This will be my 2nd segment for exploring a decent approach to 10-Play DDB Ultimate X Bonus Streak. The 1st segment revolves around simulating long term play using a specific approach and I will be updating each segment as new information is discovered.
I do not typically play Ultimate X, but what I do know about Ultimate X is that it is about setting up multipliers so that the player’s next hand can potentially pay out big, fulfilling the typical recreational gambler’s dream. The volatility of the game makes it so popular. Since the player wagers double the amount to play Ultimate X, not having multipliers will quickly burn away the bankroll. Thus it is important for the player to consistently set up multipliers to make up for the loss swings experienced for the game.
Knowledgeable Ultimate X players already know a different strategy is involved than traditional video poker, this Bonus Streak edition is no different. The optimal strategy for standard 8/5 DDB yields the highest expected return for the game, but NOT always will produce the highest chance to set up multipliers for the next hand.
Royal Flush, Straight Flush, all Four of a Kinds, and Full House will yield multipliers for the next 5 hands: 2x, 3x, 4x, 8x, 12x
Three of a Kind, Straights, Flushes will yield multipliers for the next 3 hands: 2x, 3x, 4x
* As a reminder, I am seeking to achieve an approach that is better than what the average Ultimate X player will do; not the most optimal play.
On the first segment, I mentioned a breakdown of the optimal hands.
Out of the 134459 unique (suit+rank) arrangements of 5 card draws, 78707 of them whose optimal expected value holds also produce the highest percentage of chance the player will get a Three of a Kind or better hand to get a multiplier. Thus for the rest of the 55752 arrangements, the player must weigh the situation and make non-optimal plays (sacrificing overall return) when necessary in hopes for greater chances of multipliers. This process is not straight forward and will take people like myself time to evaluate.
I am going to use “Bonus Percentage†as a guideline for my exploration. This is where I take the number of Three of a Kind or Better hands and divide them by the total possibilities.
9 ♥ J ♦ 10 ♣ 9 â™ 3 â™
The Optimal Play is to hold the Pair of 9s and draw 3 more cards. There are 16215 ways to draw 3 cards from the remaining 47 cards, and here are the possible breakdowns.
0 - Royal Flush
0 - Straight Flush
0 - 4 Aces with Any 2, 3, 4
0 - 4 Aces
0 - 4 2s, 3s, 4s with Ace, 2, 3, 4
0 - 4 2s, 3s, 4s
45 - 4 5s thru Kings
165 - Full House
0 - Flush
0 - Straight
1854 - 3 of a Kind
2592 - 2 Pairs
0 - Jacks or Better
11559 - Nothing
I add up the 3 of a Kind better hands -> 1854 + 165 + 45 = 2064 possibilities
Thus the Bonus Percentage of this hold is = 2064 / 16215 = 0.1273
No other holds produce a greater Bonus Percentage so I am going to play this hold under this situation.
Before you get too far ahead, decision making based on multipliers will be for the 3rd segment for my exploration with Ultimate X Bonus Streak.
I will leave this segment strictly to discuss the most opportune times to perform non-optimal plays and achieve a greater result.
Update 11-19-2016
I have fortunately found a few adjustments a player can incorporate to increase their long term return from 96.695 -> 96.818% (verified on the simulator).
Out of the 55752 holds, I’ve filtered out the holds that:
1. Only less than 5% loss of the most optimal returning hold
2. Will provide an increase of at least 2% chance (0.02) increase of Bonus Percentage
904 matches that filter, and an improvement was shown.
