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Push in Blackjack: the bet returns
In Blackjack, a 'Push' occurs when the player's hand total matches the dealer's hand total, excluding a player blackjack. This outcome means neither the player nor the dealer wins, and the original bet is returned to the player. For instance, if both the player and the dealer achieve a total of 18, the hand results in a push. This rule ensures the player does not lose their stake in such a tied scenario.
Blackjack Surrender, a rule modification, allows players to forfeit half their bet after the dealer checks for blackjack. This rule, while not directly a push, modifies the game's outcome by offering an alternative to losing the full stake. This player-friendly option can improve the Return to Player (RTP) by approximately 0.08 percentage points. Early surrender, though more beneficial, is rare.
The 'Don't Pass' bet in Craps also features a 'push' mechanism, specifically when a 12 is rolled before a point is established. Unlike other rolls where a 7 wins or a point is set, a 12 results in the bet being returned to the player. This specific rule contributes to the Don't Pass bet's slightly better RTP of 98.64% compared to the Pass Line bet.
Splitting in Blackjack: one hand becomes two
Splitting in Blackjack allows a player to divide a pair of cards into two separate hands, with an additional bet equal to the original wager placed on the second hand. This option is available when the initial two cards dealt are of the same rank, such as two Sevens or two Tens. The game then proceeds with each hand independently.
Blackjack rules often permit doubling down after splitting (DAS), a strategic move that allows players to double their bet after splitting a pair, receiving only one more card. This rule can significantly improve the player's RTP by approximately 0.14 percentage points, especially when combined with other liberal rules. Ass-splitting typically involves receiving only one additional card per split ace.
The effectiveness of splitting is further enhanced by the ability to resplit Aces, a rule that allows players to split Aces that are dealt after the initial split. This specific rule, known as Resplit Aces (RSA), can improve the RTP by about 0.08 percentage points. These rule variations demonstrate how adjustments can impact the house edge and player advantage.
Craps Odds Bet with 0 Percent House Edge
The 'Odds Bet' in Craps is a unique wager placed behind the Pass Line or Don't Pass Line bet once a point has been established. This bet has no house edge, meaning it offers a 0 percent house advantage. Players can bet any amount on the Odds Bet, and the payouts are based on the true probability of the point being rolled before a 7.
The mathematics behind Craps Odds Bets are crucial for understanding their advantage. For example, if a point of 4 or 10 is established, the Odds Bet pays 2:1, meaning for every 1 unit bet, the player wins 2 units. If the point is 5 or 9, the Odds Bet pays 3:2, and for a point of 6 or 8, it pays 6:5. These payouts are true odds, hence no house edge.
While the Odds Bet itself has a 0 percent house edge, it is contingent on a preceding Pass Line or Don't Pass bet, which does carry a house edge. The Pass Line bet has a house advantage of 1.41%, and the Don't Pass bet has a house advantage of 1.36%. Therefore, the overall house edge of playing Craps is influenced by the proportion of these bets relative to the Odds Bets placed.
37 vs. 38 Sectors: What the Double Zero Costs
European Roulette features a wheel with 37 sectors, numbered 1 through 36 plus a single zero (0). In contrast, American Roulette wheels have 38 sectors, including both a single zero (0) and a double zero (00). This additional sector significantly impacts the game's mathematics and the house edge.
The presence of the double zero (00) on an American Roulette wheel increases the house edge considerably compared to European Roulette. For instance, on outside bets like Red/Black, Odd/Even, or High/Low, the house edge on a European wheel is 2.70%, whereas on an American wheel, it doubles to 5.26%. This is because the probability of winning an even-money bet is reduced.
The difference in payouts also reflects the extra sector. While a straight-up bet on a single number pays 35:1 in both versions, the probability of hitting that number is lower on the 38-sector wheel. This means the 37-sector European wheel, with its single zero, offers a better RTP of 97.30% for inside bets, compared to the 38-sector wheel's RTP of 94.74%.
Split 17:1 and Corner 8:1 in Payout Comparison
In Roulette, 'Split' bets, which cover two adjacent numbers, typically pay 17:1. This payout is consistent across various European and French Roulette variants, including those with specific rules like La Partage. A 'Corner' bet, covering four numbers arranged in a square, offers a payout of 8:1.
These payouts are crucial when comparing different Roulette versions. For example, French Roulette with La Partage offers a 98.65% RTP on even-chance bets due to a rule where half the stake is returned on a zero. However, for inside bets like Splits and Corners, the RTP remains linked to the standard European wheel calculation, which is 97.30%.
