493175
Tie 8 0.095156 0.761248

Big Six

Free Bet Coupon Value in Big Six

Bet Pays Probability Return
1 1 0.444444 0.444444
2 2 0.277778 0.555556
5 5 0.12963 0.648148
10 10 0.074074 0.740741
20 20 0.037037 0.740741
Joker 40 0.018519 0.740741
Logo 40 0.018519 0.740741

Sic Bo

Free Bet Coupon Value in Sic Bo

Bet Pays Probability Return
Small, Big 1 0.486111 0.486111
4, 17 60 0.013889 0.833333
5, 16 30 0.027778 0.833333
6, 15 17 0.046296 0.787037
7, 14 12 0.069444 0.833333
8, 13 8 0.097222 0.777778
9, 12 6 0.115741 0.694444
10, 11 6 0.125 0.75
Triple 180 0.00463 0.833333
Any triple 30 0.027778 0.833333
Double 10 0.074074 0.740741

Essentially, what happens is that a player receives double their Ante for a win that follows a tie, and triple the Ante for a tie that follows another tie. The standard rules still grant double the Ante for a second tie. This adjustment reduces the house edge from 2.88% to 2.33%.

Ben B.

I found your insights into various side bets like Streak and Pair Square to be quite compelling. Do you know how these innovative games are developed and established within casinos? Are there specialists like yourself who calculate the odds? If so, are there any protections like copyrights in place for these games? Microgaming I could discuss this topic endlessly. Part of my income comes from evaluating games like these. Regulatory bodies in gaming mandate such assessments prior to a game being authorized for play. Typically, these games are created by individuals. Here in Nevada, once a game owner secures a license, there's a mandatory 30-day testing period. If it goes well, they can pursue a long-term license. This process is quite slow, and casinos are generally reluctant to take risks on new trials. Yes, the game inventor usually seeks copyright protection to prevent others from appropriating their concept.

For more in-depth information about marketing casino table games, feel free to visit my

Costa from Ottawa, Canada

Hello, Wizard! Terrific website. I’m curious if you know the House Odds for a game called \"Catch A Wave\" played at Foxwoods in Connecticut.13/ combin Feel free to ask away! Check out my page on3= 0.000424, or 1 in 2,359.

What’s the best strategy for earning money while playing solitaire in Las Vegas? Big Six wheel or Sic Bo I personally have not witnessed solitaire being played for money in Las Vegas. I understand that in the early days of the city, players did gamble on the classic Klondike version of solitaire, but I don’t know more details about it.

Stephen from Lake Grove, NY

Recently in November while in Las Vegas, I came across a game known as \"3 Way\" where players compete against the dealer in high card, blackjack, and best five cards poker, using the same cards throughout. Have you encountered this game? Are there any recommended odds or strategies? I enjoy your site!

I noticed this game at the World Gaming Expo, although I haven’t had the chance to research it thoroughly. Once I relocate to Las Vegas in February, I will be more tuned into new games like this. element of risk and house edge My inquiry pertains to understanding the House edge and risk assessments for Casino War based on Casino Niagara's rules (where you get a 3-1 payout on an additional bet and lose the initial wager). How did you derive these figures? I’m attempting to compute them but am encountering difficulties. Your assistance would be appreciated. Texas Hold 'Em Bonus Let’s denote d as the number of decks in play. The chance of a tie occurring in the first round can be calculated as (4*d-1)/(52*d-1) = 0.073955. In the second round, the probability of a tie is determined by the expression: 12*4*d/(52*d-2)*(4*d-1)/(52*d-3)+(4*d-2)/(52*d-2)*(4*d-3)/(52*d-3) = 0.073974. Let’s use p’

Paul from London

to symbolize the probability of a tie in the first round and p’

for the second round. Consequently, the return for the player is p’

)/2*(1-2) = -0.023301. If you multiply that by -1, you arrive at a house edge of 2.33%. I hope I didn’t go through this too quickly.

Kevin from Perth, Western Australia

Which casinos offer Super Fun 21? Could you provide me with a list? combin (12,n)×(6/45)n×(39/45)n-12I’ve spotted it at Regent, New York New York, and Palace Station. I’ve also heard it’s available at Sunset Station and Santa Fe Station.

