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Introduction
But first, a little Poker 101 for all you noobs out there – we’re talking about pot odds and pot equity. Most people have at least some understanding of odds in general. If you pick a number at random between 1 and 10, your odds of picking any specific number (say, 3 or 7) are exactly 1 in 10.
Poker odds and poker math can seem overwhelming but they're actually very easy to learn. Here's how to calculate proper poker odds, implied odds & equity. 100% Up To $888 and $88 free. Basic Math – Odds and Percentages Odds can be expressed both “for” and “against”. Let’s use a poker example to illustrate. The odds against hitting a flush when you hold four suited cards with one card to come is expressed as approximately 4-to-1.
Casino Hold 'Em is a poker variation, similar to Texas Hold 'Em, that is played in Egypt, Russia, South Africa, Holland, Latvia, Estonia, Ireland, Morocco, Malta, Ukraine, Panama, and Romania. It is also available to play online at casinos using Net Gaming, Real Time Gaming, Playtech, Gamesys, and Galewind Software.
The game also goes by the name Casino Hold 'Em Open. Under this name, the rules are the same except the player hole cards are dealt face up. In normal Casino Hold 'Em they are dealt face down.
Rules
The rules are as follows.
- Play begins with each player making an Ante wager. There is also an optional Progressive Jackpot side bet.
- The dealer gives the player and himself two hole cards and three community cards face up on the table.
- Each player must decide to either fold or call. If the player folds, then he gives up his cards and his Ante bet. If the player calls, then the Call bet must be equal to two times the Ante bet.
- The dealer will then deal two more community cards, for a total of five. The dealer will then turn over his own two cards.
- Both hands shall be scored according the highest poker value of the two hole cards and five community cards.
- The dealer must have a pair of fours or better to qualify. If the dealer does not qualify then the Ante will pay according to the Ante pay table below and the Call bet will push.
- If the dealer qualifies and beats the player, then the player will lose both the Ante and Call.
- If the dealer qualifies and the player beats the dealer then the Ante will pay according to the Ante pay table below and the Call bet will pay 1 to 1.
- If the dealer qualifies and the player ties the dealer then both Ante and Call bets will push.
- The Progressive Jackpot side bet pays based on the player's final seven card hand only, even if the player folded or loses to the dealer. More on this bet at the bottom of the page.
Ante Pay Table
Texas Holdem Hand Odds Calculator
| Hand | Table 1 | Table 2 | Table 3 | Table 4 |
|---|---|---|---|---|
| Royal flush | 20 | 25 | 100 | 100 |
| Straight flush | 20 | 25 | 20 | 49 |
| 4 of a kind | 10 | 12 | 10 | 17 |
| Full house | 3 | 3 | 3 | 3 |
| Flush | 2 | 2 | 2 | 2 |
| All other | 1 | 1 | 1 | 1 |
Caribbean Hold 'Em Warning
Be warned that Realtime Gaming has an imitation of this game called Caribbean Hold 'Em. However, they pay 1 to 1 on the Ante if the dealer doesn't qualify, as opposed to the full Ante Bonus pay table. Nowhere is this rule change disclosed in their game rules, I might add.
Analysis
The following table shows the number of combination, probability, and contribution to the return of all possible outcomes under ante pay table 3, which I'm told is the most frequently used. The lower right cell shows a house edge of 2.16%.
Return Table — Pay Table 3Expand
| Hand | Pays | Combinations | Probability | Return |
|---|---|---|---|---|
| Player wins with royal flush | 102 | 736259040 | 0.000026 | 0.002700 |
| Player has royal flush, dealer doesn't qualify | 100 | 119892960 | 0.000004 | 0.000431 |
| Player wins with straight flush | 22 | 6001122284 | 0.000216 | 0.004747 |
| Player has straight flush, dealer doesn't qualify | 20 | 1089672828 | 0.000039 | 0.000784 |
| Player wins with four of a kind | 12 | 41419896552 | 0.001489 | 0.01787 |
| Player has four of a kind, dealer doesn't qualify | 10 | 909499320 | 0.000033 | 0.000327 |
| Player wins with full house | 5 | 589505037660 | 0.021195 | 0.105973 |
| Player wins with flush | 4 | 505131419580 | 0.018161 | 0.072645 |
| Player wins with straight or less | 3 | 6426670016572 | 0.23106 | 0.693181 |
| Player has full house, dealer doesn't qualify | 3 | 24601676832 | 0.000885 | 0.002654 |
| Player has flush, dealer doesn't qualify | 2 | 168883536432 | 0.006072 | 0.012144 |
| Player has straight or less, dealer doesn't qualify | 1 | 5521376219148 | 0.198512 | 0.198512 |
| Tie | 0 | 678596916580 | 0.024398 | 0 |
| Player folds | -1 | 5009067102600 | 0.180093 | -0.180093 |
| Player loses | -3 | 8839701755612 | 0.317817 | -0.953451 |
| Total | 27813810024000 | 1 | -0.021576 |
The following return table is four pay table 4. The lower right cell shows a house edge of 0.35%. This pay table can be found at Internet casinos using Gamesys N.V. software titled 'Casino Hold 'Em with Zero House Edge.' As you can see, the 'Zero House Edge' part is a misnomer. The player must pay a 10% commission on any net gambling win per session. A 'session' ends after a period of one hour with no bet or 24 hours, whichever happens first.
