Enter your 5 dealt cards and a paytable to see which cards to hold, the exact expected value, and the overall return (RTP).
The optimal hold is the one of the 32 possible hold/discard combinations with the highest expected value (EV), computed by enumerating every card that could be drawn to replace the discarded cards — not by simulation. Compare it against holding the entire dealt hand ("pat") or discarding everything to see how much each choice is worth.
Two machines can look almost identical — same game name, same-looking pay chart — while paying back very different amounts, because a single number (the Full House or Flush payout) shifts the return by more than 2 percentage points. 9/6 Jacks or Better (Full House 9, Flush 6) returns 99.54% under optimal play; 8/5 Jacks or Better (Full House 8, Flush 5) returns 97.30%. Casinos rarely label which version a machine uses, so checking the actual pay chart on the machine is the only way to know.
Published strategy charts and calculators typically only cover a handful of standard paytables. This tool lets you type in whatever paytable is printed on the machine in front of you — including unusual regional or promotional pay tables — and get the exact optimal hold for your exact 5 cards against that specific paytable, not just the closest standard match.
This tool computes the exact expected value (EV) of every one of the 32 possible hold decisions for your 5-card hand, using exact probability math rather than simulation. For each hold, it enumerates every possible combination of replacement cards from the remaining 47-card deck, applies your selected paytable, and averages the payout — the hold with the highest EV is the mathematically optimal play.
The overall return (RTP) shown for the two preset paytables (9/6 and 8/5 Jacks or Better) is the published figure for that exact paytable under optimal play, assuming the maximum 5-coin bet (needed for the Royal Flush bonus payout). For a custom paytable, the RTP shown is an estimate that reuses the published 9/6 hand-frequency table — exact for paytables in the same family, and very close for other custom paytables, since optimal strategy rarely changes which hold is best. This is a probability and returns education tool, not gambling advice.
Compare the expected value (EV) of all 32 possible hold decisions (2^5, since each of the 5 dealt cards is either held or discarded) and pick the highest one. EV is computed exactly: for a given hold, every possible combination of replacement cards from the remaining 47-card deck is enumerated, the paytable is applied to each resulting hand, and the payouts are averaged. Example: dealt K-Q-J-10 of spades plus an off-suit Ace, holding the 4 spades (a 4-to-a-royal-flush draw) has an exact EV of 371/47 ≈ 7.894 per 1-coin bet under a 9/6 paytable, versus exactly 4 for holding the pat A-K-Q-J-10 straight -- so the 4-to-royal draw is correct even though it breaks a made straight.
99.54% under optimal play with the maximum 5-coin bet (needed for the 800-per-coin Royal Flush bonus). Published by wizardofodds.com and reproduced by this calculator's reference test using the same hand-frequency table.
Yes -- always. Holding 4 to a royal flush has a far higher EV than any made hand below a straight flush, because of the 800-per-coin (5-coin bet) royal payout. In the worked example above (K-Q-J-10 of spades, off-suit Ace discarded), holding the 4 spades has an exact EV of 371/47 ≈ 7.894, versus exactly 4.000 for keeping the pat A-K-Q-J-10 straight.
It's a common paytable variant that pays only 8 (instead of 9) on a Full House and 5 (instead of 6) on a Flush. Those two changes alone drop the return from 99.54% to about 97.30% -- more than 2 percentage points -- while every other payout stays identical, which is why checking the exact pay chart on the machine matters.
Almost never in a 9/6 or 8/5 paytable: holding a low pair (2s through 10s) and drawing 3 new cards nearly always beats holding a single high card or an unrelated 4-card straight/flush draw, because the pair already guarantees decent two-pair, trips, full house, or quads outs even though it doesn't pay on its own.
Yes, to earn the published RTP. The Royal Flush pays only 250 per coin at 1-4 coins, but jumps to 800 per coin (4000 total) at the maximum 5-coin bet -- an outsized bonus that pulls the whole game's long-run return up by roughly 2 percentage points, which is why maximum-coin play is always correct in Jacks or Better.
| Hand | Pays (5-coin max bet) | Probability | Return contribution |
|---|---|---|---|
| Royal Flush | 4000 (800/coin) | 0.0000248 | 1.981% |
| Straight Flush | 250 (50/coin) | 0.0001093 | 0.547% |
| Four of a Kind | 125 (25/coin) | 0.0023626 | 5.906% |
| Full House | 45 (9/coin) | 0.0115122 | 10.361% |
| Flush | 30 (6/coin) | 0.0110145 | 6.609% |
| Straight | 20 (4/coin) | 0.0112294 | 4.492% |
| Three of a Kind | 15 (3/coin) | 0.0744487 | 22.335% |
| Two Pair | 10 (2/coin) | 0.1292789 | 25.856% |
| Jacks or Better | 5 (1/coin) | 0.2145850 | 21.459% |
| Nothing | 0 | 0.5454347 | 0.000% |
Published strategy charts and calculators typically only cover a handful of standard paytables. Casinos and online sites sometimes use regional or promotional pay tables that don't match any standard chart exactly, so this tool lets you type in whatever paytable is actually printed on the machine and get the exact optimal hold for your exact cards against that specific paytable.
It's computed live, from scratch, for the exact 5 cards and paytable you enter. All 32 possible hold/discard combinations are evaluated by enumerating every combination of replacement cards from the remaining 47-card deck (not a simulation, and not a precomputed strategy chart) -- see the formula above.
The overall (deck-wide) return depends on how often each hand category occurs under that paytable's own optimal strategy, and optimal strategy shifts very slightly between paytables (a handful of borderline hands can flip which hold is best). This tool's custom-paytable RTP reuses the published 9/6 hand-frequency table, which is exact for the two preset paytables and a very close approximation for other paytables in the same Jacks-or-Better family, since strategy rarely changes.
Yes, in hands with no pair and no 4-card straight or flush draw, holding 2 unsuited cards of Jack-or-better rank is a standard part of Jacks or Better strategy -- each gives a chance at a paying Jacks-or-better pair on the next draw, which beats holding just 1 high card or discarding everything in most such hands.
No. Only which specific cards are held matters, not any left-to-right order -- the EV formula treats a hold as a set of cards, and the resulting 5-card poker hand (and its payout) is identical regardless of card order.
This is a probability and returns education tool, not gambling advice. It assumes a standard single-hand, 5-card draw video poker machine (choose cards to hold, redraw the rest once) and a coin-based paytable where Royal Flush pays a larger per-coin bonus only at the maximum 5-coin bet. The overall RTP shown for 9/6 and 8/5 Jacks or Better is the published figure under optimal play at max-coin bet; deviating from optimal strategy, or playing fewer than the maximum coins, lowers the actual long-run return. The RTP shown for a custom paytable is an estimate (see FAQ above), not an independently re-derived exact figure.
Sources: Wizard of Odds -- Jacks or Better pay table analysis, Wizard of Odds -- Video Poker