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You're welcome, thanks for the kind words!
The general formula is combin(X,Z) × pZ × (1-p)X-Z, where p = 1/combin(47,5-Y).
Combin is an Excel formula, which equals X!/[Z! × (X-Z)!].
Let's look at an example of 10-play video poker where the player holds four to a royal.
10-Play with Four to a Royal
| Royals | Probability |
|---|---|
| 10 | 0.0000000 |
| 9 | 0.0000000 |
| 8 | 0.0000000 |
| 7 | 0.0000000 |
| 6 | 0.0000000 |
| 5 | 0.0000010 |
| 4 | 0.0000378 |
| 3 | 0.0009943 |
| 2 | 0.0171513 |
| 1 | 0.1753242 |
| 0 | 0.8064914 |
| Total | 1.0000000 |
IGT was right when they said you should use the same strategy for Spin Poker as single line video poker. Mathematically speaking the odds are the same. However Spin Poker has greater volatility since 9 different lines share many of the same cards. The same is true of multi-play video poker, the strategy and return is the same for a single line game. I do get into the volatility of multi-play video poker in my video poker appendix 3.
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Thanks for the kind words. Assuming the pay table is the same the strategy and expected return are exactly the same. Be warned that multi-play games tend to have worse pay tables than single line games.
W2G forms are definitely something to think about when playing video poker at the larger bet amounts. Although you are obligated to pay taxes on your net win at the end of the year regardless of how many W2G forms you have, a payout of $1200 or more will necessitate a wait and obligate you to tip the person paying you. In less classy casinos a hand pay will also cause the tip vultures to start hovering around you. To avoid all of this sometimes the player should consider deviating from optimal strategy. For example with AAA88 in 10/7 double bonus the odds marginally favor keeping the aces only. However in a $2 to $10 game hitting four aces will pay over $1200, necessitating a W2G form, while a full house will stay under the limit. Considering the tax implications keeping the full house is the better play.
To answer your question I'll assume a four of a kind pays 25 times the bet. Kings temple live stream. Then a four of kind on the deal in a $0.20 50-play game will pay $0.20 * 5 * 50 * 25 = $1250. You will get a four of a kind on the deal once every 4165 hands, on average. If you were to drop the number of hands to 47 the win for a four of a kind on the deal would be 47 * $0.20 * 5 * 25 = $1175, staying under the W2G threshold.
Given the same pay table the strategy is exactly the same for 1-play, 3-play, 100-play, and any-play. Personally I prefer the multi-play games if the pay tables are the same. However the multi-play games usually have stingier pay tables. The more the hands, the worse the pay table.
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I also play 26 lines at the $1 denomination frequently. The reason is if you get a win of $1,200 or more it necessitates a hand pay, which slows down your game, and obligates you to tip. At 26 lines, a dealt full house in 9/6 jacks, which I happen to know is what he was playing, will pay $5 × 9 × 26 = $1,170. One more line and you would have a hand pay at $1,200. If 26 lines, or $130 a bet, is too small, I'll go up to 39 lines, where a dealt flush will pay $5 × 6 × 39 = $1,170. The next bend-point is at 59 hands, where a deal straight would be $5 × 4 × 59 = $1,180. However, I feel with 59 hands a three of a kind on the deal turns into a hand pay too often.