Expected number of repeat numbers

Repeats Expected
0 8.0804888027
1 14.9178254818
2 12.6227754077
3 6.4732181578
4 2.2407293623
5 0.5515641507
6 0.0989986937
7 0.0130547728
8 0.0012552666
9 0.0000858302
10 0.0000039614
11 0.0000001108
12 0.0000000014
Total 45


First off, I appreciate your wonderful website. Are you planning to review \"Draw Caribbean Stud\" anytime soon? I’ll be heading to Dubuque this weekend where they have it. I tried it briefly during my last visit but lacked a solid strategy, so I only played a few hands and ended up with a ten-dollar win.

Bradford Wiley from Winthrop Harbor, U.S. Lucky You ?

Matthew from Fort Wayne, IN

Thank you for your kind words. I recently spotted this game at the California casino in Las Vegas, but it hadn’t opened yet. I picked up the rule card and will delve into it when I get the chance. Currently, I don’t possess any information about it.

  1. Both players ante (or re-ante).
  2. Each player gets two cards.
  3. While I was at Treasure Island in Las Vegas last week, I noticed a game named Triple Shot that includes elements from War, Blackjack, and Poker (6 card stud). It piqued my interest, but I would like to learn about all the rules and payout structures. Can you assist? Also, which other casinos on the Vegas Strip have this game?
  4. I’ve seen Triple Shot there too and took some notes. This game is similar to
  5. which used to be found at the Las Vegas Club. In Triple Shot, players can place any mix of three bets. The first is a typical blackjack wager. The second bet pertains to a poker hand, while the third is a wager on War. I can’t recall whether the poker bet depends on the player’s hand or the dealer’s hand, but they use the best five out of six cards. If a player’s hand in blackjack is less than six cards, additional cards come into play to form six. The odds table for the poker hand indicates a house edge of 3.20%.
  6. To wrap it up for the war aspect, the player's initial card competes against the dealer's up card—higher card wins. In the event of a tie, the player loses half their stake. The house edge when playing the war portion is calculated to be 2.94%. As of now, I’m not aware of any other casinos that offer this game. It might still be in a trial phase and exclusively available at Treasure Island.
  7. I’m not sure. If you uncover any information, please share it with me. I’m especially interested because
  8. casinos recently rolled out two variations of Klondike solitaire.
  9. I’m trying to familiarize myself with Baccarat, and since players can bet on either the player or the banker, without really facing off against one another, I'm curious about the game depicted in James Bond films. For instance, in Dr. No, it appears that Bond is competing against a woman and winning money from her. Am I missing something, or is that a different game altogether? Thank you for your time.
  10. As a huge fan of James Bond, I own every Bond movie on DVD. I researched
  11. and it turns out he’s playing Chemin De Fer. The scene features dialogue in French, which doesn’t provide much clarity. There's another similar scene in
  12. . In that film, it appears that Bond is actually playing baccarat while taking on the role of the banker, but after the player makes a move, he hesitates and another character advises him, \"The odds favor standing pat.\" This line implies Bond had the choice to draw a third card, which is not an option in baccarat. As far as I understand the history of gambling, the American style of baccarat is a streamlined version of Chemin De Fer, where the rules for drawing cards are predetermined. Interestingly, according to
  13. Steps 3 to 9 repeat. Then start over at step 1.

American baccarat is said to have originated at the Capri Casino in Havana, Cuba.

Hi! I’m intrigued by the house edge concerning a game that, to my knowledge, is exclusive to Portugal. The game is called Banca Francesa (translated literally to French Bank) and it’s played with three dice. Players can bet on \"Big\" (where the total of the 3 dice equals 14, 15, or 16), \"Small\" (if it totals 5, 6, or 7), or \"Aces\" (if the total is 3 or if each die shows one spot) - the dealer will roll the dice until one of these outcomes occurs. Wins on Big and Small bets return even money, while Aces payout at 61 to 1. Thank you for your attention.

Looking at the probabilities, a total of 5 or 16 occurs in 6 out of 216 attempts, 6 or 15 in 10 out of 216, and 7 or 14 in 15 out of 216, while a total of 3 is 1 out of 216. Therefore, for any single roll, the likelihood of winning on 'Big' is 31 out of 216, 'Small' the same at 31 out of 216, and 'Aces' at 1 out of 216. The various ways these outcomes can appear totals to 2 times 31 plus 1, equaling 63 total outcomes. Hence, if one of these results occurs, the chance that it was 'Big' is 31 out of 63, same for 'Small', and 1 out of 63 for 'Aces'. Consequently, the house edge across all three bets stands at 1.59%.