Playing 8/5 DDB Standard Video Poker Optimal Strategies and the following:
1. Three to Straight Flush with no Gaps vs QJ Suited
Cards Drawn: 4 ♥ 5 ♥ 6 ♥ J ♦ Q ♦
Expected Result: 2.86339808818995
Bonus Percentage: 0.0403946962688868
Optimal Cards Held: J ♦ Q ♦
Bonus Hold
Cards Held: 4 ♥ 5 ♥ 6 ♥
Expected Result: 2.83071230342276
Bonus Percentage: 0.091581868640148
I lose 0.03 coins to increase my Bonus Percentage from 4.04% to 9.16%. Great Trade
2. Three to Straight Flush with 2 High Cards and 2 Gaps vs 4 to Inside Straight with 3 High Cards
Cards Drawn: A ♦ 8 ♥ 10 ♦ J ♥ Q ♥
Expected Result: 2.79833487511563
Bonus Percentage: 0.0601295097132285
Optimal Cards Held: 8 ♥ J ♥ Q ♥
Bonus Hold
Cards Held: J ♥ Q ♥ A ♦ 10 ♦
Expected Result: 2.65957446808511
Bonus Percentage: 0.0851063829787234
I lose 0.23 coins to increase my Bonus Percentage from 6.02% to 8.5%. Moderate Trade
3. Four to Inside Straight vs Two Suited High Cards
Cards Drawn: 8 ♦ 9 ♣ J ♠Q ♠K ♥
Expected Result: 2.74128893000308
Bonus Percentage: 0.03595436324391
Optimal Cards Held: J â™ Q â™
Bonus Hold
Cards Held: K ♥ 9 ♣ J â™ Q â™
Expected Result: 2.65957446808511
Bonus Percentage: 0.0851063829787234
I lose 0.08 coins to increase my Bonus Percentage from 3.60% to 8.5%. Good Trade
4. Three to Straight Flush with 1 Gaps vs Ace
Cards Drawn: A ♦ 6 ♣ 7 ♥ 9 ♥ 10 ♥
Expected Result: 2.37403638606229
Bonus Percentage: 0.0301796877190032
Optimal Cards Held: A ♦
Bonus Hold
Cards Held: 7 ♥ 9 ♥ 10 ♥
Expected Result: 2.28492136910268
Bonus Percentage: 0.0740055504162812
I lose 0.09 coins to increase my Bonus Percentage from 3.02% to 7.4%. Good Trade
4. Three to Straight Flush with 1 Gaps vs Ace
Cards Drawn: A ♦ 6 ♣ 7 ♥ 9 ♥ 10 ♥
Expected Result: 2.37403638606229
Bonus Percentage: 0.0301796877190032
Optimal Cards Held: A ♦
Bonus Hold
Cards Held: 7 ♥ 9 ♥ 10 ♥
Expected Result: 2.28492136910268
Bonus Percentage: 0.0740055504162812
I lose 0.09 coins to increase my Bonus Percentage from 3.02% to 7.4%. Good Trade
5. QJ Unsuited vs QJT
Cards Drawn: 2 ♥ 3 ♥ 10 ♦ J ♦ Q ♥
Expected Result: 2.28060437866173
Bonus Percentage: 0.0274437249460376
Optimal Cards Held: Q ♥ J ♦
Bonus Hold
Cards Held: Q ♥ 10 ♦ J ♦
Expected Result: 2.24791859389454
Bonus Percentage: 0.0527289546716004
I lose 0.04 coins to increase my Bonus Percentage from 2.74% to 5.27%. Good Trade
6. QT Suited vs 4 to Inside Straight with Queen High
Cards Drawn: 5 ♥ 8 ♦ 9 ♣ 10 ♥ Q ♥
Expected Result: 2.10237434474252
Bonus Percentage: 0.0349059512796793
Optimal Cards Held: 10 ♥ Q ♥
Bonus Hold
Cards Held: 10 ♥ Q ♥ 8 ♦ 9 ♣
Expected Result: 2.02127659574468
Bonus Percentage: 0.0851063829787234
I lose 0.08 coins to increase my Bonus Percentage from 3.49% to 8.51%. Great Trade
7. Queen vs 4 to Inside Straight with Queen High
Cards Drawn: 4 ♥ 8 ♦ 9 ♥ 10 ♣ Q ♥
Expected Result: 2.1115970061391
Bonus Percentage: 0.0285650211644661
Optimal Cards Held: Q ♥
Bonus Hold
Cards Held: 9 ♥ Q ♥ 8 ♦ 10 ♣
Expected Result: 2.02127659574468
Bonus Percentage: 0.0851063829787234
I lose 0.09 coins to increase my Bonus Percentage from 2.86% to 8.51%. Great Trade
*** Evaluation To Be Determined ***
Since it is a benefit to hit Three of a Kind, would it be wise to start breaking up 2 pairs if one of them is a high pair?
Cards Drawn: 9 ♥ 9 ♦ J ♣ J ♠2 ♥
Expected Result: 7.97872340425532
Bonus Percentage: 0.0851063829787234
Optimal Cards Held: 9 ♥ 9 ♦ J ♣ J â™
Bonus Hold
Cards Held: J ♣ J â™
Expected Result: 7.18686401480111
Bonus Percentage: 0.127412889300031
The Player gives up 0.80 credits to get from 8.5 to 12.74% chance at a bonus ..., on 10-play it will be 8 credits. I project that it is not a worthy tradeoff.
Good non-Optimal holds in DDB UltX Bonus Streak
-
alpax
- Video Poker Master
- Posts: 1913
- Joined: Sat Jun 14, 2014 4:42 pm
-
alpax
- Video Poker Master
- Posts: 1913
- Joined: Sat Jun 14, 2014 4:42 pm
Update 11-20-2016
Added Filter on top of the previous one. An increase in return is experienced which is a positive sign.
Only less than 7.5% loss of the most optimal returning hold and will provide an increase of at least 3% chance (0.03) increase of Bonus Percentage
1855 matches that filter, and an improvement was shown in the 100 trial simulation.
