I thought I knew how to play this game until I saw this video. Amazing work, the game is way more complicated than I thought. A lot of good insights here, thank you!
one topic that i am very interested in is: giving up royaltipoints for better scooppotential in FL.
i would love to hear you opinion about that. my main problem is basically that i dont know the average handstrengh. so i dont know how much more non-royalty-points a certain set gives me. maybe you have some math for that.
Hey! I was thinking of posting a few FL hand examples for my next video. In general, I usually consider hands that are more likely to scoop when there's a one (and occasionally two) point difference in royalties. One spot that comes up a lot boat in the back/boat in the middle that we can split up into trips and aces or kings. So we'd split up that middle boat for aces and sacrifice one royalty point. Kings it would depend on our high card hand. Our opponent fouls a lot in fantasyland so we need to account for that as well. If you have any specific hands, message me and I'll include it in my compilation.
The variance in this game is very high. Playing just as well when running awful & getting badugi hands is one the key skills after you get the basics down. For some people it may also be hard to play well when running like god. The big difference here is you don't get to choose when to play a big pot and often you can't get up (especially three-handed) because an opponent is in Fantasy. It's a good idea to be conservative with stakes till you get a feel for how extreme the swings can be.
Per your decision to place KK in the middle on your KK9d draw (ABOUT 23 minutes in): I broke down the hand myself and reached quite a different conclusion. Ill show my work and how i reached such a conclusion then await your thoughts on my math/conclusions.
First we can see the only two plays worth evaluating are Kmid/9d btm, or KK mid as Kmin/9d clearly dominates K top;
Evaluating playing 9d btm, 9s Top
Villain fouls : 0.2242, qualifies mid (draws A,Q,8, 4,2): 0.7758
Should villian qualify, we must examine the line war Evaluating "line war"
1. Villain wins bottom line: our score: -1
2. Top line: In order to win the top hero must draw: A/K+Q, or A/K/8+3+villian does not draw Q+T
P(A/K+Q (2 outer and 2 outer) AND he does not draw Q+T)=:3( 2/272/2623/25)=0.0157
P(A/K/8+3)=0.0287, 0.0287.9515=0.0273
P(villain draws Q+T): 1-32/2423/22=0.9515,
summing, we improve the top 0.043, we lose top 0.957 to give us a weighted value of: 1.0443+(-1).9556=(-0.9112)
3. The fun stuff- The middle line: (i understand the values for the villain's probabilities are slightly inflated because he can draw a Q and an 8 in my math. By leaving it as is, it overvalues villains hand, which will give us a lower bound on our score. If this is close to the other option, then i would go back and fine tune the math to get a much cleaner answer)
now i make a tree for each out w branches of our redarw outs and their value of the line and then sum up each final branch to give us the value of the middle line. I leave out the probabilties of hitting each card so i dont over count later (i will be multiplying by the 0.7742 villain qualifies), but i instead multiply it by the number of outs per card, to later divide by the total outs to give us a weighted value.
)Q-a. 0.3188 (A/K), 1---- 0.3187 2
b. 0.6812 (1), -1----- (-0.6813)2
Ill just give the finale values for each card +/- i get, instead of drawing it out
8 a. 0.4076, b. (-.5924) *2
4 a. 0..4078, b (-.5922) *3
2 a. 0..5117, b (-0.4900) *2
A a. 1 (he qualifies but we always win middle) *1
summing up these numbers we find a value (-0.5846). now we divide by 10 the get the weighted average value of the middle line: (-0.0585)
summing the top, middle and bottom values for the line we obtain (-1.9697) as our value of the line war when he qualifies.
Total EV (line war)= (-1.9697).7758+6.2242=(-0.1829)
This is our value in The line war (-0.1829)
Royalties
We have our flush 100% of the time for +4
Fantasyland: we need to draw A/K+Q: we figured this in the above part to be (2/272/2623/25)3=0.0157
QQ+FL value about 17pts (10 for FL using Jen's approximation), EV (hitting FL)=17.0157=.2669
Royalty points: 4.2669
Total Expected additional points of 9d, K placement: +4.084
Evaluating KK in Middle
Here its easier to write out the royalty section first: Royalties
As state in video hero hits flush 0.6103.
now here can hit flush and fantasy land for additional royalties (only other royalties possible): = (7/272/2618/25)*3=0.0431.