When evaluating Roulette games, it is important to note that the RTP for inside bets like a 17:1 Split or an 8:1 Corner bet remains constant at 97.30% on a standard European wheel, regardless of whether La Partage or En Prison rules apply to even-chance wagers. The house edge for these specific bets is 2.70%.
Game categories at a glance
| Category | Examples | Stakes From | Highlight |
|---|---|---|---|
| Slots | Money Train 4, Valley of the Gods, Cygnus 4 | 0,10 EUR | thousands of titles |
| Table games | Roulette, Blackjack, Baccarat | 0,50 EUR | classic rules |
| Live casino | Infinite Blackjack, Quantum Roulette | 0,20 EUR | real dealers |
| Jackpot games | Mega Moolah, Divine Fortune, Age of the Gods | 0,20 EUR | progressive pools |
| Instant games | Aviator, Plinko, Mines | 0,10 EUR | fast rounds |
| Video poker | Jacks or Better, Deuces Wild | 0,25 EUR | strategy based |
Hold or discard five cards: the decision
The video poker game Jacks or Better, with an 8/5 payout structure, presents a theoretical return to player (RTP) of 97.29%. This figure indicates a house edge of 2.71%, meaning that over extensive play, the casino expects to retain 2.71% of all wagers. The payout for a Full House is 8 units, and for a Flush is 5 units, which is a key factor in this RTP.
Compared to a 9/6 payout structure for Jacks or Better, which offers a higher RTP of 99.18%, the 8/5 version is less favourable. The reduction in payout for a Full House and Flush by two units significantly impacts the player's theoretical return. For instance, a 9/5 version yields 98.45% RTP, and an 8/6 version yields 98.39%.
For the player, this translates to a higher average cost of play. A 2.71% house edge means that for every €100 wagered, €2.71 is expected to be lost in the long run. This calculation is based on millions of simulated hands and assumes optimal strategy is employed by the player.
Dozen 2:1 Hits 12 of 37 Numbers
In European Roulette, bets on Dozens or Columns cover 12 of the 37 available numbers on the wheel. These bets offer a payout of 2:1, meaning a successful wager returns double the initial stake plus the stake itself. The wheel contains numbers 1 through 36, plus a single zero.
The house edge on European Roulette is consistently 2.70% across all bet types, including Dozen and Column bets. This is calculated from the payout structure; for example, a 2:1 payout on 12 numbers means that if the ball lands on any of the remaining 25 numbers (plus zero), the bet is lost. This results in an expected loss for the player over time.
For players, this means a theoretical loss of €2.70 for every €100 wagered on Dozen or Column bets. This edge applies uniformly to all bets in European Roulette, unlike games with varying odds for different wager types. Internal bets such as a Straight bet offer 35:1, but also contribute to the overall 2.70% house edge.
Pass Line in Craps: Process in Four Steps
The Pass Line bet in Craps is a fundamental wager where players bet on the shooter rolling a specific number sequence. The game begins with the Come Out roll, where rolling a 7 or 11 results in an immediate win for the Pass Line bet. Conversely, rolling a 2, 3, or 12 results in an immediate loss for this wager.
If a point number (4, 5, 6, 8, 9, or 10) is rolled on the Come Out roll, that number becomes the point. The shooter then continues to roll the dice in an attempt to roll the point number again before rolling a 7. Should the point number be rolled again, the Pass Line bet wins at 1:1 odds.
The house edge on the Pass Line bet in Craps is 1.41%, which is considered relatively low for casino games. This edge is consistent across the entire game progression. The theoretical average retention for the casino is €1.41 for every €100 wagered on the Pass Line.
Blackjack flow: cards, decision, payout 3:2
In Blackjack, the player aims to achieve a hand total closer to 21 than the dealer without exceeding 21. The game typically involves multiple decks, and a common payout for a Blackjack (an Ace and a ten-value card on the initial two cards) is 3:2. Other hands win at 1:1.
The game proceeds with players making decisions such as Hit (take another card), Stand (take no more cards), Double Down (double the bet and take one more card), or Split (if the first two cards have the same rank, they can be split into two separate hands). The specific rules, such as whether the dealer hits or stands on a soft 17, influence the house edge.
With liberal rules such as standing on soft 17, allowing Double After Split, and offering a 3:2 Blackjack payout, the house edge can be as low as 0.28%. This is significantly lower than many other casino games, making Blackjack a popular choice for players seeking better theoretical returns. The standard deviation for such a game is 1.15.
How many sectors does the Game Show wheel have?
