3

This site shows that using a 'simple' strategy or an 'optimal' strategy in Jacks Or Better fullpay video poker results in 99% return-to-player (RTP). RTP is defined as the fraction of money won to money wagered.

What would the RTP be in each of these 2 'dumb' strategies:

  1. Player replaces all cards every time.
  2. Whenever the player has any win in the initial draw, he replaces all cards which are not part of the win. For example if the user sees AA33J he will hold AA and replace 33J.

Thanks!

1

I believe the answer for scenario 1 is just under 63%, as I think you can just treat the game as if you just get dealt a 5 card hand, ignoring the fact that the first draw has happened. Even though when you draw to your final hand, there are 5 cards in the deck you cannot hit, this should affect the overall odds as those first 5 cards are also random. This should therefore also be the payout if you hold all 5 every hand.

/-----------------------------------------------------------------------\
|       Hand      | Combinations |     Odds     | Payout |     RTP      |
|-----------------+--------------+--------------+--------+--------------|
| Royal Flush     |            4 | 0.0000015391 |    800 | 0.0012312617 |
| Straight Flush  |           36 | 0.0000138517 |     50 | 0.0006925847 |
| Four of a Kind  |          624 | 0.0002400960 |     25 | 0.0060024010 |
| Full House      |        3,744 | 0.0014405762 |      9 | 0.0129651861 |
| Flush           |        5,108 | 0.0019654015 |      6 | 0.0117924093 |
| Straight        |       10,200 | 0.0039246468 |      4 | 0.0156985871 |
| Three of a Kind |       54,912 | 0.0211284514 |      3 | 0.0633853541 |
| Two Pair        |      123,522 | 0.0475274725 |      2 | 0.0950549451 |
| Jacks or Better |    1,098,240 | 0.4225690276 |      1 | 0.4225690276 |
| Nothing         |    1,302,540 | 0.5011773940 |      0 | 0.0000000000 |
|-----------------+--------------+--------------+--------+--------------|
|           Total |    2,598,930 | 1.0000000000 |    N/A | 0.6293917567 |
\-----------------------------------------------------------------------/

As for scenario 2, that would require some more work, so perhaps someone else will take that up for you.

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