The owner of Casino Hold 'Em wishes for me to state that Gamesys N.V. is using his game without permission.
Return Table — Pay Table 4Expand
| Hand | Pays | Combinations | Probability | Return |
|---|---|---|---|---|
| Player wins with royal flush | 102 | 736,259,040 | 0.000026 | 0.002700 |
| Player has royal flush, dealer doesn't qualify | 100 | 119,892,960 | 0.000004 | 0.000431 |
| Player wins with straight flush | 51 | 6,031,161,932 | 0.000217 | 0.011059 |
| Player has straight flush, dealer doesn't qualify | 49 | 1,096,758,936 | 0.000039 | 0.001932 |
| Player wins with four of a kind | 19 | 41,421,337,056 | 0.001489 | 0.028295 |
| Player has four of a kind, dealer doesn't qualify | 17 | 909,634,104 | 0.000033 | 0.000556 |
| Player wins with full house | 5 | 589,638,417,816 | 0.021199 | 0.105997 |
| Player wins with flush | 4 | 505,727,272,920 | 0.018183 | 0.072730 |
| Player wins with straight or less | 3 | 6,429,871,396,516 | 0.231175 | 0.693526 |
| Player has full house, dealer doesn't qualify | 3 | 24,601,738,176 | 0.000885 | 0.002654 |
| Player has flush, dealer doesn't qualify | 2 | 169,051,416,912 | 0.006078 | 0.012156 |
| Player has straight or less, dealer doesn't qualify | 1 | 5,526,154,486,512 | 0.198684 | 0.198684 |
| Tie | 0 | 679,763,871,140 | 0.024440 | 0.000000 |
| Player folds | -1 | 4,984,375,678,920 | 0.179205 | -0.179205 |
| Player loses | -3 | 8,854,310,701,060 | 0.318342 | -0.955027 |
| Total | 27,813,810,024,000 | 1.000000 | -0.003511 |
I would like to thank Stephen How of Discount Gambling for supplying the combinations in pay table 4.
The only pay tables fully analyzed are 3 and 4, because it takes my computer about a month to cycle through all possible combinations. However, assuming the player was following optimal strategy under pay table 3 but playing under pay table 1 or 2, the house edge under pay table 1 would be 2.40%, and under pay table 2 would be 1.96%. The actual house edge under pay tables 1 and 2 would be slightly less or equal to these figures.
Strategy
Unfortunately, there is no easy way to quantify optimal strategy for this game. I can say that the optimal strategy player will raise 82% of the time. So only in the worst 18% of hands should the player fold. In general these are when the player has two singletons in the hole that are low compared to the flop, with little or no chance for a straight or flush.
Side Bets
The only side bet I am aware of for this game is known as the AA+. It pays based on the poker value of the player's hand after the flop. There are three known pay tables, as follows:
AA+ Pay Tables
| Hand | Pay Table 1 | Pay Table 2 | Pay Table 3 |
|---|---|---|---|
| Royal Flush | 25 | 100 | 100 |
| Straight flush | 25 | 50 | 50 |
| 4 of a kind | 25 | 40 | 40 |
| Full house | 25 | 30 | 30 |
| Flush | 25 | 20 | 20 |
| Straight | 7 | 7 | 10 |
| Three of a kind | 7 | 7 | 8 |
| Two pair | 7 | 7 | 7 |
| Pair of aces | 7 | 7 | 7 |
| House edge | 6.40% | 6.26% | 2.97% |
Pay tables 1 and 2 can be found in land casinos. Pay table 3 is used by Internet casinos using Gamesys software.
