Hole Carding Let It Ride/3 Card Poker

I understand that it's nearly impossible to see a hole card in the game of Let It Ride due to the Dealer bottom burn card. Regardless of this fact I'm trying to set up a small training session and am wondering the player advantage for seeing a card on the game. The math is too complicated for me because it would all depend on whether the card was ten or higher and whether the player had any cards ten or higher. Is there any source where I can look over the numbers? I'm guessing Beyond Counting may delve into it but I just don't have $500 to invest in it to find out that the math hasn't been completed there. Second part of the question I can't seem to find the numbers for seeing two cards in 3 Card Poker. Help on either would be greatly appreciated! Thanks!

Exhibit CAA would have your answers. Cost $250. If I was sure I could get the hole card information, then the book is a steal!

Quote: Seastkc

I understand that it's nearly impossible to see a hole card in the game of Let It Ride due to the Dealer bottom burn card. Regardless of this fact I'm trying to set up a small training session and am wondering the player advantage for seeing a card on the game. The math is too complicated for me because it would all depend on whether the card was ten or higher and whether the player had any cards ten or higher. Is there any source where I can look over the numbers? I'm guessing Beyond Counting may delve into it but I just don't have $500 to invest in it to find out that the math hasn't been completed there. Second part of the question I can't seem to find the numbers for seeing two cards in 3 Card Poker. Help on either would be greatly appreciated! Thanks!

To answer your first question only, use the data from the Wizard of Odds' Appendix 1 explaining his method for determining the return for Let It Ride here.

Assuming the pay table is 1000, 200, 50, 11, 8, 5, 3, 2, 1, -1, he gets a return of 22.85% for betting only on the positive EV four-card hands. For the initial mandatory bet, he gets a return of -37.27%. And if you add up just hands with positive EV in his table of five-card hands, you will get 38.85%.

You can combine these three returns based on which community cards you see. If you are lucky to see both on the deal, then your return based on your initial bet is -37.27% + 38.85% + 38.85% = 40.43%. If you happen to see the second community card, then your return is -37.27% + 22.85% + 38.85% = 24.43%. And if you happen to see only the first community card, then your return is -37.27% + 22.85% + 22.85% = 8.44%.

According to my calculations, with perfect strategy the player gains an 11.25% advantage if he sees the first community card and a 32.58% if the second is seen. Remember that the strategy changes, not only depending on the card value, but also the card suit. The breakdown per card value is as follows (assuming the suit is also known):

2 Value: Card1-6.05% Card2-0.72%
3 Value: Card1-5.77% Card2-0.26%
4 Value: Card1-5.48% Card2+0.19%
5 Value: Card1-5.20% Card2+0.64%
6 Value: Card1-5.20% Card2+0.64%
7 Value: Card1-5.17% Card2+0.66%
8 Value: Card1-5.12% Card2+0.68%
9 Value: Card1-5.05% Card2+0.72%
10 Value: Card1+16.53% Card2+21.53%
J Value: Card1+16.22% Card2+21.06%
Q Value: Card1+15.89% Card2+20.58%
K Value: Card1+15.53% Card2+20.09%
A Value: Card1+15.42% Card2+20.04%
Avg Value*4: Card1+11.25% Card2+32.58%

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Quote: Kelmo

According to my calculations, with perfect strategy the player gains an 11.25% advantage if he sees the first community card and a 32.58% if the second is seen. Remember that the strategy changes, not only depending on the card value, but also the card suit. The breakdown per card value is as follows (assuming the suit is also known):

2 Value: Card1-6.05% Card2-0.72%
3 Value: Card1-5.77% Card2-0.26%
4 Value: Card1-5.48% Card2+0.19%
5 Value: Card1-5.20% Card2+0.64%
6 Value: Card1-5.20% Card2+0.64%
7 Value: Card1-5.17% Card2+0.66%
8 Value: Card1-5.12% Card2+0.68%
9 Value: Card1-5.05% Card2+0.72%
10 Value: Card1+16.53% Card2+21.53%
J Value: Card1+16.22% Card2+21.06%
Q Value: Card1+15.89% Card2+20.58%
K Value: Card1+15.53% Card2+20.09%
A Value: Card1+15.42% Card2+20.04%
Avg Value*4: Card1+11.25% Card2+32.58%

Made an error on average value by multiplying by 4. without doing this, the average value is Card1 +2.81% and Card2 +8.14%. This is the advantage per unit bet. If you multiply by three for all three wagers, the EV is 8.44% and 24.43%, which agrees with ChesterDog's description. I guess I just did it the long way, but at least we now know it is correct.