Number of 96.00% to 96.10% Return: 2
Number of 96.10% to 96.20% Return: 0
Number of 96.20% to 96.30% Return: 4
Number of 96.30% to 96.40% Return: 2
Number of 96.40% to 96.50% Return: 3
Number of 96.50% to 96.60% Return: 5
Number of 96.60% to 96.70% Return: 8
Number of 96.70% to 96.80% Return: 12
Number of 96.80% to 96.90% Return: 17
Number of 96.90% to 97.00% Return: 13
Number of 97.00% to 97.10% Return: 9
Number of 97.10% to 97.20% Return: 10
Number of 97.20% to 97.30% Return: 5
Number of 97.30% to 97.40% Return: 3
Number of 97.40% to 97.50% Return: 5
Number of 97.50% to 97.60% Return: 0
Number of 97.60% to 97.70% Return: 1
Number of 97.70% to 97.80% Return: 1
Number of 97.80% to 97.90% Return: 0
Number of 97.90% to 98.00% Return: 0
Total Average of 100 trials is 212758585 for return of 96.881%
8. Four to Outside Straight VS Low Pair (5s thru 10s)
Cards Drawn: 6 ♥ 6 ♦ 3 ♦ 4 ♥ 5 ♥
Expected Result: 3.61517113783534
Bonus Percentage: 0.127289546716004
Optimal Cards Held: 6 ♥ 6 ♦
Bonus Hold
Cards Held: 4 ♥ 5 ♥ 6 ♥ 3 ♦
Expected Result: 3.40425531914894
Bonus Percentage: 0.170212765957447
I lose 0.21 coins to increase my Bonus Percentage from 12.73% to 17.02%. Good Trade
9. Three to Straight Flush with 1 High Cards and 2 Gaps vs Ace
Cards Drawn: A ♦ 8 ♥ 9 ♣ 10 ♥ Q ♥
Expected Result: 2.31071118212654
Bonus Percentage: 0.0299105766265803
Optimal Cards Held: A ♦
Bonus Hold
Cards Held: 8 ♥ 10 ♥ Q ♥
Expected Result: 2.29879740980574
Bonus Percentage: 0.0601295097132285
I lose 0.01 coins to increase my Bonus Percentage from 2.99% to 6.01%. Outstanding Trade
10. Jack vs 4 to Inside Straight with Jack High
Cards Drawn: 2 ♠7 ♠8 ♥ 9 ♦ J ♣
Expected Result: 2.18369635298405
Bonus Percentage: 0.0315813079920388
Optimal Cards Held: J ♣
Bonus Hold #1
Cards Held: 8 ♥ 9 ♦ J ♣ 7 â™
Expected Result: 2.02127659574468
Bonus Percentage: 0.0851063829787234
I lose 0.16 coins to increase my Bonus Percentage from 3.16% to 8.51%. Good Trade
Added Filter on top of the previous one. An increase in return is experienced which is a positive sign.
Only less than 7.5% loss of the most optimal returning hold and will provide an increase of at least 3% chance (0.03) increase of Bonus Percentage
1855 matches that filter, and an improvement was shown in the 100 trial simulation.
Number of 96.00% to 96.10% Return: 2
Number of 96.10% to 96.20% Return: 0
Number of 96.20% to 96.30% Return: 4
Number of 96.30% to 96.40% Return: 2
Number of 96.40% to 96.50% Return: 3
Number of 96.50% to 96.60% Return: 5
Number of 96.60% to 96.70% Return: 8
Number of 96.70% to 96.80% Return: 12
Number of 96.80% to 96.90% Return: 17
Number of 96.90% to 97.00% Return: 13
Number of 97.00% to 97.10% Return: 9
Number of 97.10% to 97.20% Return: 10
Number of 97.20% to 97.30% Return: 5
Number of 97.30% to 97.40% Return: 3
Number of 97.40% to 97.50% Return: 5
Number of 97.50% to 97.60% Return: 0
Number of 97.60% to 97.70% Return: 1
Number of 97.70% to 97.80% Return: 1
Number of 97.80% to 97.90% Return: 0
Number of 97.90% to 98.00% Return: 0
Total Average of 100 trials is 212758585 for return of 96.881%
8. Four to Outside Straight VS Low Pair (5s thru 10s)
Cards Drawn: 6 ♥ 6 ♦ 3 ♦ 4 ♥ 5 ♥
Expected Result: 3.61517113783534
Bonus Percentage: 0.127289546716004
Optimal Cards Held: 6 ♥ 6 ♦
Bonus Hold
Cards Held: 4 ♥ 5 ♥ 6 ♥ 3 ♦
Expected Result: 3.40425531914894
Bonus Percentage: 0.170212765957447
I lose 0.21 coins to increase my Bonus Percentage from 12.73% to 17.02%. Good Trade
9. Three to Straight Flush with 1 High Cards and 2 Gaps vs Ace
Cards Drawn: A ♦ 8 ♥ 9 ♣ 10 ♥ Q ♥
Expected Result: 2.31071118212654
Bonus Percentage: 0.0299105766265803
Optimal Cards Held: A ♦
Bonus Hold
Cards Held: 8 ♥ 10 ♥ Q ♥
Expected Result: 2.29879740980574
Bonus Percentage: 0.0601295097132285
I lose 0.01 coins to increase my Bonus Percentage from 2.99% to 6.01%. Outstanding Trade
10. Jack vs 4 to Inside Straight with Jack High
Cards Drawn: 2 ♠7 ♠8 ♥ 9 ♦ J ♣
Expected Result: 2.18369635298405
Bonus Percentage: 0.0315813079920388
Optimal Cards Held: J ♣
Bonus Hold #1
Cards Held: 8 ♥ 9 ♦ J ♣ 7 â™
Expected Result: 2.02127659574468
Bonus Percentage: 0.0851063829787234
I lose 0.16 coins to increase my Bonus Percentage from 3.16% to 8.51%. Good Trade
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alpax
- Video Poker Master
- Posts: 1913
- Joined: Sat Jun 14, 2014 4:42 pm
Update 11-21-2016
Some good news for today (at least in my personal opinion). I’ve found a better way to look through the report of 55752 card arrangements where the optimal play does not give the best chance at the bonus percentage.
