Odds at Video Poker WITHOUT a royal figured in

We all know that video poker has one of the lowest house advantages available. But I have never gotten a royal. When I play it seems my money just gets sucked away quickly most times. All chasing that royal flush.

So if getting a royal flush was NOT part of the overall odds calculation, what would the house advantage be? Am I losing my money faster than playing keno for example? lol

taking a 9/6 jacks or better machine that pays back 0.99543904
with a royal returning 0.01980661

the return would be somewhere between (.99543904-.01980061) and (.99543904)

your playing strategy would alter a bit so it would be greater than (.99543904-.019860061)

like keeping unsuited QJ,KQ,KJ,AJ,AQ,AK over suited TJ, TQ, TK.

plus you can still get dealt a pat royal and im assuming you are still going to draw to a royal when you get dealt 4 to a royal unless you are specifically dealt 9TJQK of all the same suit.

Quote: rudeboyoi

taking a 9/6 jacks or better machine that pays back 0.99543904
with a royal returning 0.01980661

the return would be somewhere between (.99543904-.01980061) and (.99543904)

your playing strategy would alter a bit so it would be greater than (.99543904-.019860061)

like keeping unsuited QJ,KQ,KJ,AJ,AQ,AK over suited TJ, TQ, TK.

plus you can still get dealt a pat royal and im assuming you are still going to draw to a royal when you get dealt 4 to a royal unless you are specifically dealt 9TJQK of all the same suit.

It's not hitting Quads and Full Houses over a long session that can really start to drain on you. Royal's make up about 2% of the EV, Quads 6% and FH's 10%.

You should hit Quads ~1-in-500 hands, FH and Flushes about 1 in 90. I once counted about 60 dealt trips before hitting a Quad on the draw (was last day of the trip, in a bar in the Old Frontier, down to my last few gambling dollars when I hit a natural set of 7's... which happened to be Quad of the Day for a bonus ($50 bonus as I recall) made my day after a rather crappy run of gambling).

Quote: thecesspit

It's not hitting Quads and Full Houses over a long session that can really start to drain on you. Royal's make up about 2% of the EV, Quads 6% and FH's 10%.

You should hit Quads ~1-in-500 hands, FH and Flushes about 1 in 90. I once counted about 60 dealt trips before hitting a Quad on the draw (was last day of the trip, in a bar in the Old Frontier, down to my last few gambling dollars when I hit a natural set of 7's... which happened to be Quad of the Day for a bonus ($50 bonus as I recall) made my day after a rather crappy run of gambling).

or not hitting enough quads in FPDW which makes up ~32.5 of your return.

Quote: thecesspit

Royal's make up about 2% of the EV, Quads 6% and FH's 10%.

So, on a 9/6 JOB, if I played normal strategy, but never hit a royal, my money would slowly go away at only a .97543904 return rate. (.99543904 - "2%") Is that correct? That is just slightly better than a single zero roulette wheel at 2.7% house edge, yes?

Twist my arm. I guess I will continue to play VP.

One other thing to consider (depending on your gambling style/bankroll etc) - Playing one coin only reduces the variance and the return, but you do get to add a small percentage back to the fact that the royal for one coin is 250 coins. For 9/6 JoB - this makes the total return 98.22% including that 250 coin royal. Of course this is a worse return than the 99.54%, but if you're "removing" the royal, the 4000 coin royal has a greater effect on the overall return than the 250 coin (per coin that is).

-B

I'm not sure if it is correct to simply subtract the return that a Royal Flush provides, since it is still a possible outcome.

Instead of doing that, consider this: pretend that a Royal Flush pays the same 250 coins that a Straight Flush does. If you use perfect strategy for such a game, when the Royal actually pays 4000 coins, then the return would be 99.2132% for 9/6 Jacks or Better, and the variance would be reduced from 19.51 to 13.82.

The basic strategy (ignoring exceptions) would then look like this:

1. Royal Flush
2. Straight Flush
3. Four of a Kind
4. Full House
5. Flush
6. Three of a Kind
7. Straight
8. Two Pair
9. 4 to a Royal Flush
10. 4 to a Straight Flush
11. One Pair (Jacks or Better)
12. 4 to a Flush
13. Unsuited TJQK
14. 3 to a Royal Flush (JQK)
15. One Pair (2's through 10's)
16. Unsuited 2345 through 9TJQ
17. 3 to a Royal Flush (except JQK)
18. 3 to a Straight Flush (345 through 9TJ; 89J; 8TJ; 8JQ; 9TQ; 9JQ; 9JK; 9QK)
19. Unsuited JQKA
20. Suited JQ
21. 3 to a Flush with 2 high cards
22. Suited JK; QK
23. Unsuited 9JQK; TJQA; TJKA; TQKA
24. 3 to a Straight Flush (Ace-low; 78J; 79J; 7TJ; 89Q; 8TQ; 9TK)
25. Suited JA; QA; KA
26. 3 to a Straight Flush (234; 235; 245; 346; 356; 457; 467; 568; 578; 679; 689; 78T; 79T)
27. Unsuited JQK
28. Unsuited JQ; JK; QK
29. Unsuited JA; QA; KA
30. Jack; Queen; King; Ace
31. 3 to a Straight Flush (236; 246; 256; 347; 357; 367; 458; 468; 478; 569; 579; 589; 67T; 68T; 69T)
32. Discard everything

The return from the above strategy would be 99.2071%, and the variance would be 13.77 per coin. (The differences in those figures from the ones quoted above are attributable to the exceptions.)