CharlesMousseau
CharlesMousseau
Joined: Nov 1, 2016
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September 9th, 2019 at 8:35:02 PM permalink
Hello all,

doing some analysis on Lunar Poker, a game covered in detail on Stephen How's Discount Gambling website.

One of the features in the game involves paying a 1x Ante cost when the dealer does not qualify, to make them discard their highest card and replace it with a random card from the deck. Note that if you do this, and the dealer still does not qualify, you will no longer receive an Ante payment; if the dealer DOES qualify, you are paid on your Ante and Raise wagers as before.

Stephen gives two example hands. The first is:

player: Qd Qs Qh Ac 6h
dealer: Ad 9c 7d 5s 4c
forceEV: +0.7143

But when I work through this by hand, I get a force EV of exactly 1.0

If you force the dealer, they will discard their highest card (the ace), and draw one of the 42 remaining cards in the deck.

There are three 4s, three 5s, three 7s, and three 9s left, for a total of 12 cards that will give the dealer a qualifying hand of one pair. If they get one pair, you will win seven units (2x raise bet @ 3:1 + 1:1 Ante). On the remaining 30 cards, you will push the hand.

This gives a total expected value (before factoring in the 1-unit cost to force) of:

12 * 7 / 42 = 84 / 42 = 2.0000
and then subtracting the one-unit flat cost, you get an EV of 1.0000

It's worth noting that I am off by Stephen's figure by 0.2857 which equals 12/42, or 1 unit per winning replacement card

Similarly, on the second example:

player: 4d 4s 4c Qc 2h
dealer: Tc 8s 6s 5c 2s
forceEV: +0.5714

here there are now only eleven cards that make the dealer a qualifying hand when they throw away their top card (the ten), namely: two 2s, three 5s, three 6s, and three 8s.

I get an EV of 11 * 7 / 42 = 1.8333, and after subtracting the one-unit cost to force, I get 0.8333

This differs from Stephen's figure by 0.2619 which equals 11/42, or again, one unit per winning replacement card.

This suggests to me that my calculations are right and that the figures on Stephen's site are either not paying the Ante when the forced dealer now qualifies, or it's double-counting the cost on the winning hands only.

HOWEVER there is a very good chance that I'm missing something as this game has given me a migrane and a half; I've never played one hand and I'm already sick of it :P so if there's something I'm missing here PLEASE I'm all ears.

Thanks,

Charles.
MichaelBluejay
MichaelBluejay
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September 9th, 2019 at 11:23:52 PM permalink
This is over my head, but is there some reason you haven't asked Stephen How himself? (Or maybe you did, and he didn't reply? He might not reply to Joe Blow, but I'm sure he'd reply to you.) Or maybe you prefer to have an independent third party give their take?
CharlesMousseau
CharlesMousseau
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September 9th, 2019 at 11:29:03 PM permalink
Stephen participates on this forum, plus any third party. Basically just looking for a vote of confidence is all.
kubikulann
kubikulann
Joined: Jun 28, 2011
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September 10th, 2019 at 2:19:59 AM permalink
Donít know the game, so itís just from your examples.
It appears like Howís figures are based on a x6 rather than x7 payment.
So essentially it would mean that when forcing the dealer you forfeit your (original) ante?

OR
You already got this ante paid when the dealer did not qualify, and this calculation is only for the *net* value of buying a forced redraw.
Reperiet qui quaesiverit
charliepatrick
charliepatrick
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September 10th, 2019 at 4:29:49 AM permalink
If I understand it, if you force then you don't get the Ante and also have to pay 1 unit. However you will be paid out (for Trips) 3xRaise = 6 units. There are 12 winning outs so...
(i) 12 wins (win 6, paid 1 to force) = 5x12 =+60.
(ii) 30 losses (no win, paid 1 to force) = -1x30 = -30.
So net EV = 30/42.
When there are only 11 ways to win, the figures are 5x11 (+55) - 1x31 (-31) -> EV = 24/42.