Texas Hold'em Poker Odds Calculator
As an example, following is the full return table for Pay Table 1.
AA+ Side Bet — Pay Table 1
| Hand | Pays | Combinations | Probability | Return |
|---|---|---|---|---|
| Royal Flush | 25 | 4 | 0.000002 | 0.000038 |
| Straight flush | 25 | 36 | 0.000014 | 0.000346 |
| 4 of a kind | 25 | 624 | 0.000240 | 0.006002 |
| Full house | 25 | 3744 | 0.001441 | 0.036014 |
| Flush | 25 | 5108 | 0.001965 | 0.049135 |
| Straight | 7 | 10200 | 0.003925 | 0.027473 |
| Three of a kind | 7 | 54912 | 0.021128 | 0.147899 |
| Two pair | 7 | 123552 | 0.047539 | 0.332773 |
| Pair of aces | 7 | 84480 | 0.032505 | 0.227537 |
| Other | -1 | 2316300 | 0.891241 | -0.891241 |
| Total | 2598960 | 1 | -0.064023 |
Progressive Jackpot
The Progressive Jackpot bet shall pay based on the player's two hole cards and the five community cards only. It does not matter whether or not the player folds or loses to the dealer. In the event of a straight flush or royal flush on the board, all players who made the Progressive Jackpot bet shall split the win.
The following table shows the probability and contribution to the return for each event. Obviously, the return from the top two awards will depend on the jackpot size, so are treated as unknowns.
Progressive Jackpot
| Hand | Pays | Combinations | Probability | Return |
|---|---|---|---|---|
| Royal flush | Jackpot | 4,324 | 0.000032 | x |
| Straight flush | 10% of Jackpot | 37,260 | 0.000279 | y |
| 4 of a kind | $100.00 | 224,848 | 0.001681 | 0.168100 |
| Full house | $10.00 | 3,473,184 | 0.025961 | 0.259610 |
| Other | $0.00 | 130,044,944 | 0.972047 | 0.000000 |
| Total | $0.00 | 133,784,560 | 1.000000 | 0.487931+x+y |
The table above shows the fixed wins return 42.77% of the amount bet. Assuming the player is playing alone, for every $1,000 in the meter the return will increase by 6.02%. Under the same assumption, the break-even point is $9,503.22. Due to jackpot sharing, the return will go down slightly according to the number of other players making the bet.
Jumbo Jackpot
There is another progressive jackpot called the 'Jumbo Jackpot.' The following table shows the wins, probabilities and the contribution to the return for each type of winning hand.
Jumbo Jackpot
| Hand | Pays | Combinations | Probability | Return |
|---|---|---|---|---|
| 7-card straight flush | ? | 32 | 0.00000024 | x |
| 6-card straight flush | $5,000.00 | 752 | 0.00000562 | 0.028105 |
| 5-card straight flush | $250.00 | 40,800 | 0.00030497 | 0.076242 |
| 4 of a kind | $50.00 | 224,848 | 0.00168067 | 0.084034 |
| Full house | $5.00 | 3,473,184 | 0.02596102 | 0.129805 |
| Flush | $4.00 | 4,047,644 | 0.03025494 | 0.121020 |
| Straight | $2.00 | 6,180,020 | 0.04619382 | 0.092388 |
| Other | $0.00 | 119,817,280 | 0.89559871 | 0.000000 |
| Total | $0.00 | 133,784,560 | 1.00000000 | 0.531593 |
The return for the top award depends on the amount in the jackpot. I can say that all the other wins return 53.16% of money bet. For every 100,000 bet units in the meter the return increases by 2.39%. At a jackpot of $1,958,300.75 the return reaches 100%.
Progressive Jackpot Side Bet
There is yet another side bet based on the player's first two cards and the three-card flop. I put information about it in my page titled Casino Hold Em Progressive Jackpot Side Bet'.
Casino Razz Bonus
I believe this side bet pays according to the poker value of the player's two hole cards and the three cards on the flop -- the lower the poker value, the more it pays. For all the rules and analysis, please see my page on Casino Razz Bonus.
Methodology
The above analysis was performed using a brute force combinatorial program that analyzed all 27,813,810,024,000 possible outcomes, and played every hand according to optimal player strategy. It took my computers about a month to crank though the 27.8 trillion hands.
External Links
Texas Hold'em Poker Odds On Hands
The web site for Casino Hold'em, as well as other games, is www.casinopokergames.com.
There is a good Casino Hold 'Em calculator at beatingbonuses.com.
Odds Of Texas Holdem Hands
