Joker poker questions

Hi everyone,

I managed to get three 4 of a kinds in 5's, after about 600 hands in Joker Poker, and was wondering:

(i) what is the chance of getting a 4 of a kind in 5's, in any one round?
(ii) what is the chance of getting three x 4 of a kind in 5's, after 600 rounds?

NB: For calculation purposes, the chance of any 4 of a kind (2 to Ace) for the above questions is about 0.8140%*** per round.

NB: for question (ii), I didn't count each individual round, but I can do about 540 to 660 rounds per hour, and I played for an hour

about 0.8140%*** : 199,990,738,944 / 24,568,865,521,200 = 0.00814... (according to the WoO website, video poker section)



thanks

Hi again,

I just worked out the game is not a 'true' video poker, in that it doesn't remove cards from the second draw:

example: first draw was JD JH JC JS & 10 of hearts, kept 4 of a kind and drew again, got a 10 of hearts

for this reason please disregard the NB in the original post that starts off with "for calculation purposes..."

I will also restate the questions from the OP and any new queries at the end of this post.

------------------------
Game: Joker Poker (two pair)

Pay-table (1 coin)

Royal Flush --- 300
5 of a Kind --- 400
Wild Royal --- 240
Straight Flush -- 50
4 of a Kind*** -- 20
Full House ------- 6
Flush ------------- 4.5
Straight -----------3.5
3 of a Kind ------ 2.5
2 Pair ------------ 1.5
All Else ------------ 0

4 of a Kind***: bonus of 200 instead of 20, when you get a 4 of a Kind in 5's
----------------------------
RTP (please fill in the blanks, if possible):

Base Game: 101.289...% + Gain from 4 of a kind bonus in 5's: ?
less
Cost of not being a 'true' video poker game: ?

Combined total RTP = ?
-------------------------------

strategy

One Joker Dealt

Pat Hand: Full House; Straight Flush; Wild Royal Flush; Five of a Kind
4 of a kind: Any 4 of a kind
4 to Royal Flush: Any 4 to a Royal
4 to a Straight Flush: 3 low to Jack High (no Gaps)
4 to a Straight Flush: 2 low to Queen high (one gap)
Pat Hand: Flush
3 of a Kind: Any 3 of a kind
4 to a Straight Flush: Ace low to king high (two gaps)
Pat Hand: Straight
3 to a Royal Flush: Any 3 to a royal flush
3 to a Straight Flush: 4 low to 10 high (no gaps)
4 to a Straight: 3 low to queen high (no gaps)
3 to a Straight Flush: 2 low to Jack high (one or two gaps)
4 to a flush: Any 4 to a flush
One Pair: 7 or 8
One Pair: 6 or 9
One Pair: 5 or 10
One Pair: 4 or Jack
One Pair: Queen
One Pair: Ace
One Pair: King

No Jokers Dealt

Pat Hand: Full House; Straight Flush; Natural Royal Flush
4 of a kind : Any 4 of a kind
4 to Royal: Flush Any 4 to a Royal
Pat Hand: Flush
3 of a Kind : Any 3 of a kind
Pat Hand: Straight
4 to a Straight Flush: Any four 2 to a Straight Flush
Two Pair: Two Pair
3 to a Royal Flush: 3 to a Royal Flush
4 to a flush: 4 to a Flush
One Pair: Any Pair

*^*^*
3 to a Straight Flush: 3 to a Straight Flush (no gap)
4 to a Straight: 2 low to King high (no gap)
3 to a Straight Flush: 3 to a Straight Flush (With Gap)
4 to a Straight: 4 to a Straight (With Gap)
2 to Royal: Any Ten Royal (NOT Ace-10)
2 to a Straight Flush: 4 low 9 high (no gap)
3 to a Flush: Any 3 to a Flush
2 to Royal JK; QK
2 to a Straight Flush: 4 low to Jack high (one gap)
2 to Royal: Any Other Royal
Garbage

*^*^*: separated the strategy this way to make questions 4a & 4b easier (so you can read the strategy and questions on the same 'page')

NB: Strategy calculated manually (so may have errors), and is based on 'standard' video poker rules
NB; Strategy doesn't include exceptions, for example: a pair of 5's vs two pair (correct strategy: keep the pair of 5's only)

------------

(1) what is the chance of getting a 4 of a kind in 5's, in any one round?

(2) what is the chance of getting three x 4 of a kind in 5's, after 600 rounds?

(3) Please fill in the blanks (?) for the RTP section,

(4a) On the first draw, what is the combined/TOTAL chance of getting a hand between 'garbage' to '3 to a Straight Flush (no gap)'?

(4b) On the first draw, what are the individuals chances of getting a hand, for hands between 'garbage' to '3 to a Straight Flush (no gap)'?

(5) Please post correct strategy if you find any errors (see example below)?

example: some of the marginal hands near the bottom of the strategy may be worse than 'garbage' when the discarded cards are able to be dealt on the 2nd draw


thanks