Expanded UTH combinations table
September 24th, 2026 at 4:54:34 PM
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I received a DM asking if I could prepare an table similar to Mike's table ( https://wizardofodds.com/games/ultimate-texas-hold-em/ ) but with the category 'Less than straight' expanded to show counts for each type of lesser hand. I did some spot checks and my right-hand column seems to be identical to Mike's 'COMBINATIONS' column for hands higher than straight, so I assume my expanded table is correct.
Let me know if you see anything amiss or have other questions.
Let me know if you see anything amiss or have other questions.
Large Yes High Card Player 0
Large Yes One Pair Player 1540402830960
Large Yes Two Pair Player 1732499238840
Large Yes Three of a Kind Player 398148096080
Large Yes Straight Player 246174692160
Large Yes Flush Player 241047929080
Large Yes Full House Player 295405180920
Large Yes Four of a Kind Player 23008208760
Large Yes Straight Flush Player 1818135760
Large Yes Royal Flush Player 596356920
Large No High Card Player 433149381600
Large No One Pair Player 904600506240
Large No Two Pair Player 151807752000
Large No Three of a Kind Player 67239396000
Large No Straight Player 81416649960
Large No Flush Player 50874988680
Large No Full House Player 0
Large No Four of a Kind Player 0
Large No Straight Flush Player 229686840
Large No Royal Flush Player 90386280
Large ??? Any Push 285142270600
Large Yes Any Dealer 3931554359920
Large No Any Dealer 102655952400
Medium Yes High Card Player 0
Medium Yes One Pair Player 397206766824
Medium Yes Two Pair Player 1303923602376
Medium Yes Three of a Kind Player 413709285564
Medium Yes Straight Player 133100158992
Medium Yes Flush Player 152618008784
Medium Yes Full House Player 289401836880
Medium Yes Four of a Kind Player 18537793620
Medium Yes Straight Flush Player 2704129504
Medium Yes Royal Flush Player 112333500
Medium No High Card Player 10540265748
Medium No One Pair Player 816509223576
Medium No Two Pair Player 253178274756
Medium No Three of a Kind Player 3535705512
Medium No Straight Player 45053788356
Medium No Flush Player 38820798396
Medium No Full House Player 0
Medium No Four of a Kind Player 0
Medium No Straight Flush Player 358131456
Medium No Royal Flush Player 8830620
Medium ??? Any Push 191611691060
Medium Yes Any Dealer 1841155221088
Medium No Any Dealer 7978353108
Small Yes High Card Player 0
Small Yes One Pair Player 574281746088
Small Yes Two Pair Player 716413685352
Small Yes Three of a Kind Player 84337863632
Small Yes Straight Player 395087247768
Small Yes Flush Player 190959227136
Small Yes Full House Player 43297986840
Small Yes Four of a Kind Player 859737984
Small Yes Straight Flush Player 1962591576
Small Yes Royal Flush Player 42135660
Small No High Card Player 124443379236
Small No One Pair Player 562334043180
Small No Two Pair Player 31539562044
Small No Three of a Kind Player 2262474288
Small No Straight Player 136018223484
Small No Flush Player 40911000804
Small No Full House Player 0
Small No Four of a Kind Player 0
Small No Straight Flush Player 269696304
Small No Royal Flush Player 6109020
Small ??? Any Push 418339128088
Small Yes Any Dealer 2700150685692
Small No Any Dealer 47223220344
Small ??? Any FOLD 5335144079760
Last edited by: unnamed administrator on Sep 24, 2026
Gambling is a math contest where the score is tracked in dollars. Try not to get a negative score.
September 24th, 2026 at 6:01:52 PM
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Edited for formatting. (Close paren broke link)
May the cards fall in your favor.
September 24th, 2026 at 7:18:06 PM
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It is relatively easy to go through the 27,813,810,024,000 combinations, rank the player versus dealer hands, and count the outcomes. However, you do not know what the betting decision is at that point. Only after you run through billions of flop, turn/river, and dealer hands do you know the optimal strategy for betting.
To address this, I run through the combinations twice. Once to get the strategy right, and a second time to add the counts to the correct lines in the table based on the strategy (Large/Medium/Small bet or fold. In order to do this task, I do create and store a huge cache of strategy decisions for one pair of player hole cards at a time. I delete this cache after I move on to the next player hole card pair. It is impractical to store the strategy for the whole UTH game in memory (even on a powerful desktop computer).
To address this, I run through the combinations twice. Once to get the strategy right, and a second time to add the counts to the correct lines in the table based on the strategy (Large/Medium/Small bet or fold. In order to do this task, I do create and store a huge cache of strategy decisions for one pair of player hole cards at a time. I delete this cache after I move on to the next player hole card pair. It is impractical to store the strategy for the whole UTH game in memory (even on a powerful desktop computer).
Gambling is a math contest where the score is tracked in dollars. Try not to get a negative score.
September 24th, 2026 at 7:35:50 PM
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So is the "Wizard strategy" on his site the best strategy? That's the one I use.
September 25th, 2026 at 4:38:48 AM
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The best strategy is to use a computer for every decision after the flop using the exact cards on the board. The Wizard's UTH page gives a pre-flop which is optimal and a post-flop and river strategy that are a simple heuristic, and definitely not optimal.Quote: GenoDRPhSo is the "Wizard strategy" on his site the best strategy? That's the one I use.
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Quote: Wizard strategy
Medium Raise: Make the 2X raise with any of the following:
Two pair or better.
Hidden pair*, except pocket deuces.
Four to a flush including a hidden 10 or better to that flush
* Hidden pair = Any pair with at least one card in your hole cards (thus the pair is hidden to the dealer).
Small Raise: Make the 1X raise with any of the following, otherwise fold:
Hidden pair or better.
Less than 21 dealer outs beat you.
You can find more complex strategy guidelines posted online. I only play UTH occasionally and always online. I just use a UTH calculator for any tough decisions, so I have never even counted outs. I am not interested in producing a better human-executable strategy for B&M UTH.
Gambling is a math contest where the score is tracked in dollars. Try not to get a negative score.
September 25th, 2026 at 5:39:17 AM
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I just looked into your Hand Counts table and found that these “Any” player hands haven’t been expanded yet. Any plan on this part?
For my purpose of calculating the combined variance between UTH and Trips, I only need the combination counts for player’s trips hands, but I also need these counts when player loses or pushes to dealer. So, these details “high card”, “one pair”, and “ two pair” are not needed toward this goal.
For my purpose of calculating the combined variance between UTH and Trips, I only need the combination counts for player’s trips hands, but I also need these counts when player loses or pushes to dealer. So, these details “high card”, “one pair”, and “ two pair” are not needed toward this goal.
September 25th, 2026 at 8:12:19 AM
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Quote: acesideI just looked into your Hand Counts table and found that these “Any” player hands haven’t been expanded yet. Any plan on this part?
For my purpose of calculating the combined variance between UTH and Trips, I only need the combination counts for player’s trips hands, but I also need these counts when player loses or pushes to dealer. So, these details “high card”, “one pair”, and “ two pair” are not needed toward this goal.
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Okay, I already have those stats you asked for within my program. It seems that the dealer always qualifies when you lose or tie with the dealer. It is a simple matter to change the code, but it takes 24 hours to do the calculation. It would be faster if I could use multiple processors on the Mac, but this version of the program is single-threaded at the moment.
Gambling is a math contest where the score is tracked in dollars. Try not to get a negative score.