Pete Braff from Long Beach

I’ve started playing 3-card guts online using play money (they also offer live games), and I’m looking for guidance to identify a medium starting hand in games with 10, 9, 8 players, etc. The hand rankings follow the same structure as three card poker. I found the probabilities for three card poker on your site, but I’m unsure how to go deeper to uncover the median expected hand. Can you assist?

Here’s the median high hand based on the number of players. This estimation assumes independence among hands, which may not hold true, but it should come quite close.

I’ve been searching for a risk-of-ruin table associated with full-pay pick ’em poker or related variance information. The $1 full-pay machines clearly yield the highest returns in the Buffalo-Niagara area, but I’m uncertain about the recommended bankrolls. Any guidance would be greatly appreciated. Thank you.

Lon from Brooks, CA

My Super Pan 9 In Pick ‘em Poker, the standard deviation is 3.87. Conventional video poker usually has a standard deviation ranging from 4.4 to 6.4. Unfortunately, I do not possess any risk of ruin tables for Pick ‘em Poker. Therefore, my best advice would be to reference the 'jacks or better' table in my

. Jacks or Better features the lowest standard deviation within that appendix at 4.42, thus allowing for a bit more aggressive play relative to what that table suggests.

Vince from North Collins, NY

I have a free bet coupon provided by Mohegan Sun, usable on baccarat, sic bo, or big six. If I win, I can keep the earnings, but either way, I have to forfeit the coupon. Which game would yield the best bet for this coupon?

Clark County Table Game Count

Game Tables
21 2537
Roulette 405
Craps 334
Other 243
Baccarat 233
Three Card Poker 208
Pai Gow Poker 194
Mini baccarat 143
Let It Ride 98
Pai Gow 80
Wheel of Fortune (Big Six) 37
Caribbean Stud Poker 22
Sic Bo 1
Chuck-a-Luck 1


Generally, it's advisable to place it on a long shot bet. This is because winning doesn't allow you to retain the coupon, which reduces its value based on the probability of winning. The lower the likelihood of winning, the less the value is diminished. Below are three tables illustrating the best bets for the three games mentioned. You’ll find that the top choice is a tie between the numbers 12, 30, 60, triple, and any triple in sic bo.

I saw that you've recently updated your assessment of the house edge for pontoon. Previously, it was indicated as .17%, which made the game appealing. Now, it's listed as .38%, which significantly diminishes its attractiveness. From my understanding, your site has maintained the .17% figure for many years, but it's now showing .38%. Could there have been an oversight that you just became aware of? What exactly prompted such a substantial change in the house advantage?

Albert from Uncasville

I must admit that the .17% figure I previously provided was incorrect. I identified this mistake when I recently re-evaluated the analysis for the

rules of the game. I sincerely apologize to everyone who played based on my earlier figure of .17%.

In Chinese poker, each of the four players is dealt 13 cards. What are the odds of one player receiving a Dragon, which is defined as having no pairs in their hand?

I have come across a variation of Oasis Poker The chance of an individual player being dealt a Dragon is calculated as 4 * (52, 13) = 0.000106. The likelihood that exactly one player will receive a Dragon can be approximated by the formula 4 * 0.000106 * (1 - 0.000106).

Martin from Tallinn

The bonus package provided at Mohegan Sun consists of two ten-dollar betting coupons. It's important to note that these are not for match play. A ten-dollar wager on a bet that pays even money, such as on the Big Six wheel, will yield a return of ten dollars. The house retains any coupons wagered, regardless of whether the player wins or loses, and the player does not need to contribute any of their own funds. The only games eligible for these bets are the

What are the optimal games to utilize these coupons on? I have placed high and low bets on Sic Bo, only losing if a triple comes up. I have also bet on the one and two in the wheel during the same spin.