Thus hero will hit fantasy land 0.0431/.(.6103)=.0706 of the time she hits a flush. so we can calculate the royalty section as such:This is to properly weight hitting flush, and not FL and hitting flush and FL
EV (flush)= 4.6103(1-0.706) = 2.2688
EV (flush and FL)= 21.0706.6103=0.905
Royaties: 3.5928
Line War
Here its easiest to make a grid with the probabilities for each mix of outcomes and evaluate the scoring lines:
Both foul (0.22420.3997) * 0 pts (value for hero)=0
P1 foul, p2 (hero) qualifies =0.2242.61036=.1368 *6=.8208
p1 qualifies, p2 fouls= .7758.3997-6=(-1.8605)
P1 and P2 qualfy=.7758.6103x=.4735x
x being the sum of the line value for p2 (hero). Plainly if both qualify hero wins middle, villain wins the bottom, so its entirely up to the top line.
Hero is currently behind and would need to Draw A/Q/3 (5 outs) and diamond
P(A/Q/3 + d)= (5/277/2614/25)*3=0.0838. now since we already stipulated hero had drawn the diamond we have to determine what percentage of the time he draws AQ3 given he drew a diamond (wording may be slightly off, but....) = 0.0838/.4735=0.1769
Of this time we need p1 not to draw Q+T which from part 1 is .9515, thus hero wins the top: 0.1769*0.9515=0.1683, villian wins 0.8317
Ev top line given qual/qual= 1.1683-1.8317=(-0.6634)
recombining:
Both foul (0.22420.3997) * 0 pts (value for hero)=0
P1 foul, p2 (hero) qualifies =0.2242.61036=.1368 *6=.8208
p1 qualifies, p2 fouls= .7758.3997-6=(-1.8605)
P1 and P2 qualfy=.7758.6103x=.4735(-0.6634)=(-0.3141)
we sum for the total line war value: (-1.3538)
Thus the total additional value for KK is: +2.239
Even without doing the fine tuning math we can still see 9d, K is far superior (by almost 2 points) 4.089 to 2.239
The play should be 9d btm, K middle
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I thought I knew how to play this game until I saw this video. Amazing work, the game is way more complicated than I thought. A lot of good insights here, thank you!
low middle is boring
one topic that i am very interested in is: giving up royaltipoints for better scooppotential in FL.
i would love to hear you opinion about that. my main problem is basically that i dont know the average handstrengh. so i dont know how much more non-royalty-points a certain set gives me. maybe you have some math for that.
Hey! I was thinking of posting a few FL hand examples for my next video. In general, I usually consider hands that are more likely to scoop when there's a one (and occasionally two) point difference in royalties. One spot that comes up a lot boat in the back/boat in the middle that we can split up into trips and aces or kings. So we'd split up that middle boat for aces and sacrifice one royalty point. Kings it would depend on our high card hand. Our opponent fouls a lot in fantasyland so we need to account for that as well. If you have any specific hands, message me and I'll include it in my compilation.
what a fantastic video… i was surprised and very interested to hear the thinking behind the Qs/AdAsJs/3c set … really great stuff.
So glad you enjoyed it, tyvm!
How would you compare The volatility of This variant compared to other forms of poker..less or more?
The variance in this game is very high. Playing just as well when running awful & getting badugi hands is one the key skills after you get the basics down. For some people it may also be hard to play well when running like god. The big difference here is you don't get to choose when to play a big pot and often you can't get up (especially three-handed) because an opponent is in Fantasy. It's a good idea to be conservative with stakes till you get a feel for how extreme the swings can be.
Per your decision to place KK in the middle on your KK9d draw (ABOUT 23 minutes in): I broke down the hand myself and reached quite a different conclusion. Ill show my work and how i reached such a conclusion then await your thoughts on my math/conclusions.
