Greedy Play & Multipliers on DDB UltX Bonus Streak
Posted: Sat Nov 26, 2016 7:50 pm
This third segment will be focusing on the other half of the decision making process that a player needs to make while playing Ultimate X, which is the state of the game board. The first two segments were entirely based on decision making solely on the cards the players are dealt with. There is more than meets the eye with the multipliers, and will be evaluated in two subparts.
The exhaustive efforts of this segment did not improve the overall result by much.
Part 1 - Evaluating the Need for Greed Plays
Update: This part is less relevant
When a player hits a 3 of a Kind or better and a streak starts, the player is tempted to go for the best opportunity to get another 3 of a Kind or better outcome in order to transform the stack into all 12X multipliers to set up the big win. This part is to explore if the tendency of being greedy has its benefits.
From my understanding of the game I have determined that a potential bonus streak is the following:
If a hand has a stack of 2 or more multipliers AND if the active multiplier is not 8 or 12
If there is only 1 multiplier remaining and if a 3 of a Kind or better is hit, the multipliers are added on for a whole new streak. If there are only two multipliers left in a streak, and it starts at 8x, it will be insignificant to hit a Three of a Kind since the next multiplier will be 12x. If a player hits a 3 of a kind or better on a hand where it is already 12X, it will not increase the multiplier beyond the 12X.
Long story short, this greedy play should only be done when the entire board has a streak ongoing. There are 10 hands on the board, and each hand that is not on the streak will reduce the chance of achieving the bonus streak by 1.2%. If you play greedy with just one hand on an active streak, you have nearly 12% chance at getting a Bonus outcome, and need 1 in 10 chance to hit the hand, hence the 1.2%
You will likely only fill out the board with the help of a dealt Bonus outcome hand.
The part that gets most Ultimate X players excited is when they are dealt a good hand so that the entire board is full of multipliers.
Three of a Kind - 1 in 46.3
Straight - 1 in 254
Flush - 1 in 508
Full House 1 in 693
4 of a Kind of any variant - 1 in 4164
Straight Flush - 1 in 72192
Royal Flush - 1 in 649740
On average, 1 in about every 35 hands. Thus the opportunity to get greedy will happen every few minutes.
Omitted useless information as of 12-4-2016
Part 2 - Considering Multipliers when playing suboptimal holds
This is more important
The following logic is inspired from the Ultimate X playing approaches at the Wizard of Odds website, so I give credit to Shackleford where it is due.
Though it is a constant reminder that increasing the Bonus Percentage comes at a cost of expected return on some card deals, it is important to be aware that the cost will only get magnified with the presence of multipliers. Despite how high the multipliers get, the Bonus Percentage remains constant.
This is where the concept of the “Average Multiplier†comes into factor. Mastering this will give the player a few additional hundredth percentage in return, but it will break the simplicity of mastering the strategy if player chooses to.
Before taking a look at the cards on the deal, for every round the player should total up the current multipliers on each of the ten hands. If there is no multiplier, then add a value of 1 to the overall sum.
If Hand 2 and 4 have 2x and if Hand 5 has 3x, while others do not have multipliers, it will be a total of 14X. The total is divided into the number of hands played, in this case 10, for the AVERAGE MULTIPLIER of 1.4X for the hand.
Take for example
Discard Entire Hand VS 3 to Flush with No High Cards
Cards Drawn: 2 ♦ 5 ♥ 6 ♣ 9 ♥ 10 ♥
Expected Result: 1.6127694777954
Bonus Percentage: 0.0277651197342267
Optimal Cards Held:
Bonus Hold
Cards Held: 5 ♥ 9 ♥ 10 ♥
Expected Result: 1.40148011100833
Bonus Percentage: 0.0499537465309898
The suboptimal play of 3 to a Flush with no High Cards results in a loss of .211 credits to gain about 2.22% in Bonus Percentage. With the Average Multiplier of 1.4X which is considered low, the player will be losing 0.2954 credits. It might still be worth making the play. If the Average Multiplier is 5.5X, it will become a more serious loss of 1.1605 credits to trade off for the 2.22% Bonus Percentage. The Player must decide to his or her own weather the suboptimal play will be worthwhile or not.