  1. Typically, these complimentary betting coupons are restricted to even money wagers, making this situation quite unique. My recommendation is to use the free bet on a long-shot option in order to reduce the impact of the rule dictating that you lose the free bet even if you win. In Big Six, the longest shot is betting on the joker/logo, which has a winning probability of 1 in 54. I'm unsure whether Mohegan Sun pays 40 or 45 for the joker, but assuming a payout of 45, the value of the free bet would be (1/54) * 45 = 83.33% of its nominal value. In Sic Bo, the biggest long shots are for the six triples, and while I don't know the payout for a specific triple, I would estimate it to be 180. Thus, the expected value of any triple bet would be (1/216) * 180 = 83.33% of the expected value. Hence, in terms of expected value, both options are equal, but I would personally lean towards the bet with a higher chance of winning, which is the joker/logo in Big Six, though ultimately the decision is yours.
  2. I was perusing your section that differentiates between the
  3. various elements involved. First off, I presume that the risk taken is dependent on employing the correct strategy as per the house advantage. I have a theory that the ideal strategy for certain games may vary if your aim is to minimize risk. For instance, in
  4. it would certainly make sense to play hands such as a 5/2 offsuit. My instinct suggests that by playing all possible hands, you might be able to keep the risk lower than the stated figure of 0.53%.
  5. You are correct in stating that by straying from my suggested strategy, you can indeed reduce the risk element by opting to raise on hands that have an expected value slightly below -1. In your example, a 5/2 offsuit holds an expected value of -1.019987 under the rules used in Las Vegas. This means if you raise through that hand, you're likely to lose approximately 1.02 times your initial bet by the conclusion of the hand. After your first raise and any further raises after the flop and turn, the average wager on this hand will be approximately 3.627374 units. In my analysis, making that raise yields a valuation of -0.0109987 units versus 2.627374 additional units wagered. The ratio of the extra win to the additional bet by raising amounts to -0.0109987/2.627374 = -0.00761, which is lower than the overall expected value of the game standing at -2.04%. Therefore, if your objective is to minimize your losses relative to total money wagered, including raises, you should indeed deviate from my core strategy and raise with that hand. Similar instances can be identified across various games involving raising.
  6. In conclusion, if your intent is to reduce losses per hand, you ought to adhere to the house edge strategies outlined on this site. However, if your intention is to limit losses relative to the total amount wagered, you might consider increasing your bets in borderline situations.

Greetings. In Australia, we have a Lotto system where a major cash prize is awarded if all six numbers you select match those drawn from a possible set of 45 numbers (1-45). Many individuals opt to buy a 'Slik Pik,' where they receive 12 games comprised of six allegedly random selections. My friends and I often marvel at how the same number can repeat up to 6 or 7 times across those 12 games. That does not seem random at all! My question is, what is the expected frequency of a number repeating 6 or 7 times, under the assumption that selections are made randomly?

Insurance in Russian Poker

Dealer’s Up Card Combinations Probability Exp. Value
A 132804 0.335714 -0.328571
K 132804 0.335714 -0.328571
Q 108528 0.457143 -0.085714
J 108732 0.456122 -0.087755
10 108936 0.455102 -0.089796
9 109140 0.454082 -0.091837
8 109140 0.454082 -0.091837
7 109140 0.454082 -0.091837
6 109140 0.454082 -0.091837
5 109140 0.454082 -0.091837
4 108936 0.455102 -0.089796
3 108732 0.456122 -0.087755
2 108528 0.457143 -0.085714

The expected frequency of any number appearing n times across 12 games is represented by the formula

. The table below illustrates the anticipated occurrences from zero to twelve.

I played 66 hands of Pick ’Em Poker To respond to your inquiry, you can expect a number to show up exactly six times around 0.099 times for each set of cards, or approximately once every 10.1 sets. The occurrence of a number appearing precisely seven times will happen about 0.0131 times per set of cards, occurring roughly once every 76.6 sets.

Dave from Overland Park, KS

Could you clarify the rules for playing the game 'guts,' as depicted in the film?

