Anyone want to do the math on this VP problem

[shadroch]

Heres the situation. Ten Play Dueces Wild.
I'm dealt 22277. 5 of a kind pays 75, so if I keep the hand I win 750 credits.
But....
4 2s pays 1000 credits. No matter what happens, I have at least 250 credits (10 x 25), but I'll be drawing twenty cards, each with a 1/49 chance of being a 2. I'll also have ten shots at getting a 5 of a kind, ten shots at straight flushs, ect.
The software says to keep the 5 7s, and take 750 credits.
What are the chances of improving the hands worth?

btw- I ignored the software and went for it. Hand ended up paying almost 4,000 credits but that was just luck as I caught 3 2s and 2 Royals.

 

[actuary]

The proper strategy is always the same for one hand or a million hands. In other words, the move that maximizes EV for one hand play is the same for ten hand play.

I think you are mistaken about proper strategy being to stand pat. For full pay deuces, the move that maximizes your EV (for one hand play or ten hand pay,) is to ditch the 7s.

Staying pat has an EV of 75 per hand. The probability of drawing that last 2 is 1/47 and we can draw it either on the 4th or 5th spot. Prob(drawing the last 2) = Prob(2 on 4th) + Prob(2 on 5th) = 1/47*46/46 + 46/47*1/46 = 2/47 or 4.25%. Going for the 4 2's has an EV of 1000*2/47 + prob of all the other hands times their payouts = $75.29. So you did the right thing by holding the 2s and ditching the 7s, even though you thought you were playing wrong!