ThatDonGuy
Joined: Jun 22, 2011
• Posts: 4269
Thanks for this post from:
September 14th, 2020 at 4:56:21 PM permalink
Quote: logicGuy

Thanks ThatDonGuy, but could the removal of the Ante Bonus swing the edge from player 3.48% to house 3.833% ? Seems a rather huge swing for a bonus that doesn't pay all that often.

Well, I did find a problem - I was using the wrong number of hands when determining whether to play or fold a given hand.

I still get a house edge, but it's "only" 1.8022%. When I put the ante bonus back in, I get the numbers the Wizard gets - a player edge of 3.483% with one card shown, and a house edge of 3.373% with no cards shown.
Last edited by: ThatDonGuy on Sep 14, 2020
ThatDonGuy
Joined: Jun 22, 2011
• Posts: 4269
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September 15th, 2020 at 6:31:07 AM permalink
Here is what I get for the strategy if the dealer shows a card:

If the dealer shows an Ace: play A9 or better
If the dealer shows a King: play K9 or better
If the dealer shows a Queen: play Q9 or better
If the dealer shows a 2 through Jack: always play - of the 1128 possible pairs of down cards, there are at most 132 ways the dealer can have a qualifying hand (6 pairs of Aces, 6 pairs of Kings, 6 pairs of Queens, 3 pairs of the up card, 3 ways to make a straight flush, 45 ways to make a straight (e.g. with a 6 showing, 16 8-7s, 16 7-5s, 16 5-4s, minus the three straight flushes), and 63 ways to make a flush)
Last edited by: ThatDonGuy on Sep 15, 2020
logicGuy
Joined: Oct 24, 2017
• Posts: 8
September 15th, 2020 at 10:54:39 AM permalink
Quote: ThatDonGuy

If the dealer shows a 2 through Jack: always play - of the 1128 possible pairs of down cards, there are at most 132 ways the dealer can have a qualifying hand (6 pairs of Aces, 6 pairs of Kings, 6 pairs of Queens, 3 pairs of the up card, 3 ways to make a straight flush, 45 ways to make a straight (e.g. with a 6 showing, 16 8-7s, 16 7-5s, 16 5-4s, minus the three straight flushes), and 63 ways to make a flush)

I may be misinterpreting your description, but it seems there some additional ways the dealer can qualify. What about a single Ace, King, or Queen - that would be 12 more. And what about any pair of the two down cards, not just K, Q, A?

Thanks for the analysis!
ThatDonGuy
Joined: Jun 22, 2011
• Posts: 4269
September 15th, 2020 at 11:39:45 AM permalink
Quote: logicGuy

I may be misinterpreting your description, but it seems there some additional ways the dealer can qualify. What about a single Ace, King, or Queen - that would be 12 more. And what about any pair of the two down cards, not just K, Q, A?

Good question.

Here's what I get for having a Jack face up:
Of the 1275 possible pairs of down cards ("didn't you say 1128?" Yes, but that assumes you are looking at a specific 3-card player hand)
3 are pairs of Jacks
72 are other pairs (12 ranks; for each, there are 6 different pairs)
144 are Jack and something else (for each of the 3 remaining Jacks, there are 4 Aces, 4 Kings, ..., 4 2s)
176 are Ace and something besides Ace and Jack (which have already been counted - for each of the 4 Aces, there are 4 Kings, 4 Queens, 4 10s, ..., 4 2s)
160 are King and something besides Ace, King, and Jack
144 are Queen and something besides Ace, King, Queen, and Jack
16 are 10/9 (which makes a Jack-high straight)
35 are the same suit as the face-up Jack that have not already been counted (there are 66 total, but the 11 with an Ace, the 10 others with a King, the 9 others with a Queen, and 10/9 have already been counted)
This is 750 qualifying hands; the other 525 do not.
logicGuy
Joined: Oct 24, 2017
• Posts: 8
September 15th, 2020 at 2:28:04 PM permalink
Quote: ThatDonGuy

This is 750 qualifying hands; the other 525 do not.

So why would I always make the Play wager in this case? If I have a non-qualifying hand, and dealer shows a Jack, the strategy says to make the Play wager, hoping the dealer won't qualify. But based on your numbers it looks like the dealer will qualify 750/1275 times and I would lose more often than not.
ThatDonGuy
Joined: Jun 22, 2011
• Posts: 4269
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September 15th, 2020 at 3:08:06 PM permalink
Quote: logicGuy

So why would I always make the Play wager in this case? If I have a non-qualifying hand, and dealer shows a Jack, the strategy says to make the Play wager, hoping the dealer won't qualify. But based on your numbers it looks like the dealer will qualify 750/1275 times and I would lose more often than not.

If you fold, you lose 1.
If you play with a non-qualifying hand, then you lose 2 750/1275 of the time and you win 1 525/1275 of the time, which is an expected loss of 975/1275, which is a better result than a loss of 1.
logicGuy
Joined: Oct 24, 2017
• Posts: 8
September 15th, 2020 at 3:13:38 PM permalink
Quote: ThatDonGuy

If you fold, you lose 1.
If you play with a non-qualifying hand, then you lose 2 750/1275 of the time and you win 1 525/1275 of the time, which is an expected loss of 975/1275, which is a better result than a loss of 1.

It certainly is! Thanks!
gordonm888
Joined: Feb 18, 2015
• Posts: 2561
September 15th, 2020 at 7:34:01 PM permalink
Eliot Richardson did an analysis of strategy and House Edge for "hole card exposure" for 3-card poker and published it in his book. I'm not finding his book in my office - can someone quote from his book please?
So many better men, a few of them friends, were dead. And a thousand thousand slimy things lived on, and so did I.
ssho88
Joined: Oct 16, 2011
• Posts: 451
September 16th, 2020 at 5:17:18 AM permalink
Quote: ThatDonGuy

Here is what I get for the strategy if the dealer shows a card:

If the dealer shows an Ace: play A9 or better
If the dealer shows a King: play K9 or better
If the dealer shows a Queen: play Q9 or better
If the dealer shows a 2 through Jack: always play - of the 1128 possible pairs of down cards, there are at most 132 ways the dealer can have a qualifying hand (6 pairs of Aces, 6 pairs of Kings, 6 pairs of Queens, 3 pairs of the up card, 3 ways to make a straight flush, 45 ways to make a straight (e.g. with a 6 showing, 16 8-7s, 16 7-5s, 16 5-4s, minus the three straight flushes), and 63 ways to make a flush)

I did this three years ago, Combination Analysis results for 3CP, delear show 1 card, WITHOUT ante bonus, raise if equal or better than X92( X is dealer's upcard, Q, K or ACE).

I proposed the X92 strategy as well but it may NOT the optimum strategy. Anyone can verify it ? gordonm888 ?

See image : https://ibb.co/52DjWwy
ThatDonGuy
Joined: Jun 22, 2011