Video Poker

Video Poker (similar to Jacks or Better) is a game where in the first turn 5 cards will be drawn and the player can then choose to redraw any of these 5 cards on their second (last) turn. Since the redraw and thus the outcome depends on the player's input, the player should understand the game and otherwise decreases their chances of winning. The player can win by combining cards and making specific poker hands. Read more about Video Poker and an explanation on poker hands.

Hands, Probability and Multiplier

There are 52 cards in a deck, thus the probability of hitting one specific card is 1.923% (100/52). A player receives 5 cards and can choose to redraw either of those, thus the player has 32 total combinations of playing a specific hand (2^5=32). There are 9 hands that give a payout and can be achieved through several combinations. The hands have the following probabilities and multipliers:

Outcome	Combinations	Probability	Multiplier
Royal Flush	26,529,694	0.0016%	100x
Straight Flush	172,142,759	0.01036%	50x
Four of a Kind	3,894,667,337	0.23446%	30x
Full House	18,948,816,693	1.14074%	8x
Flush	19,698,441,627	1.18587%	6x
Straight	25,304,047,279	1.52333%	5x
Three of a Kind	121,441,079,723	7.31087%	3x
Two Pairs	210,032,363,727	12.64415%	2x
Jacks or Better	343,085,127,609	20.65406%	1x
Other	918,499,326,652	55.29456%	0x
Total	1,661,102,543,100	100%	-

The multipliers can be verified in the Video Poker contract at the first number displayed after return:

return (100, 9);                         // royal flush
return (50, 8);                          // straight flush
return (30, 7);                          // four of a kind
return (8, 6);                           // full house
return (6, 5);                           // flush
return (5, 4);                           // straight
return (3, 3);                           // three of a kind
return (2, 2);                           // two pairs
return (1, 1);                           // jacks or better
return (0, 0);                           // less than a pair of jacks

The average return is calculated at 0.994445.

You can use this Video Poker Analyser to verify the return: Standard Video Poker -> Jacks or Better -> input all the multipliers correctly in the Prize column and change wager coin to 1 -> Analyze. You can also use this https://www.beatingbonuses.com/vp_pay.php.

House Edge

The house edge is incorporated in the multiplier. With the return being 0.994445, the house edge is 0.5555% ((1-0.994445)*100).

Odds

The above leads to the following odds for Video Poker:

Odds	Outcome
Decimal odds	0.994445
Return to Player	99.4445%
Player odds	49.72225%