I did stumble over this game in Prague many years ago (driving back from Hungary), but had no idea of the correct strategy, so didn't do too well.
gordonm888
gordonm888
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Thanks for this post from:
charliepatrick
September 10th, 2019 at 6:10:55 AM permalink
Quote: charliepatrick

If I understand it, if you force then you don't get the Ante and also have to pay 1 unit. However you will be paid out (for Trips) 3xRaise = 6 units. There are 12 winning outs so...
(i) 12 wins (win 6, paid 1 to force) = 5x12 =+60.
(ii) 30 losses (no win, paid 1 to force) = -1x30 = -30.
So net EV = 30/42.
When there are only 11 ways to win, the figures are 5x11 (+55) - 1x31 (-31) -> EV = 24/42.

I did stumble over this game in Prague many years ago (driving back from Hungary), but had no idea of the correct strategy, so didn't do too well.



charliepatrick is 5 or 6 time zones ahead of me, so he almost always beats me to it. And, dang it, he always gets it right. Which I believe he has done here.

My only contribution is to point out that you (Charles Mousseau) also mis-spelled 'migraine.'
So many better men, a few of them friends, were dead. And a thousand thousand slimy things lived on, and so did I.
CharlesMousseau
CharlesMousseau
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September 10th, 2019 at 7:18:52 AM permalink
Quote: charliepatrick

If I understand it, if you force then you don't get the Ante and also have to pay 1 unit. However you will be paid out (for Trips) 3xRaise = 6 units. There are 12 winning outs so...
(i) 12 wins (win 6, paid 1 to force) = 5x12 =+60.
(ii) 30 losses (no win, paid 1 to force) = -1x30 = -30.
So net EV = 30/42.
When there are only 11 ways to win, the figures are 5x11 (+55) - 1x31 (-31) -> EV = 24/42.

I did stumble over this game in Prague many years ago (driving back from Hungary), but had no idea of the correct strategy, so didn't do too well.



See, that's the thing, both rule sheets on Stephen's site and on the Wizard's state that, if the dealer qualifies after a force, the Ante is paid.

"With a cost of 1x ante, the player may, if dealer doesn't qualify, exchange one card (always the highest one) from the dealers hand to make the dealer to qualify. Player hand will push (no ante will be paid) if the dealer still doesn't qualify after this." - WoO

"If the dealer qualifies after the draw, then the playerís Ante and Raise resolve as before. If the dealer doesnít qualify, then the Ante and Raise push." - DG

So the net win should be 6 units when a forced dealer qualifies, not 5.
charliepatrick
charliepatrick
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September 10th, 2019 at 8:06:10 AM permalink
I think there are various rules (one I found some that don't allow you to force the dealer but just pays the Ante at 4-1 for good hands).
- https://www.ukcasinotablegames.info/pokerlunar.html - I'm not sure this is correct as it still pays the Ante before you can force the dealer with a payment and isn't clear what the subsequent payout is on a win.
- https://www.skycityauckland.co.nz/casino/table-games/ - if you click the game it will open a PDF, which says (p4) you don't get paid on the Ante etc.
MichaelBluejay
MichaelBluejay
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September 10th, 2019 at 10:20:47 AM permalink
Quote: CharlesMousseau

Stephen participates on this forum, plus any third party.

Okay, but he might not see your post, though. I can't count how many times someone started a thread here addressed to me, just because I'm a forum member, and I didn't see it until years later when I was searching for something else.

Then again, maybe he *will* see it.
CharlesMousseau
CharlesMousseau
Joined: Nov 1, 2016
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September 10th, 2019 at 10:46:33 AM permalink
Quote: charliepatrick

I think there are various rules (one I found some that don't allow you to force the dealer but just pays the Ante at 4-1 for good hands).
- https://www.ukcasinotablegames.info/pokerlunar.html - I'm not sure this is correct as it still pays the Ante before you can force the dealer with a payment and isn't clear what the subsequent payout is on a win.
- https://www.skycityauckland.co.nz/casino/table-games/ - if you click the game it will open a PDF, which says (p4) you don't get paid on the Ante etc.



Would you agree then that, assuming the rules are as I reported (i.e. if you pay to switch you now get paid on Raise AND Ante if dealer qualifies) that my EV calculations are good? Like I should be confident it's super simple and the difference in results is so obvious but still just insecure :P

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