The exhaustive efforts of this segment did not improve the overall result by much.
Part 1 - Evaluating the Need for Greed Plays
Update: This part is less relevant
When a player hits a 3 of a Kind or better and a streak starts, the player is tempted to go for the best opportunity to get another 3 of a Kind or better outcome in order to transform the stack into all 12X multipliers to set up the big win. This part is to explore if the tendency of being greedy has its benefits.
From my understanding of the game I have determined that a potential bonus streak is the following:
If a hand has a stack of 2 or more multipliers AND if the active multiplier is not 8 or 12
If there is only 1 multiplier remaining and if a 3 of a Kind or better is hit, the multipliers are added on for a whole new streak. If there are only two multipliers left in a streak, and it starts at 8x, it will be insignificant to hit a Three of a Kind since the next multiplier will be 12x. If a player hits a 3 of a kind or better on a hand where it is already 12X, it will not increase the multiplier beyond the 12X.
Long story short, this greedy play should only be done when the entire board has a streak ongoing. There are 10 hands on the board, and each hand that is not on the streak will reduce the chance of achieving the bonus streak by 1.2%. If you play greedy with just one hand on an active streak, you have nearly 12% chance at getting a Bonus outcome, and need 1 in 10 chance to hit the hand, hence the 1.2%
You will likely only fill out the board with the help of a dealt Bonus outcome hand.
The part that gets most Ultimate X players excited is when they are dealt a good hand so that the entire board is full of multipliers.
Three of a Kind - 1 in 46.3
Straight - 1 in 254
Flush - 1 in 508
Full House 1 in 693
4 of a Kind of any variant - 1 in 4164
Straight Flush - 1 in 72192
Royal Flush - 1 in 649740
On average, 1 in about every 35 hands. Thus the opportunity to get greedy will happen every few minutes.
Omitted useless information as of 12-4-2016
Part 2 - Considering Multipliers when playing suboptimal holds
This is more important
The following logic is inspired from the Ultimate X playing approaches at the Wizard of Odds website, so I give credit to Shackleford where it is due.
Though it is a constant reminder that increasing the Bonus Percentage comes at a cost of expected return on some card deals, it is important to be aware that the cost will only get magnified with the presence of multipliers. Despite how high the multipliers get, the Bonus Percentage remains constant.
This is where the concept of the “Average Multiplier†comes into factor. Mastering this will give the player a few additional hundredth percentage in return, but it will break the simplicity of mastering the strategy if player chooses to.
Before taking a look at the cards on the deal, for every round the player should total up the current multipliers on each of the ten hands. If there is no multiplier, then add a value of 1 to the overall sum.
If Hand 2 and 4 have 2x and if Hand 5 has 3x, while others do not have multipliers, it will be a total of 14X. The total is divided into the number of hands played, in this case 10, for the AVERAGE MULTIPLIER of 1.4X for the hand.
Take for example
Discard Entire Hand VS 3 to Flush with No High Cards
Cards Drawn: 2 ♦ 5 ♥ 6 ♣ 9 ♥ 10 ♥
Expected Result: 1.6127694777954
Bonus Percentage: 0.0277651197342267
Optimal Cards Held:
Bonus Hold
Cards Held: 5 ♥ 9 ♥ 10 ♥
Expected Result: 1.40148011100833
Bonus Percentage: 0.0499537465309898
The suboptimal play of 3 to a Flush with no High Cards results in a loss of .211 credits to gain about 2.22% in Bonus Percentage. With the Average Multiplier of 1.4X which is considered low, the player will be losing 0.2954 credits. It might still be worth making the play. If the Average Multiplier is 5.5X, it will become a more serious loss of 1.1605 credits to trade off for the 2.22% Bonus Percentage. The Player must decide to his or her own weather the suboptimal play will be worthwhile or not.