First we can see the only two plays worth evaluating are Kmid/9d btm, or KK mid as Kmin/9d clearly dominates K top;
Evaluating playing 9d btm, 9s Top
Villain fouls : 0.2242, qualifies mid (draws A,Q,8, 4,2): 0.7758
Should villian qualify, we must examine the line war
Evaluating "line war"
1. Villain wins bottom line: our score: -1
2. Top line: In order to win the top hero must draw: A/K+Q, or A/K/8+3+villian does not draw Q+T
P(A/K+Q (2 outer and 2 outer) AND he does not draw Q+T)=:3( 2/272/2623/25)=0.0157
P(A/K/8+3)=0.0287, 0.0287.9515=0.0273
P(villain draws Q+T): 1-32/2423/22=0.9515,
summing, we improve the top 0.043, we lose top 0.957 to give us a weighted value of: 1.0443+(-1).9556=(-0.9112)
3. The fun stuff- The middle line: (i understand the values for the villain's probabilities are slightly inflated because he can draw a Q and an 8 in my math. By leaving it as is, it overvalues villains hand, which will give us a lower bound on our score. If this is close to the other option, then i would go back and fine tune the math to get a much cleaner answer)
Card, # outs, % chance, # redraw outs, % redraw
Q, 2, 0.2137, 3, 0.3188
8, 2, 0.2137, 4, 0.4977
4, 3, 0.3080, 4, 0.4077
2, 2, 0.2137, 5, 0.5115
A, 1, .1022, any, 1.0
now i make a tree for each out w branches of our redarw outs and their value of the line and then sum up each final branch to give us the value of the middle line. I leave out the probabilties of hitting each card so i dont over count later (i will be multiplying by the 0.7742 villain qualifies), but i instead multiply it by the number of outs per card, to later divide by the total outs to give us a weighted value.
)Q-a. 0.3188 (A/K), 1---- 0.3187 2
b. 0.6812 (1), -1----- (-0.6813)2
Ill just give the finale values for each card +/- i get, instead of drawing it out
8 a. 0.4076, b. (-.5924) *2
4 a. 0..4078, b (-.5922) *3
2 a. 0..5117, b (-0.4900) *2
A a. 1 (he qualifies but we always win middle) *1
summing up these numbers we find a value (-0.5846). now we divide by 10 the get the weighted average value of the middle line: (-0.0585)
summing the top, middle and bottom values for the line we obtain (-1.9697) as our value of the line war when he qualifies.
Total EV (line war)= (-1.9697).7758+6.2242=(-0.1829)
This is our value in The line war (-0.1829)
Royalties
We have our flush 100% of the time for +4
Fantasyland: we need to draw A/K+Q: we figured this in the above part to be (2/272/2623/25)3=0.0157
QQ+FL value about 17pts (10 for FL using Jen's approximation), EV (hitting FL)=17.0157=.2669
Royalty points: 4.2669
Total Expected additional points of 9d, K placement: +4.084
Evaluating KK in Middle
Here its easier to write out the royalty section first:
Royalties
As state in video hero hits flush 0.6103.
now here can hit flush and fantasy land for additional royalties (only other royalties possible): = (7/272/2618/25)*3=0.0431.
Thus hero will hit fantasy land 0.0431/.(.6103)=.0706 of the time she hits a flush. so we can calculate the royalty section as such:This is to properly weight hitting flush, and not FL and hitting flush and FL
EV (flush)= 4.6103(1-0.706) = 2.2688
EV (flush and FL)= 21.0706.6103=0.905
Royaties: 3.5928
Line War
Here its easiest to make a grid with the probabilities for each mix of outcomes and evaluate the scoring lines:
P1 fouls 0.2242, P1 qualifies: 0.7758
P2 fouls 0.3997 P2 qualifies: 0.6103
Both foul (0.22420.3997) * 0 pts (value for hero)=0
P1 foul, p2 (hero) qualifies =0.2242.61036=.1368 *6=.8208
p1 qualifies, p2 fouls= .7758.3997-6=(-1.8605)
P1 and P2 qualfy=.7758.6103x=.4735x
x being the sum of the line value for p2 (hero). Plainly if both qualify hero wins middle, villain wins the bottom, so its entirely up to the top line.
Hero is currently behind and would need to Draw A/Q/3 (5 outs) and diamond
P(A/Q/3 + d)= (5/277/2614/25)*3=0.0838. now since we already stipulated hero had drawn the diamond we have to determine what percentage of the time he draws AQ3 given he drew a diamond (wording may be slightly off, but....) = 0.0838/.4735=0.1769
Of this time we need p1 not to draw Q+T which from part 1 is .9515, thus hero wins the top: 0.1769*0.9515=0.1683, villian wins 0.8317
Ev top line given qual/qual= 1.1683-1.8317=(-0.6634)
recombining:
Both foul (0.22420.3997) * 0 pts (value for hero)=0
P1 foul, p2 (hero) qualifies =0.2242.61036=.1368 *6=.8208
p1 qualifies, p2 fouls= .7758.3997-6=(-1.8605)
P1 and P2 qualfy=.7758.6103x=.4735(-0.6634)=(-0.3141)
we sum for the total line war value: (-1.3538)
Thus the total additional value for KK is: +2.239
Even without doing the fine tuning math we can still see 9d, K is far superior (by almost 2 points) 4.089 to 2.239
The play should be 9d btm, K middle
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