The provided data does not specify the number of sectors on a Game Show wheel. However, it does detail the mathematics behind certain casino games, such as Sic Bo, which involves dice rolls rather than a spinning wheel. In Sic Bo, specific bets have significantly different house edges.
For example, in Sic Bo, the 'Single Number' bet has the lowest special bet house edge at 7.87%, with payouts ranging from 1:1 to 3:1 depending on how many times the chosen number appears on the dice. Conversely, the 'Specific Double' bet carries the highest house edge of 18.52%, paying out at 10:1.
The RTP for Sic Bo special bets ranges from 81.48% to 92.13%, indicating a substantial house advantage. For instance, an 'Any Triple' bet has a house edge of 13.89%, and a 'Specific Triple' pays 180:1 but still contributes to a high house advantage.
Game Shows: sectors, multipliers, and bet ranges
Specific multipliers for Sic Bo special bets can vary significantly, impacting the house edge. For instance, a Specific Triple bet offers a payout of 180:1, while a Single Number bet can range from 1:1 to 3:1 depending on the number of dice matching. This disparity means the house edge on these bets ranges from 7.87% to 18.52%.
The house edge on Sic Bo's special bets is a critical factor for players to consider. The most favourable special bet is the Single Number, with a house edge of 7.87%. Conversely, the Specific Double bet presents the highest house edge among special bets, at 18.52%.
Understanding the payout structure for Sic Bo special bets is essential for informed play. Bets like Any Triple have a payout of 30:1, leading to a house edge of 13.89%. A Two-Dice Combo bet pays 5:1, resulting in a house edge of 16.67%, highlighting the importance of choosing bets with lower house advantages.
Declining Insurance: The Most Common Blackjack Mistake
The 'Late Surrender' rule in Blackjack offers players a strategic option to forfeit half their bet after the dealer checks for blackjack, improving the RTP by approximately 0.08 percentage points. This rule is distinct from 'Early Surrender', which is far more valuable but rarely encountered.
While Late Surrender provides a slight RTP improvement, it's crucial to differentiate it from other rule effects that influence gameplay. For example, Doubling After Split (DAS) improves RTP by about 0.14 percentage points, demonstrating the cumulative effect of favourable rules.
The impact of rule variations on Blackjack RTP is substantial. For instance, the Blackjack Liberal Vegas Strip variant, with favourable rules like S17, DAS, Resplit, and Late Surrender, achieves an RTP of 99.72% with a house edge of only 0.28%.
Corner Pays 8:1, Dozen Only 2:1
European Roulette, with its single zero, features distinct payout ratios for different bet types, contributing to a consistent house edge across all wagers. A Corner bet, covering four numbers, pays 8:1, while a Dozen bet, covering twelve numbers, pays 2:1. Both bets operate on the same underlying mathematical structure.
The payout for a Dozen bet in European Roulette is 2:1, covering twelve numbers. This means for every unit staked, a successful outcome returns two units plus the original stake. The house edge on this bet, as with all bets on this wheel, remains at 2.70%.
A Corner bet in European Roulette pays 8:1, covering a group of four numbers. Despite the different payout, the house advantage remains consistent at 2.70% due to the inclusion of the single zero on the wheel, which has 37 sectors in total.
Straight 35:1 Instead of 36:1: Where House Edge Originates
The origin of the house edge in Roulette can be traced to the payout structure for Straight bets. Instead of a true 36:1 payout for a single number bet on a wheel with 36 numbered pockets, the payout is 35:1. This reduction of one unit per winning bet establishes the house advantage.
In European Roulette, which features 37 sectors including a single zero, a Straight bet pays 35:1. This means that for every 37 units wagered on single numbers over the long term, players can expect to receive 36 units back, creating a 2.70% house edge.
The constant house edge of 2.70% in European Roulette applies to all bet types, including those with seemingly lower odds like Dozen or Column bets paying 2:1. This is because the payouts are calculated based on 36 sectors, not the actual 37 available numbers.
Dozen 2:1: Twelve Numbers, One Third Coverage
In European Roulette, a Dozen bet covers twelve numbers and pays out at 2:1. This means a winning bet returns twice the amount wagered, plus the original stake. Despite covering one-third of the available numbers, the payout reflects the house edge, not true odds.
The payout for a Dozen bet in European Roulette is 2:1, which is consistent with other outside bets like Column or Red/Black. The inclusion of the single zero on the wheel ensures that the house edge for all bets remains fixed at 2.70%.
Players should be aware that even though a Dozen bet covers twelve numbers, the payout of 2:1 is fixed, contributing to the overall house advantage. This structure applies across all 37 sectors of the European Roulette wheel, making the edge consistent for all wager types.
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