hitting 4K: a single hand "endgame" strategy

[Minn. Fatz]

Assuming
you’re playing Triple Double Bonus in the VP.com Classic Single Hand
contest and need only a 4000-point jackpot hand, either a RF or four
Aces with a kicker (2, 3 or 4), to move into the lead, what should your
strategy be?Here is my back of the envelope strategy table for this situation with approximate odds against filling a jackpot hand. Note that it is often best to go for an "intermediate" 2K payoff (four 2s, 3s or 4s with an A-4 kicker): 
1. dealt RF, 4K(A) + kicker or 4K(2-4) + kicker; pat hand2. 4K(A); 1:43. 4K(2-4); 1:44. 4/RF or 3K(A) + kicker; 1:475. 3K(2-4) + kicker; 1:476. 3K(A); 1:90 [see note (a)]7. 3K(2-4); 1:908. 3/RF or 1P(A) + kicker; 1:1081 [see note (b)]9. 1P(2-4) + kicker; 1:108110. 1P(A); 1:135111. 1P(2-4); 1:135112. A + one or fewer “penalty cards;” 1:14684 [see note (c)]13. A + two or more “penalty cards” or 2/RF with no A; 1:16215 [see note (c)]14. draw five; 1:102263 [see note (d)]
Notes:
(a) If your dealt hand is, say, Ah
Kh Qh As Ac, you should obviously hold the three Aces rather than the AKQ of hearts.
(b) From a dealt 2P, Aces and kickers, hold the pair of Aces and one kicker.(c) If your dealt hand contains only one Ace, with or without exactly one
other RF card, what you should hold depends on how many “penalty cards”
(kickers and up to one other RF card) are in the dealt hand. If there
is at most one “penalty card” in the dealt hand, hold only the Ace. If
there are two or more “penalty cards” in the dealt hand, hold the Ace
plus any one of the “penalty cards.”

(c)
The odds against filling a jackpot hand given on line 14 assumes there
is exactly one “penalty card” in the dealt hand. These odds are worse
if there are two or more “penalty cards” in the hand; so I would rather
hold a pair of Jacks or better (paying at least 5 and up to 250) without an A than draw five, looking to lay up extra points and making it less likely some later contestant will get into the same
position of only needing a jackpot hand to pass me for
the lead in turn. ‘S’upta you. But never hold just one “penalty card,” draw five cards hoping
for one of the 15 remaining jackpot hands instead. Good mathematics, as Mrs. Minn. would say.

[BillyJoe]

When I am playing a VP.Com contest game, I play ALL the games with the thought of only the bigger 2k or 4k payouts. Catching a bunch of straights, flushes or regular 4oaks for 250 just burns hands, and will not get you on the board. Just my approach. I think the 100 hand limit session makes the bigger picture return 'math' a moot point. Of course, I have never won one of those contests, either.   

[Minn. Fatz]

The strategy in the OP, then, gives you a roadmap for how to play TDB if your objective is to maximize your probability of a 4K or 2K hand. I'd suggest something like playing a max EV strategy up to the point where you are within 4K of the contest leader, switching to a jackpot-maximizing strategy, and switching back to max EV after getting into the lead in order to pile up points against later contestants.The jackpot-maximizing strategy isn't that different from max EV, the major exceptions as you note being straights, flushes and non-royal straight flushes, since there's no 4-card combinations of these possible in hands that also contain 2P or 3K. In TPB, you still hold Aces (plus a kicker in the jackpot-maximizing mode) from Aces up and break Aces full to go for quad Aces.I'd be inclined to hold four to a flush or straight with a maximum of one J, Q or K than to hold one non-Ace high card hoping to wrap a RF. The analytical question is should I keep the chance I have this hand for a few points or give it up for the remoter chance of a jackpot hand. I haven't exhaustively run the numbers on that though; as I say, it's up to you.

[Minn. Fatz]

Looking at the dealt hand deuces full of Aces (222AA), it turns out holding the three deuces with an Ace kicker is at least 5% worse (more so the fewer hands that are left in the session) than holding the pair of Aces with a deuce kicker if your objective is to make at least 4000 points before the session ends. The calculation takes the following form:for holding AA2, [probability of making 4K(A)+k] + { [probability of not making 4K(A)+k] x [probability of making one 4K or two 2K hands before session ends] }for holding 222A, { [probability of making 4K(2)+k] x [probability of making either a 4K or 2K hand before session ends] } + { [probability of not making 4K(2)+k] x [probability of making one 4K or two 2K hands before session ends] }So, add a note (d) to the above: hold 1P(A)+k in preference to 3K(2-4)+k if you are more than 2000 behind the current leader.I'll tackle the question of whether to hold 4K(2) from a dealt quad deuces with no kicker or draw five and let you all know. Good Mathematics until then.

[Minn. Fatz]

Here is the comprehensive strategy table for the above situation given a 100-hand session, with some approximate odds against given. “k” stands for all kicker cards (rank
2, 3 or 4, plus A with 4K(k))

1. RF, 4K(A)+k, 4K(k)+k; pat hand
2. 4K(A); 1:4
3. 4K(k); 1:4 [draw five if < 4 hands left]
4. 4/RF or 3K(A)+k; 1:47 [break a FH, A over k]
5. 3K(A); 1:90 [hold this rather than 3/RF]
6. 3K(k)+A; 1:47 [except hold AAk from a FH, k over A]* [hold Ak if < 34 hands left]
7. 3K(k)+k; 1:47 [draw five if < 4 hands left]
8. 3/RF or 1P(A)+k; 1:1081
9. 1P(A); 1:1351
10. A + one or fewer “penalty cards;” 1:14684 [see Notes]
11. A + two or more “penalty cards” or 2/RF; 1:16215 [see Notes]
12. draw five; 1:102263 [see Notes]

* disregard if you need 2000 or less to move into the lead

Notes: If your dealt hand contains only one Ace, with or without exactly one other RF card, what you hold depends on how many “penalty cards” (kickers and up to one other RF card) are in the dealt hand. If there is at most one
“penalty card” in the dealt hand, hold only the Ace. If there are two or more “penalty cards” in the dealt hand, hold the Ace plus one of the “penalty cards.” The odds given on line 12 assume exactly one “penalty card.” Never hold just a pair of kickers; draw five instead.

[BillyJoe]

Interesting, Fatz. But one other thing in the daily contests. You have only a maximum of 8 sessions of 100 hands each to play. The leader's point value  may be increasing/changing as you are playing your sessions, so just playing to get the lead at some point in time during the contest period may not be good enough. You may run out of sessions.

[Minn. Fatz]

True enough. The strategy here is calculated to give you maximum expected value for the hands remaining in your session under the assumption that you want to first maximize your probability of hitting either a 4K hand or a 2K hand followed by a 2K or 4K hand. To maximize your probability of hitting one or more 4K hands, simply disregard any line that can only hit a 2K hand (always hold AA2 rather than A222 from AA222, for example).

A wiser man than me said there is no such thing as luck, everything is mathematics. So good mathematics, whichever strategy you choose!