Keep it Straight -- Second Chance

Quote: Gialmere

Was it any fun? It sounds frustrating what with all the cards involved, three of which only apply to one of the side bets. And really? You have to pay extra to get the namesake "second chance"?
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It's a pretty simple game and goes slow. The other players at the table seemed to like it.

Once I had a six-card straight, so I made the 4x raise. As the rules state, with a 6- or 7-card straight, the raise pays 2 to 1. However, the dealer didn't qualify, so I won the Ante only. I would have likely won 8x the Ante had the dealer qualified. Same frustrating problem as in Caribbean Stud. I think one of the side bets should be based on the straight value of the player's hand only. Of course, I wouldn't have made it, but I could see other players not liking missing a big payday because the dealer didn't qualify.

I have updated my page on Keep it Straight Second Chance to include a strategy and house edge. I welcome all comments and especially a verification.

Bottom line is a house edge of 2.81%.

Quote: Wizard

I have updated my page on Keep it Straight Second Chance to include a strategy and house edge. I welcome all comments and especially a verification.

Bottom line is a house edge of 2.81%.
link to original post

I am getting only 2.77% as the house edge, and I have "raise 2x" on J-10-9

Question: can the raise be any amount between 2x and 4x, or is it limited to, say, 2x, 3x, and 4x? This could affect the house edge.
EDIT: I don't think so, and here's why:
Let the ante bet be 1, and the raise bet be B
For any particular player hand, let W, T, L, and Q be the number of dealer hands that are player wins, ties, losses, and non-qualified, respectively
The value of the hand (for hands less than a 6-straight) is ((B + 1) W - (B + 1) L + Q) / (W + T + L + Q)
= ((B + 1) (W - L) + Q) / (W + T + L + Q)
= B (W - L) / (W + T + L + Q) + (W - L + Q) / (W + T + L + Q)
If W > L, then this is positive, and since it increases as B increases, the bet should be the maximum (raise 4).
If W < L, then increasing B will only increase the amount multiplied by (W - L), which is negative, so it decreases the overall hand value; therefore, the bet should be the minimum (raise 2).

Quote: ThatDonGuy

Quote: Wizard

I have updated my page on Keep it Straight Second Chance to include a strategy and house edge. I welcome all comments and especially a verification.

Bottom line is a house edge of 2.81%.
link to original post

I am getting only 2.77% as the house edge, and I have "raise 2x" on J-10-9

Well, based on playing the game for an hour, folding on 10-9-8 just doesn't feel right to me.

Perhaps what we could do is make a table of the probability of each hand from A-2-3 to 89TJQKA, just to make sure we're both scoring correctly.

Quote:

Question: can the raise be any amount between 2x and 4x, or is it limited to, say, 2x, 3x, and 4x? This could affect the house edge.
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I think so, but I think there is no situation where the player should bet anything in the middle. For the same reason you should never bet 3x on the Big raise in Ultimate Texas Hold 'Em and never double for less in blackjack.

Quote: Wizard

Quote: ThatDonGuy

I am getting only 2.77% as the house edge, and I have "raise 2x" on J-10-9

Well, based on playing the game for an hour, folding on 10-9-8 just doesn't feel right to me.

You misunderstand. Here's what I get for the strategy:
Fold with A-2-3 or less (we agree on this)
Raise 2x with 2-3-4 through 9-10-Jack
Raise 4x with 10-Jack-Queen or higher
The only difference between your strategy and mine is, with 9-10-Jack, you raise 4x, while I raise only 2x.
I think 9-10-Jack is the one hand where, while a 4x raise has a positive value, a 2x raise has a higher positive value.

Quote: Wizard

Perhaps what we could do is make a table of the probability of each hand from A-2-3 to 89TJQKA, just to make sure we're both scoring correctly.

Here's what I have:

So if you had 9,10,J. You should 4x. What if you saw one of your outs in your neighbors hand or two of of your outs would you still 4x? Would some of the 2x hands become folds?

Quote: Hunterhill

So if you had 9,10,J. You should 4x. What if you saw one of your outs in your neighbors hand or two of of your outs would you still 4x? Would some of the 2x hands become folds?
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You don't get to draw, so that wouldn't matter much. I suppose if you saw the other players with cards in the middle ranks, it would improve your chances very moderately.

Quote: ThatDonGuy

I am getting only 2.77% as the house edge, and I have "raise 2x" on J-10-9
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I found a bug in my program in scoring wheel hands.

I'll update my page in about an hour, but it looks like the smallest 4x raise should be on 10-J-Q. This gives a house edge of 2.78%, based on a limited simulation. Running a longer one now.

In related news, here is how often I get each high hand.

Cards in straight	High card	Count
7	A	16,384
7	K	16,384
7	Q	16,384
7	J	16,384
7	10	16,384
7	9	16,384
7	8	16,384
7	7	16,384
6	A	135,168
6	K	118,784
6	Q	118,784
6	J	118,784
6	10	118,784
6	9	118,784
6	8	118,784
6	7	118,784
6	6	135,168
5	A	630,272
5	K	495,104
5	Q	495,104
5	J	495,104
5	10	495,104
5	9	495,104
5	8	495,104
5	7	495,104
5	6	495,104
5	5	630,272
4	A	2,183,296
4	K	1,553,024
4	Q	1,553,024
4	J	1,553,024
4	10	1,553,024
4	9	1,553,024
4	8	1,553,024
4	7	1,553,024
4	6	1,553,024
4	5	1,553,024
4	4	2,166,912
3	A	5,402,496
3	K	3,436,288
3	Q	3,538,688
3	J	3,641,088
3	10	3,743,488
3	9	3,829,504
3	8	3,915,520
3	7	4,017,920
3	6	4,001,536
3	5	3,985,152
3	4	3,985,152
3	3	4,907,392
All 1 or 2 card straight		60,598,640
Total		133,784,560

This game is such an obvious twist on Chase the Flush and High Card Flush.

I actually have studied straights of n-length as a function of number of cards drawn, but I don't think you need my expertise on this one. One interesting nugget is that having a straight in your hand slightly increases the chances of a straight (of equal or greater length) in your opponent's hand. Its because every card in your hand is a straight blocker for specific straights such as 6-2 or K-9, and when you have multiple cards in a row, they all block many of the same potential straights -which is less efficient at blocking straights than having widely spaced ranks.

I'm surprised this game designer didn't allow a discard and draw of, say, 1 or 2 cards to the initial hand. It would have increased the interest level and wagering, but I guess it would have slowed the game and limited the number of players who can be dealt from a 52 card deck.

I ran a longer simulation of almost five billion hands. Based on the strategy of raising 4x on 10-J-Q or higher, I get a house edge of 2.80%.

My page has been updated.

I'm not saying Don is wrong, but I think I'm happy if we agree on the strategy and are within 0.03% on the house edge.