  • Four of a kind: 13 combinations
  • High (9-A) three of a kind: 1,152 combinations
  • I hope you’re content; I've replayed that scene frequently for at least an hour, attempting to grasp the rules. I've participated in guts numerous times over many years and locations, and I've never encountered it played as it was shown in that movie. Let’s designate the player who acts first as Player 1, and the dealer as Player 2. Here's my comprehension of how they played.
  • Two high pairs: 540 combinations
  • Player 1 is required to state whether they are 'in' or 'check.' In the case of a check, proceed to rule 4. If they opt to go in, proceed to rule 7.
  • Player 2 must decide whether to go in or check as well. If they choose to check, refer to rule 5. If they decide to go in, follow rule 6.
While two checks did not occur in the film, I assume that both players would restart from step 1 in such an event.66The responsibility then returns to Player 1, who must declare whether they are in or folding. If they opt to go in, proceed to rule 8. In the case of a fold, refer to rule 9.

Player 2 must declare 'in' or 'fold.' If they decide to go in, refer to rule 8. If they choose to fold, move to rule 9. Dragon Tiger The two hands are compared, and the hand with the higher rank wins. The victor collects the pot, while the losing player must match it, thus creating a new pot. This is effectively the same as the loser simply giving the winner the amount of the pot. Although a tie was never depicted in the film, I assume that no funds would change hands in that situation. Then, continue to rule 10.

Johnny from Cambodia

When a player folds, the other player claims the pot. After that, a new hand begins following step 1. combin (8,2)/combin(52*8,2) = 1,456/86,320 = 1.69%. The house edge is 13.98%.

Each player is dealt an additional card to enhance their existing two-card hand, forming a three-card hand. This third card is placed face down over the two face-up cards. I'm uncertain whether straights or flushes are recognized at the three-card stage, but I prefer to play with the understanding that they do count (though not during the two-card stage).

anonymous

That game Flip It During my visit to the Borgata casino in Atlantic City, I observed a new Pair Plus pay table that offers payouts of 100-1 for Mini Royal, 50-1 for Straight Flush, 40-1 for Three of a Kind, 6-1 for Straight, 3-1 for Flush, and 1-1 for Pair. What is the house edge for this particular pay table?

anonymous

The house edge associated with that pay table is relatively low, standing at 1.85%. Kudos to the Borgata, assuming your information holds true.

  • Based on feedback from patrons, the Borgata reduced the payout for a three of a kind to 30 to 1 at some point during 2008.
  • J = count of jokers left in the shoe
  • if J-C < 0 then bet on black
  • If J+C < 0 then bet on red

In the game of Super Pan 9 that utilizes eight decks, does a tie payout of 8 to 1 offer a player advantage? My rough calculations indicate that the player has an edge of approximately 2.5%.

red = 100
black = 75
jokers = 10

The remaining cards would be:

red = 108
black =133
jokers = 14

The page indicates that the probability of a tie is 11.3314%. Therefore, if a tie pays out at 8 to 1, the expected return would be 9 * 0.113314 - 1 = 0.019826. While a player advantage of 1.98% is slightly lower than your estimate, it's still a favorable wager. Where can I find this game?

If I'm betting $50 on the Ante in Ultimate Texas Hold 'Em What has become of the 3-5-7 card game in Las Vegas? I've searched everywhere and can't seem to find it.

100xOdds

I've been informed that the game was removed from U.S. casinos due to patent infringement issues. According to the Fourth Quarter 2008 Statistical Report from the Nevada Gaming Control Board, the table game counts in Clark County are as follows.

Regrettably, they do not specify what the 243 'other' games consist of, so this information may not directly address your question, but it's worth noting. Wizard of Vegas .

I observed that you've recently revised your estimation of the house advantage for pontoon. It was previously noted as .17%, which made the game quite appealing. Now, however, it's set at .38%, significantly reducing its attractiveness. For quite some time, your site indicated a .17% advantage, and now it shows .38%. Did something go unnoticed that led to this significant adjustment? Can you clarify what prompted such a drastic change in the house advantage?

I must admit that the .17% figure I previously mentioned was incorrect. I realized there was a mistake in my calculations when I updated them for the

anonymous

Yes, indeed Bond was playing Chemin de fer , not baccarat rules. I sincerely apologize to anyone who played based on that .17% figure.

  • In Chinese poker, four players are dealt 13 cards each. What are the chances that one of those players ends up with a Dragon, which is defined as a hand that contains no pairs?
  • The likelihood of any single player being dealt a Dragon is 4, (52,13) = 0.000106. To find the probability that exactly one player gets a Dragon, we can approximate it with the formula 4*0.000106*(1-0.000106).