Thus far, I was able to pinpoint some nice finds that provide significant trades. And running through the simulation with these changes yielded a very positive outcome from our progress.
100 Simulation Trial Breakdown
Number of 96.00% to 96.10% Return: 0
Number of 96.10% to 96.20% Return: 0
Number of 96.20% to 96.30% Return: 0
Number of 96.30% to 96.40% Return: 0
Number of 96.40% to 96.50% Return: 1
Number of 96.50% to 96.60% Return: 1
Number of 96.60% to 96.70% Return: 7
Number of 96.70% to 96.80% Return: 1
Number of 96.80% to 96.90% Return: 6
Number of 96.90% to 97.00% Return: 12
Number of 97.00% to 97.10% Return: 11
Number of 97.10% to 97.20% Return: 19
Number of 97.20% to 97.30% Return: 18
Number of 97.30% to 97.40% Return: 13
Number of 97.40% to 97.50% Return: 4
Number of 97.50% to 97.60% Return: 3
Number of 97.60% to 97.70% Return: 2
Number of 97.70% to 97.80% Return: 0
Number of 97.80% to 97.90% Return: 2
Number of 97.90% to 98.00% Return: 0
Total Average of 100 trials is 213321629.00000 for return of 97.141%
The total number of deals with the combined filters: 3919
New Holds:
11. KT Suited + 6/7/8 Flush Penalty VS 4 to Inside Straight
Cards Drawn: 6 ♥ 8 ♦ 9 ♦ 10 ♥ K ♥
Expected Result: 2.07815434642447
Bonus Percentage: 0.0279651276876069
Optimal Cards Held: K ♥
Bonus Hold
Cards Held: 6 ♥ 10 ♥ 8 ♦ 9 ♦
Expected Result: 1.70212765957447
Bonus Percentage: 0.0851063829787234
I lose 0.37 coins to increase my Bonus Percentage from 2.80% to 8.51%. Average Trade
This one is tricky. In 5 for 1 DDB payouts, if KT suited has a flush penalty, you only hold the King. And high cards in DDB is better than Inside Straights, but in UltX, you go for the latter since you are playing for multipliers.
12. Ace VS 4 to Ace-Low Inside Straight
Cards Drawn: A ♦ 2 ♦ 3 ♥ 4 ♥ Q ♥
Expected Result: 2.24578813107953
Bonus Percentage: 0.0284304656182547
Optimal Cards Held: A ♦
Bonus Hold
Cards Held: 3 ♥ 4 ♥ A ♦ 2 ♦
Expected Result: 2.02127659574468
Bonus Percentage: 0.0851063829787234
I lose 0.16 coins to increase my Bonus Percentage from 3.16% to 8.51%. Good Trade
13. Three to Royal VS 4 to Flush
Warning: This one is a broad situation and will need further insight.
The range of EV varies on 3 to the Royal. The ones with Ace and Ten are the least in terms of EV value, and the sequential ones QJT and JQK are worth the most. Will need to do breakdowns.
Low End - Ace+Ten (EV loss of about 0.7 coins)
Cards Drawn: 10 ♥ 10 ♦ A ♥ 7 ♥ K ♥
Expected Result: 6.11933395004625
Bonus Percentage: 0.0536540240518039
Optimal Cards Held: A ♥ 10 ♥ K ♥
Bonus Hold #1
Cards Held: A ♥ 7 ♥ 10 ♥ K ♥
Expected Result: 5.42553191489362
Bonus Percentage: 0.191489361702128
High End - KQJ Suited (EV loss of about 1.4 coins)
Cards Drawn: 2 ♥ 3 ♦ J ♥ Q ♥ K ♥
Expected Result: 7.1322849213691
Bonus Percentage: 0.0693802035152636
Optimal Cards Held: J ♥ Q ♥ K ♥
Bonus Hold #1
Cards Held: 2 ♥ J ♥ Q ♥ K ♥
Expected Result: 5.74468085106383
Bonus Percentage: 0.191489361702128
The loss return may vary due to the type of 3 to the Royal and the straight penalties. In all cases, making the hold to 4 to the Flush gives the player a big jump in Bonus Percentage from 19.15%. If the player can resist the temptation, it can be an outstanding trade
Some good news for today (at least in my personal opinion). I’ve found a better way to look through the report of 55752 card arrangements where the optimal play does not give the best chance at the bonus percentage.
