Quote:acesideNobody responded, so I investigated this myself. A pocket aces hand happens once every 221 hands, and if it happens, the average EV of this hand is +3.6. If we do 8X raise preflop, the player’s EV gain (from the original UTH of 4X raise) is 4X3.6=14.4 on this hand; therefore, the player’s EV gain percentage (divided by the Ante bet amount of 1 unit) of 4X3.6/221=6.5%. This number sounds too good to be true! Is this calculation correct?

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Is that correct? Isn't the original +3.6 already based upon the 4X raise? If so, wouldn't the gain only be another 3.6?

Quote:acesideNobody responded, so I investigated this myself. A pocket aces hand happens once every 221 hands, and if it happens, the average EV of this hand is +3.6. If we do 8X raise preflop, the player’s EV gain (from the original UTH of 4X raise) is 4X3.6=14.4 on this hand; therefore, the player’s EV gain percentage (divided by the Ante bet amount of 1 unit) of 4X3.6/221=6.5%. This number sounds too good to be true! Is this calculation correct?

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I believe from the WoV calculator:

https://wizardofodds.com/games/ultimate-texas-hold-em/calculator/

3.601073 is the expected gain in units, which assumes that you would be making the 4x Raise, so the 8x raise would be roughly double that amount. I think it would be a little bit more than double the amount in EV because you aren't adding anything to the Blind Bet, obviously, so I would assume that Ante/Play has a better per unit expectation (even on wired Aces) than does the Blind Bet, though I could be wrong. I'm pretty sure I'm right, however, as a wired pair would make everything that pays out on the blind bet, except FH and Quads, less likely as opposed to more likely...or less likely than other hands, such as being suited for a flush.

If we just call it double, then you would have an expectation of roughly +7.202146 units, except only 3.601073 units of that is actual value added as the House Edge/EoR of the game already assumes that Raising 4x with Wired Aces is a possibility.

If you would normally expect to lose 0.02185 units, on average, relative to initial ante bet, but now you are expecting to win an additional 3.601073 units roughly 1/221 hands, then:

(3.601073 * 1/221) - (0.02185 * 220/221) = -0.00545668325

Which means that the game would still see the player at a disadvantage, overall. Another thing that would be too complicated for me to consider is the fact that the House Edge should actually go slightly up on the right side because we should no longer be counting dealt aces into that. The 3.601073 is good on the left side because that is value added as the House Edge (relative to ante only) assumes that you can get dealt aces anyway.

***Please recall that this isn't exactly right as I think the EV added will be slightly more than double as the Ante/Play certainly has a greater advantage in this situation than the Blind Bet does, but it should be close enough.

Quote:acesideYou are right. I investigated this a second time and found the problem. The player’s EV gain (besides the original UTH of 4X raise) is 3.6 on this hand; therefore, the player’s EV gain percentage (divided by the Ante bet amount of 1 unit) of 3.6/221=1.6%. This number sounds good now, because the original UTH house edge is 2.2%, so even with is promotion, the house still has an edge of +0.6%.

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Not a math person, forgive if this is an ignorant statement. That is just the house edge on the blind/ante right? This is not the element of risk based on all money bet?

Wizard on his page IIRC has the element of risk at 0.54% right? So that would mean on all money bet this would maybe be barely a player advantage if we use the element of risk instead of house edge on ante/blind bet?

The element of risk is not an accurate measure for this game because different people might use very different strategies to play the game to obtain different EORs.

Prize | Combinations | Probability | Return |
---|---|---|---|

509 | 854,100 | 0.000040718 | 0.020725716 |

508 | 56,700 | 0.000002703 | 0.001373187 |

59 | 794,700 | 0.000037887 | 0.002235313 |

58 | 56,700 | 0.000002703 | 0.000156781 |

19 | 175,977,840 | 0.008389596 | 0.159402315 |

12 | 1,766,425,440 | 0.084212847 | 1.010554166 |

10.5 | 329,888,200 | 0.015727142 | 0.165134996 |

10 | 111,376,440 | 0.005309778 | 0.053097781 |

9.5 | 51,143,400 | 0.002438219 | 0.023163077 |

9 | 11,929,203,960 | 0.568714766 | 5.118432891 |

8 | 3,449,306,700 | 0.164442796 | 1.315542367 |

0 | 114,023,120 | 0.005435956 | 0.000000000 |

-10 | 3,046,616,700 | 0.145244889 | -1.452448888 |

Totals | 20,975,724,000 | 1.000000000 | 6.417369702 |

The change in EV is: 2.816297064

2.816297064/221 = 0.012743426