Note:
The bonus offer at Mohegan Sun consists of two ten-dollar vouchers, which cannot be used for match play. If a player makes a ten-dollar wager on an even-money bet, such as at the Big Six wheel, the return would still be ten dollars. The house retains any bets made using these coupons regardless of the outcome, and the player doesn’t need to stake any additional funds. The game options available for these coupons are limited to the

In terms of optimal usage of these coupons, I have made bets ranging from high to low in sic bo, only losing if a triple appears. I've also placed bets on the one and two on the wheel during the same spin.

Typically, these complimentary betting coupons restrict players to even-money wagers, making this a unique situation. I recommend using your free bet on a longer shot to reduce the impact of the rule that results in loss of the free bet even if you win. The highest long-shot in Big Six is the joker/logo, with a win probability of 1/54. I’m uncertain whether Mohegan Sun pays 40 or 45 for the joker, but if we assume it’s 45, the expected value of the free bet would be (1/54)*45 = approximately 83.33% of its face value. In Sic Bo, the largest long-shots are the six triples, and while I don’t know the payout for a specific triple, I'd estimate it to be around 180. Therefore, the value from one of the six triples would equal (1/216)*180, translating to roughly 83.33% of the expected value as well. Thus, in terms of expected value, both options are equivalent. Personally, I would lean toward the bet that has a higher chance of winning, specifically the joker/logo in Big Six, but the choice is ultimately yours.

I was perusing your section about the distinctions between the

  • 2:09 — Thunderball
  • 4:19 — On Her Majesty's Secret Service
  • 7:30 — For Your Eyes Only

and I gathered that risk is determined by following the correct strategy based on the house advantage. However, I argue that optimal strategies may differ if the goal is to reduce risk exposure. For instance, in

it's often advisable to play hands like 5/2 off-suit. My intuition suggests that if one played every possible hand, they might lower the risk below the cited rate of 0.53%.

You are correct; it is possible to decrease risk by veering away from my suggested strategy, particularly by raising on hands with expected values slightly below -1. In the case of 5/2, it has an expected value of -1.019987 per the Las Vegas rules. This indicates that by raising, you would likely lose about 1.02 times your initial wager when all is said and done. After the initial raise and any potential follow-up raises post-flop and turn, the average total bet on that hand is roughly 3.627374 units. From my perspective, placing that raise would yield approximately -0.0109987 units for the player, considering the additional 2.627374 units wagered. This results in a marginal win-to-marginal bet ratio of -0.0109987/2.627374 = -0.00761, which is less favorable than the overall game expectation of -2.04%. Therefore, if your aim is to minimize losses relative to total betting amount, including raises, then it would be prudent to deviate from my foundational strategy and raise on such a hand. Similar scenarios can be identified across various games involving raises.

To summarize, if your objective is to minimize losses per hand, it’s best to adhere to the strategies on this site designed to minimize the house edge. Conversely, if you want to limit losses regarding the total amount wagered, consider increasing your stakes on borderline plays.

Hello, in Australia we have a lottery called Lotto, where a major cash prize is awarded if your six chosen numbers are drawn from a pool of 45 numbers (from 1 to 45). Many players buy a 'Slik Pik' ticket, which includes 12 games, each containing six supposedly random picks. My friends and I often find it curious that within those 12 games, the same number can appear up to 6 or 7 times. Surely this can't be random! My question is, statistically, what would be the expected frequency of any given number repeating 6 or 7 times, assuming the selection process is indeed random? Wizard of Vegas .

The anticipated number of occurrences of any specific number appearing exactly n times across 12 games is calculated using the binomial distribution. The following table displays the expected occurrences from 0 to 12.

Vegasrider

To respond to your inquiry, you can expect to see the same number appearing exactly six times approximately 0.099 times per set of tickets, translating to roughly once every 10.1 sets. Similarly, witnessing the same number come up exactly seven times will occur around 0.0131 times per set, equating to about once every 76.6 sets.