Thus far, I was able to pinpoint some nice finds that provide significant trades. And running through the simulation with these changes yielded a very positive outcome from our progress.
100 Simulation Trial Breakdown
Number of 96.00% to 96.10% Return: 0
Number of 96.10% to 96.20% Return: 0
Number of 96.20% to 96.30% Return: 0
Number of 96.30% to 96.40% Return: 0
Number of 96.40% to 96.50% Return: 1
Number of 96.50% to 96.60% Return: 1
Number of 96.60% to 96.70% Return: 7
Number of 96.70% to 96.80% Return: 1
Number of 96.80% to 96.90% Return: 6
Number of 96.90% to 97.00% Return: 12
Number of 97.00% to 97.10% Return: 11
Number of 97.10% to 97.20% Return: 19
Number of 97.20% to 97.30% Return: 18
Number of 97.30% to 97.40% Return: 13
Number of 97.40% to 97.50% Return: 4
Number of 97.50% to 97.60% Return: 3
Number of 97.60% to 97.70% Return: 2
Number of 97.70% to 97.80% Return: 0
Number of 97.80% to 97.90% Return: 2
Number of 97.90% to 98.00% Return: 0
Total Average of 100 trials is 213321629.00000 for return of 97.141%
The total number of deals with the combined filters: 3919
New Holds:
11. KT Suited + 6/7/8 Flush Penalty VS 4 to Inside Straight
Cards Drawn: 6 ♥ 8 ♦ 9 ♦ 10 ♥ K ♥
Expected Result: 2.07815434642447
Bonus Percentage: 0.0279651276876069
Optimal Cards Held: K ♥
Bonus Hold
Cards Held: 6 ♥ 10 ♥ 8 ♦ 9 ♦
Expected Result: 1.70212765957447
Bonus Percentage: 0.0851063829787234
I lose 0.37 coins to increase my Bonus Percentage from 2.80% to 8.51%. Average Trade
This one is tricky. In 5 for 1 DDB payouts, if KT suited has a flush penalty, you only hold the King. And high cards in DDB is better than Inside Straights, but in UltX, you go for the latter since you are playing for multipliers.
12. Ace VS 4 to Ace-Low Inside Straight
Cards Drawn: A ♦ 2 ♦ 3 ♥ 4 ♥ Q ♥
Expected Result: 2.24578813107953
Bonus Percentage: 0.0284304656182547
Optimal Cards Held: A ♦
Bonus Hold
Cards Held: 3 ♥ 4 ♥ A ♦ 2 ♦
Expected Result: 2.02127659574468
Bonus Percentage: 0.0851063829787234
I lose 0.16 coins to increase my Bonus Percentage from 3.16% to 8.51%. Good Trade
13. Three to Royal VS 4 to Flush
Warning: This one is a broad situation and will need further insight.
The range of EV varies on 3 to the Royal. The ones with Ace and Ten are the least in terms of EV value, and the sequential ones QJT and JQK are worth the most. Will need to do breakdowns.
Low End - Ace+Ten (EV loss of about 0.7 coins)
Cards Drawn: 10 ♥ 10 ♦ A ♥ 7 ♥ K ♥
Expected Result: 6.11933395004625
Bonus Percentage: 0.0536540240518039
Optimal Cards Held: A ♥ 10 ♥ K ♥
Bonus Hold #1
Cards Held: A ♥ 7 ♥ 10 ♥ K ♥
Expected Result: 5.42553191489362
Bonus Percentage: 0.191489361702128
High End - KQJ Suited (EV loss of about 1.4 coins)
Cards Drawn: 2 ♥ 3 ♦ J ♥ Q ♥ K ♥
Expected Result: 7.1322849213691
Bonus Percentage: 0.0693802035152636
Optimal Cards Held: J ♥ Q ♥ K ♥
Bonus Hold #1
Cards Held: 2 ♥ J ♥ Q ♥ K ♥
Expected Result: 5.74468085106383
Bonus Percentage: 0.191489361702128
The loss return may vary due to the type of 3 to the Royal and the straight penalties. In all cases, making the hold to 4 to the Flush gives the player a big jump in Bonus Percentage from 19.15%. If the player can resist the temptation, it can be an outstanding trade
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alpax
- Video Poker Master
- Posts: 1913
- Joined: Sat Jun 14, 2014 4:42 pm
Analyzing the Two Pair with Face Cards Situation
I did give it a try to include the situation whenever a hand with two pairs is dealt, where a player will drop the other pair when dealt two pairs with face card in all situations (multipliers, streaks, nothing). In the long run, this move had a negative effect towards the overall return. It is not yet to be determined if this is a completely bad play, which it will be evaluated again when Segment 3 is explored with Multipliers/Streaks/Greedy Plays.
