Two Pair in DW question
March 24th, 2010 at 7:02:08 AM
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If the Dw pay table is 1-2-3-4-4-9-15 etc., with a full house paying 4, is it still right to keep only one pair from a hand with two pair?
March 24th, 2010 at 7:31:08 AM
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Check Wizard Of Odds - Simple Strategy for Deuces Wild. Here's a telling excerpt:
Quote:Any hand that does not appear on the above lists should never be played. Most notably a two pair, keeping a single pair has a higher expected value.
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March 24th, 2010 at 8:15:41 AM
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DJ, in a pay table where a 4 of a Kind pays the same as a full house, the correct play IS to keep two pair.
See the Wizard's Not So Ugly Deuces Wild Strategy here. The pay table for NSUD is 1-2-3-4-4-10-16-25-200-800.
Think of it this way. When you have two pair, the only way you will make the full house is by pulling a 2 or a matching card. There are only 8 ways to do this out of 47 card remaining with an EV of 4*8/47-1 = .68085
Where as with a pair, the EV is 0.546778. Even though you have three ways to draw to a 3 of a Kind or Better, Full House, 4 of a Kind, or Better, since the 4 of Kind pays the same as a full house, it is actually better to keep the two pair.
Here is the detailed calculation.
Total combinations of the remaining 3 cards: 47 x 47 x 45 / 6 = 16,215.
M = Matching the pair
2 = Deuce
Other - non match and non-deuce
8,866 / 16,251 = .546778 which matches the Wizard's EV in Not So Ugly Deuces. Keeping the two pair has an EV of .68085.
If you decide to keep the pair instead of two pair in a pay table as shown above, you will be throwing away .1340 units or 13.4% of your bet. So it's a pretty significant strategy change that you need to consider.
In the case where FH pays 3 and the 4 of a Kind pays 4, then the EV is keeping the pair drops to .5215 while the EV of keeping 2 pair drops even lower to .510638 so it's better in this case to keep one pair.
See the Wizard's Not So Ugly Deuces Wild Strategy here. The pay table for NSUD is 1-2-3-4-4-10-16-25-200-800.
Think of it this way. When you have two pair, the only way you will make the full house is by pulling a 2 or a matching card. There are only 8 ways to do this out of 47 card remaining with an EV of 4*8/47-1 = .68085
Where as with a pair, the EV is 0.546778. Even though you have three ways to draw to a 3 of a Kind or Better, Full House, 4 of a Kind, or Better, since the 4 of Kind pays the same as a full house, it is actually better to keep the two pair.
Here is the detailed calculation.
Total combinations of the remaining 3 cards: 47 x 47 x 45 / 6 = 16,215.
M = Matching the pair
2 = Deuce
Other - non match and non-deuce
| Cards Drawn | Result | Combinations | Win | Exp Value | |
|---|---|---|---|---|---|
| 2M/2M/2M | 5 of a kind | 20 | 16 | 320 | |
| 2M/2M/Other | 4 of a kind | 615 | 4 | 2,460 | |
| 2M/Pair | Full House | 369 | 4 | 1,476 | |
| 3 of a Kind | Full House | 41 | 4 | 164 | |
| 2M/Others | 3 of a Kind | 4,446 | 1 | 4,446 | 3 Others | Nothing | 7,349 | 0 | 0 |
| Totals | 16,215 | 8,866 |
8,866 / 16,251 = .546778 which matches the Wizard's EV in Not So Ugly Deuces. Keeping the two pair has an EV of .68085.
If you decide to keep the pair instead of two pair in a pay table as shown above, you will be throwing away .1340 units or 13.4% of your bet. So it's a pretty significant strategy change that you need to consider.
In the case where FH pays 3 and the 4 of a Kind pays 4, then the EV is keeping the pair drops to .5215 while the EV of keeping 2 pair drops even lower to .510638 so it's better in this case to keep one pair.
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