Ask the Slot Expert: What does NSU have against aces?

I'm used to not holding suited ace-10 from playing 9/6 Jacks, but the NSU strategy says to not hold any 2-card royal with an ace.

What does NSU have against aces?

Let's look at a sample hand to see why we're better off throwing away all of the cards instead of holding the 2-card with an ace.

		Dealt hand: A♣ K♣ 3♦ 7♥ 9♠
		Hold: A♣ K♣				Hold: none
Hand	Pays	Ways	Tot Pays	Prob.	Cont.	Ways	Tot Pays	Prob.	Cont.
Royal flush	800	1	800	0.0001	0.049337	3	2,400	>0.0000	0.001565
4 Deuces	200	0	0	0	0	43	8,600	>0.0000	0.005606
Wild royal	25	34	850	0.0021	0.052421	378	9,450	0.0002	0.006161
5-of-a-kind	16	0	0	0	0	454	7,264	0.0003	0.004736
Straight flush	10	0	0	0	0	1,492	14,920	0.0010	0.009727
4-of-a-kind	4	62	248	0.0038	0.015294	21,725	86,900	0.0142	0.056652
Full house	4	54	216	0.0033	0.013321	7,602	30,408	0.0050	0.019823
Flush	3	329	987	0.0203	0.060870	8,783	26,349	0.0057	0.017177
Straight	2	297	594	0.0183	0.036633	42,599	85,118	0.0277	0.055490
3-of-a-kind	1	1,453	1,453	0.0896	0.089608	224,574	224,574	0.1464	0.146403
Nothing	0	13,985	0	0.8625	0	1,226,326	0	0.7995	0
Totals		16,215	5,148	1	0.317484	1,533,939	495,983	1	0.323339

Note: ">0.0000" means that the probability is not 0 and is 0.0000 when rounded to four decimal places. In other words, small, really small.

Not only are we more likely to have a paying hand when we toss all five cards, the mix of paying hands we can achieve gives discarding all cards a higher EV (0.323339) than holding the 2-card royal with an ace (0.317484).

What happens if our hand has a queen or jack instead of a king? Does that affect any of the EVs?

Hint: I was going to write that it doesn't matter whether the 2-card royal is A-K or A-Q or A-J, but then I checked the numbers and discovered that I was wrong. (Phew. Glad I checked.) It does matter what the second card is.

What changes and why?

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John Robison

John Robison is an expert on slot machines and how to play them. John is a slot and video poker columnist and has written for many of gaming’s leading publications. He holds a master's degree in computer science from the prestigious Stevens Institute of Technology.

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