There is one noticeable aspect in which that can attribute to the negative result aside from the loss of Expected Value from dropping the pair.
In 10-Play Ultimate X, there are two levels of bonuses to consider.
The Big Bonus is 29X worth of multipliers over 5 hands, the Small Bonus is 9x worth of multipliers over 3 hands.
KK99 - Holding the two pairs, the only bonus you will get is the Big Bonus
4 Full House - Big Bonus
43 2 Pairs - No Bonus
4 / 47 = 8.51% Big Bonus and 0% Small Bonus
KK - When the player drops the other pair, three cards are drawn and it expands the number of outcomes from 47 to 16215. There is a 12.74% chance at getting the Bonus, the impact is substantial
45 4 5s thru Kings - Big Bonus
169 Full House - Big Bonus
1852 3 of a Kind - Small Bonus
2629 2 Pairs - No Bonus
11520 Jacks or Better - No Bonus
214 / 16215 = 1.32% chance you get the Big Bonus
1852 / 16215 = 11.42% chance you get the Small Bonus
The drop in the Big Bonus may account for most of the loss. The Bonus outcomes do not come out often and it seems to reason that having more hands to gain the opportunity to form 12X multipliers is vital.
Dropping the other pair reduces this Big Bonus by more than 7%.
I did give it a try to include the situation whenever a hand with two pairs is dealt, where a player will drop the other pair when dealt two pairs with face card in all situations (multipliers, streaks, nothing). In the long run, this move had a negative effect towards the overall return. It is not yet to be determined if this is a completely bad play, which it will be evaluated again when Segment 3 is explored with Multipliers/Streaks/Greedy Plays.
There is one noticeable aspect in which that can attribute to the negative result aside from the loss of Expected Value from dropping the pair.
In 10-Play Ultimate X, there are two levels of bonuses to consider.
The Big Bonus is 29X worth of multipliers over 5 hands, the Small Bonus is 9x worth of multipliers over 3 hands.
KK99 - Holding the two pairs, the only bonus you will get is the Big Bonus
4 Full House - Big Bonus
43 2 Pairs - No Bonus
4 / 47 = 8.51% Big Bonus and 0% Small Bonus
KK - When the player drops the other pair, three cards are drawn and it expands the number of outcomes from 47 to 16215. There is a 12.74% chance at getting the Bonus, the impact is substantial
45 4 5s thru Kings - Big Bonus
169 Full House - Big Bonus
1852 3 of a Kind - Small Bonus
2629 2 Pairs - No Bonus
11520 Jacks or Better - No Bonus
214 / 16215 = 1.32% chance you get the Big Bonus
1852 / 16215 = 11.42% chance you get the Small Bonus
The drop in the Big Bonus may account for most of the loss. The Bonus outcomes do not come out often and it seems to reason that having more hands to gain the opportunity to form 12X multipliers is vital.
Dropping the other pair reduces this Big Bonus by more than 7%.
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alpax
- Video Poker Master
- Posts: 1913
- Joined: Sat Jun 14, 2014 4:42 pm
Might be the last update that wraps up this part.
I looked deeper into the low EV hands, there are TONS of them whose best play averages about 2 to 2.5 units. To squeeze value out of them, did not do it on one lucky guess, but with trial and error, I give up up to 0.4 units EV to at least get 2% more Bonus Percentage.
The following added filter boosted the affected deals from 3909 to 11504. This means about 1/5 or 20% of the hands whose non-optimal plays have better Bonus Percentage than its optimal plays will be considered.
Number of 96.00% to 96.10% Return: 0
Number of 96.10% to 96.20% Return: 0
Number of 96.20% to 96.30% Return: 0
Number of 96.30% to 96.40% Return: 1
Number of 96.40% to 96.50% Return: 0
Number of 96.50% to 96.60% Return: 0
Number of 96.60% to 96.70% Return: 0
Number of 96.70% to 96.80% Return: 0
Number of 96.80% to 96.90% Return: 2
Number of 96.90% to 97.00% Return: 4
Number of 97.00% to 97.10% Return: 10
Number of 97.10% to 97.20% Return: 16
Number of 97.20% to 97.30% Return: 17
Number of 97.30% to 97.40% Return: 14
Number of 97.40% to 97.50% Return: 12
Number of 97.50% to 97.60% Return: 8
Number of 97.60% to 97.70% Return: 7
Number of 97.70% to 97.80% Return: 6
Number of 97.80% to 97.90% Return: 2
Number of 97.90% to 98.00% Return: 0
Total Average of 100 trials is 213729915.00000 for return of 97.327%
New Holds:
14. 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
Normally a play for 7-for-1 Flush pay schedules, but a Flush is valuable even at 5-for-1, the original Ultimate X awarded the 2nd highest multiplier in most games. Losing about .21 credits to gain 0.02 Bonus Chance.
