## Poll

 Yes -- I love multipliers! 2 votes (12.5%) Call me maybe. No votes (0%) Only to vulture. 7 votes (43.75%) Nah. 7 votes (43.75%) I still don't understand the rules. No votes (0%) Purim reminder -- Feb 23, 2021 2 votes (12.5%) I hate leaf blowers. 2 votes (12.5%) What's the status of a 2021 Spring Fling? 3 votes (18.75%) Total eclipse reminder April 8 2024 5 votes (31.25%) I believe MDawg. 1 vote (6.25%)

16 members have voted

CroquetIsOK
Joined: Dec 28, 2021
• Posts: 6
January 23rd, 2022 at 6:30:00 PM permalink
Quote: CroquetIsOK

The return to player on a single round played with the multipliers in the initial power-up state is 105.3286 % of the wager for this particular set of parameters. In most versions, the power-up return to player is in the range 98%-100%.

Some more information about the 105.3% return in the powerup state for this 10-play game...Suppose a player starts with the machine in the power-up state and plays exactly 100 rounds, with a strategy of maximizing the expected pay on each individual round. Then his expected return is 103.3 %. But if the player plays 1000 rounds from the power-up state using the same strategy, his expected return is 96.7 %, with a 95% confidence interval ranging from 81% to 120%. There's a 0.01 probability that his return exceeds 130% from the 1000 rounds played.
CroquetIsOK
Joined: Dec 28, 2021
• Posts: 6
Thanks for this post from:
January 24th, 2022 at 6:16:54 AM permalink
Quote: Wizard

Quote: BobDancer

In the video, the Wizard had a hand of 44333 (or maybe it was 33444). There was no multiplier on the full house (worth 35) but a 9x multiplier on four 2s-4s (now worth 1800) in addition to a small multiplier on 3-of-a-kind. . to me it seems seat-of-pants obvious to just hold the 3-of-a-kind although in the video Shack didn't even consider that play.link to original post

Ooops. I should have considered that.

In doing the math, I see my expected win was 78.73265495 holding three of a kind and a fixed 35 for the full house. What is my punishment?

After the (33344) hand was dealt, the video shows a 9X multiplier for Quad 3's, a 1X multiplier for full house, and a 1X multiplier for 3-Kind. This makes the expected win from holding the 3's 92.1974 coins, not 78.7326. The math for the ending hands after the draw:
Quad 3's: 46/1081 * 1800 coins
Full Hse: 67/1081 * 35 coins
Trip 3's: 968/1081 * 15 coins
Total = 92.1974.

But there are ten ending hands, not just one. So the expected immediate pay from holding trip 3's is 921.97 coins, and the expected pay from standing on the full house is 350 coins, making the error in standing on the house be (921.97 - 350) = 572 coins of expected immediate pay. This is a pretty substantial mistake.

But hitting quad 3's also removes the 9X multiplier from that category and puts a 1X multiplier in its place. This removes hidden equity from the machine, and represents an opportunity cost for future rounds of play. I calculate that holding trip 3's instead of standing on the full house has an expected opportunity cost of 415.74 coins. So if you hold trip 3's instead of standing on the house, you are gaining (921.97 - 350 - 415.74) = 156.23 coins in long-run value. Thus holding only the 3's is both long-run optimal as well as short-run optimal, and the wizard's error as a long-run optimizing player is only 156.23 pushups, not 572 pushups.
wali22
Joined: Feb 15, 2022