  • Win: 58.82%
  • Loss: 38.47%
  • Tie: 2.72%

Could you clarify the rules of the 'guts' game as depicted in the movie

Hello, in Australia we have a lottery called Lotto, where a major cash prize is awarded if your six chosen numbers are drawn from a pool of 45 numbers (from 1 to 45). Many players buy a 'Slik Pik' ticket, which includes 12 games, each containing six supposedly random picks. My friends and I often find it curious that within those 12 games, the same number can appear up to 6 or 7 times. Surely this can't be random! My question is, statistically, what would be the expected frequency of any given number repeating 6 or 7 times, assuming the selection process is indeed random? Wizard of Vegas .

What is the player advantage in Ultimate Texas Hold 'Em I’ve replayed that scene numerous times, attempting to decipher the rules. I've played guts many times over the years in different places, and the way it was portrayed in the film seems quite different. For clarity, let’s label the first player as Player 1 and the second player (the dealer) as Player 2. Here’s how I understood the game was played.

Eliot from Santa Barbara

Player 1 needs to declare ‘in’ or ‘check.’ If they choose to check, proceed to rule 4. If they go in, reference rule 7. Player 2 is then required to state whether they are in or checking. If they check, move to rule 5. If they opt to go in, go to rule 6.

Although double checks never occurred in the film, I presume that both players would revert to step 1.

The turn returns to Player 1, who must indicate whether they are in or folding. If they decide to go in, proceed to rule 8. If they fold, reference rule 9.

seabarrister

Good question. Mississippi Stud Player 2 must then disclose if they are ‘in’ or ‘folding.’ If they declare in, go to rule 8. If they fold, continue to rule 9.

Once the two hands are revealed, the higher hand is declared the winner. The winner claims the pot while the losing player must match the amount, thereby creating a new pot. This is akin to the loser just compensating the winner for the pot's total. Although there were no ties depicted in the movie, I assume that in such a case, no money would change hands. Afterwards, refer to rule 10.

If a player folds, the opposing player collects the pot and they move on to a fresh hand starting from step 1.

Each player is dealt an additional card, augmenting their existing 2-card hand to form a 3-card hand. The third card is dealt face down atop the two face-up cards. I’m not sure if straights or flushes are considered at this 3-card point, but I personally prefer a version of the game where they do count (though not at the 2-card threshold).

House Edge with Payout Cap

Bet $50,000 Cap $80,000 Cap $100,000 Cap
$15 5.02% 4.91% 4.91%
$20 5.15% 4.91% 4.91%
$25 5.22% 5.04% 4.91%
$50 5.38% 5.28% 5.22%
$75 5.49% 5.37% 5.33%
$100 5.64% 5.41% 5.38%

Hello, in Australia we have a lottery called Lotto, where a major cash prize is awarded if your six chosen numbers are drawn from a pool of 45 numbers (from 1 to 45). Many players buy a 'Slik Pik' ticket, which includes 12 games, each containing six supposedly random picks. My friends and I often find it curious that within those 12 games, the same number can appear up to 6 or 7 times. Surely this can't be random! My question is, statistically, what would be the expected frequency of any given number repeating 6 or 7 times, assuming the selection process is indeed random? Wizard of Vegas .

Steps 3 through 9 repeat. If both players go 'in,' refer to rule 12.

anonymous

The exact answer is 450528/407170400 = 0.001106485 = 1/904.

Players receive two more cards to add to their 3-card hands, thus forming 5-card hands. These additional cards are dealt face down on top of the three face-up cards.

If you closely observe the movie, Huck should have lost a total of $11,000, beginning with only $10,000. I scrutinized the scene repeatedly to trace the missing $1,000. My best guess is that when Huck declared in on his last two-card hand, he should have matched the $4,000 pot but only had $3,000 available. Similar to standard poker conventions, it seems he could only win what he was willing to risk. In the final hand, Huck folded. I’m uncertain if this was due to his inability to beat his father’s two-card hand on the table, or if he was compelled to fold since he lacked sufficient funds to match the pot should he have lost.

Three Card Poker Tie

Hand Hand 1 Hand 2 Product
Three of a kind 52 0 0
Flip It 48 3 144
anonymous 288 26 7,488
J = count of jokers left in the shoe 432 25 10,800
if J-C < 0 then bet on black 1,096 3 3,288
If J+C < 0 then bet on red 3,744 3 11,232
red = 100 6,576 26 170,976
black = 75 9,864 25 246,600
jokers = 10 22,100 450,528