*15. King VS 3 to Flush with King -AND- Queen VS 3 to Flush with Queen
Cards Drawn: 2 ♥ 6 ♦ 7 ♣ 9 ♥ K ♥
Expected Result: 2.11204552462647
Bonus Percentage: 0.0285874470888347
Optimal Cards Held: K ♥
Bonus Hold
Cards Held: 2 ♥ 9 ♥ K ♥
Expected Result: 1.90101757631822
Bonus Percentage: 0.0499537465309898
*Jack VS 3 to Flush will have higher EV loss 0.28 for less bonus gain, barely less than 0.02 Questionable. I included that in the first run through
Player loses about 0.2 coins to increase my Bonus Percentage from 2.86% to 5%. Good Trade
**16. Ace + High + Low 3 to Flush Suited VS Ace + High Suited
Cards Drawn: A ♥ 8 ♦ 9 ♥ 10 ♣ Q ♥
Expected Result: 2.62503854455751
Bonus Percentage: 0.0288621646623497
Optimal Cards Held: A ♥ Q ♥
Bonus Hold #1
Cards Held: A ♥ 9 ♥ Q ♥
Expected Result: 2.40055504162812
Bonus Percentage: 0.0499537465309898
** Two suited King + Queen/Jack + Low will have higher EV loss 0.28 for less bonus gain, barely less than 0.02 Questionable. I included that in the first run through
The Player loses about .22 credits for slightly better than 2% Bonus Percentage gain.
17. Three to Straight Flush with 1 or 2 Gaps VS 4 to Inside Straight
Worst Case Scenario
Cards Drawn: 5 ♦ 9 ♥ 10 ♦ Q ♥ K ♥
Expected Result: 2.81221091581869
Bonus Percentage: 0.0601295097132285
Optimal Cards Held: 9 ♥ Q ♥ K ♥
Bonus Hold #1
Cards Held: 9 ♥ Q ♥ K ♥ 10 ♦
Expected Result: 2.34042553191489
Bonus Percentage: 0.0851063829787234
The Player loses about 0.30 to 0.45 credits for slightly better than 2.5% Bonus Percentage gain by giving up such a difficult and less rewarding hand outcome (1 in over 9000 for 50-for-1 payout), might as well try to set up Bonus for quads which have more value in DDB.
Will start the concepts for Segment 3 which I anticipate will be the hardest to fine tune.
I looked deeper into the low EV hands, there are TONS of them whose best play averages about 2 to 2.5 units. To squeeze value out of them, did not do it on one lucky guess, but with trial and error, I give up up to 0.4 units EV to at least get 2% more Bonus Percentage.
The following added filter boosted the affected deals from 3909 to 11504. This means about 1/5 or 20% of the hands whose non-optimal plays have better Bonus Percentage than its optimal plays will be considered.
Number of 96.00% to 96.10% Return: 0
Number of 96.10% to 96.20% Return: 0
Number of 96.20% to 96.30% Return: 0
Number of 96.30% to 96.40% Return: 1
Number of 96.40% to 96.50% Return: 0
Number of 96.50% to 96.60% Return: 0
Number of 96.60% to 96.70% Return: 0
Number of 96.70% to 96.80% Return: 0
Number of 96.80% to 96.90% Return: 2
Number of 96.90% to 97.00% Return: 4
Number of 97.00% to 97.10% Return: 10
Number of 97.10% to 97.20% Return: 16
Number of 97.20% to 97.30% Return: 17
Number of 97.30% to 97.40% Return: 14
Number of 97.40% to 97.50% Return: 12
Number of 97.50% to 97.60% Return: 8
Number of 97.60% to 97.70% Return: 7
Number of 97.70% to 97.80% Return: 6
Number of 97.80% to 97.90% Return: 2
Number of 97.90% to 98.00% Return: 0
Total Average of 100 trials is 213729915.00000 for return of 97.327%
New Holds:
14. 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
Normally a play for 7-for-1 Flush pay schedules, but a Flush is valuable even at 5-for-1, the original Ultimate X awarded the 2nd highest multiplier in most games. Losing about .21 credits to gain 0.02 Bonus Chance.
*15. King VS 3 to Flush with King -AND- Queen VS 3 to Flush with Queen
Cards Drawn: 2 ♥ 6 ♦ 7 ♣ 9 ♥ K ♥
Expected Result: 2.11204552462647
Bonus Percentage: 0.0285874470888347
Optimal Cards Held: K ♥
Bonus Hold
Cards Held: 2 ♥ 9 ♥ K ♥
Expected Result: 1.90101757631822
Bonus Percentage: 0.0499537465309898
*Jack VS 3 to Flush will have higher EV loss 0.28 for less bonus gain, barely less than 0.02 Questionable. I included that in the first run through
Player loses about 0.2 coins to increase my Bonus Percentage from 2.86% to 5%. Good Trade
**16. Ace + High + Low 3 to Flush Suited VS Ace + High Suited
Cards Drawn: A ♥ 8 ♦ 9 ♥ 10 ♣ Q ♥
Expected Result: 2.62503854455751
Bonus Percentage: 0.0288621646623497
Optimal Cards Held: A ♥ Q ♥
Bonus Hold #1
Cards Held: A ♥ 9 ♥ Q ♥
Expected Result: 2.40055504162812
Bonus Percentage: 0.0499537465309898
** Two suited King + Queen/Jack + Low will have higher EV loss 0.28 for less bonus gain, barely less than 0.02 Questionable. I included that in the first run through
The Player loses about .22 credits for slightly better than 2% Bonus Percentage gain.
17. Three to Straight Flush with 1 or 2 Gaps VS 4 to Inside Straight
Worst Case Scenario
Cards Drawn: 5 ♦ 9 ♥ 10 ♦ Q ♥ K ♥
Expected Result: 2.81221091581869
Bonus Percentage: 0.0601295097132285
Optimal Cards Held: 9 ♥ Q ♥ K ♥
Bonus Hold #1
Cards Held: 9 ♥ Q ♥ K ♥ 10 ♦
Expected Result: 2.34042553191489
Bonus Percentage: 0.0851063829787234
The Player loses about 0.30 to 0.45 credits for slightly better than 2.5% Bonus Percentage gain by giving up such a difficult and less rewarding hand outcome (1 in over 9000 for 50-for-1 payout), might as well try to set up Bonus for quads which have more value in DDB.
Will start the concepts for Segment 3 which I anticipate will be the hardest to fine tune.
-
alpax
- Video Poker Master
- Posts: 1913
- Joined: Sat Jun 14, 2014 4:42 pm
Need to Add 10b to this list.
4 to the Inside Straight is ALSO preferred over Jack-Ten Suited
10b. Jack vs 4 to Inside Straight with Jack+Ten Suited
Cards Drawn: 2 ♥ 7 ♦ 9 ♦ 10 ♥ J ♥
Expected Result: 2.17422139993833
Bonus Percentage: 0.037804502004317
Optimal Cards Held: 10 ♥ J ♥
Bonus Hold
Cards Held: 10 ♥ J ♥ 7 ♦ 9 ♦
Expected Result: 2.02127659574468
Bonus Percentage: 0.0851063829787234
4 to the Inside Straight is ALSO preferred over Jack-Ten Suited
10b. Jack vs 4 to Inside Straight with Jack+Ten Suited
Cards Drawn: 2 ♥ 7 ♦ 9 ♦ 10 ♥ J ♥
Expected Result: 2.17422139993833
Bonus Percentage: 0.037804502004317
Optimal Cards Held: 10 ♥ J ♥
Bonus Hold
Cards Held: 10 ♥ J ♥ 7 ♦ 9 ♦
Expected Result: 2.02127659574468
Bonus Percentage: 0.0851063829787234
-
alpax
- Video Poker Master
- Posts: 1913
- Joined: Sat Jun 14, 2014 4:42 pm
18. From analyzing the Average Multiplier play, I was able to learn that holding the two pair and the full house containing Aces is a good sub optimal play
Cards Drawn: A ♥ A ♦ 9 ♣ 9 ♠J ♣
Expected Result: 9.6013
Bonus Percentage: 0.16702
Optimal Cards Held: A ♥ A ♦
Bonus Hold
Cards Held: A ♥ A ♦ 9 ♣ 9 â™
Expected Result: 7.9787
Bonus Percentage: 0.3404
19. Also QT Suited over Ace is a good Bonus play
Cards Drawn: A ♥ 3 ♣ 4 ♥ 10 ♦ Q ♦
Expected Result: 2.2543
Bonus Percentage: 0.03405
Optimal Cards Held: A ♥
Bonus Hold
Cards Held: 10 ♦ Q ♦
Expected Result: 2.173
Bonus Percentage: 0.0436
Cards Drawn: A ♥ A ♦ 9 ♣ 9 ♠J ♣
Expected Result: 9.6013
Bonus Percentage: 0.16702
Optimal Cards Held: A ♥ A ♦
Bonus Hold
Cards Held: A ♥ A ♦ 9 ♣ 9 â™
Expected Result: 7.9787
Bonus Percentage: 0.3404
19. Also QT Suited over Ace is a good Bonus play
Cards Drawn: A ♥ 3 ♣ 4 ♥ 10 ♦ Q ♦
Expected Result: 2.2543
Bonus Percentage: 0.03405
Optimal Cards Held: A ♥
Bonus Hold
Cards Held: 10 ♦ Q ♦
Expected Result: 2.173
Bonus Percentage: 0.0436
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