T9o
61.55%
Wins 60.66%, ties 1.78%
53s
38.45%
Wins 37.56%, ties 1.78%
T9o against 53s: the numbers
| Hand | Wins | Ties | Loses | Equity |
|---|---|---|---|---|
| T9o | 60.657 | 1.779 | 37.564 | 61.546 |
| 53s | 37.564 | 1.779 | 60.657 | 38.454 |
T9o, an offsuit hand, plays 53s, a suited hand. Neither hand shares a rank with the other, so this is a contest of high cards, connection and suits.
The lead is steady rather than large, and the flop still has plenty of say in who wins. About 1.78% of boards chop the pot, which is why equity sits slightly above the win figure for both hands.
The hand ranking puts T9o at 78 and 53s at 146 out of 169 starting hands.
| Hand | Boards won, about | Boards tied, about | Boards lost, about |
|---|---|---|---|
| T9o | 49,854,000 | 1,462,000 | 30,874,000 |
| 53s | 30,874,000 | 1,462,000 | 49,854,000 |
The total is exact: 48 specific deals times 1,712,304 boards. The three counts are approximate, worked out from the percentages to five decimals and rounded to the nearest thousand.
| Hand | Equity as odds (to 1) | Wins one deal in | Loses one deal in | Pot odds needed to call (to 1) |
|---|---|---|---|---|
| T9o | 1.601 | 1.649 | 2.662 | 0.625 |
| 53s | 0.625 | 2.662 | 1.649 | 1.601 |
The last column is the break-even price: the pot odds a call needs to offer, as a ratio of pot to call.
Who is ahead on which flops
By flop texture, T9o's equity runs from 50.47% on low rainbow flops (nine high or lower) up to 66.18% on rainbow flops topped by a ten or better. T9o stays ahead on all five textures, but the swing between them is large, so how the flop looks matters a great deal.
| Flop | Share of flops | T9o wins | Ties | 53s wins | T9o equity |
|---|---|---|---|---|---|
| Rainbow, ten or higher | 25.341 | 65.595 | 1.167 | 33.238 | 66.178 |
| Rainbow, nine or lower | 5.689 | 50.166 | 0.614 | 49.220 | 50.473 |
| Two-tone | 46.667 | 59.833 | 1.002 | 39.165 | 60.334 |
| Monotone | 5.212 | 58.242 | 3.006 | 38.752 | 59.745 |
| Paired | 17.091 | 59.816 | 4.820 | 35.364 | 62.226 |
A rainbow flop shows three suits, a two-tone flop repeats one suit, a monotone flop is a single suit, and a paired flop repeats a rank.
Compared with a random hand
The table below sets each hand against its own random-hand baseline: a change of +10.02 points for T9o, from 51.53%, and -1.24 for 53s, from 39.69%.
| Case | Equity here | Against a random hand | Change in points | Times the random-hand equity |
|---|---|---|---|---|
| T9o, all flops | 61.546 | 51.532 | +10.014 | 1.19433 |
| T9o, rainbow, ten or higher | 66.178 | 51.532 | +14.646 | 1.28421 |
| T9o, rainbow, nine or lower | 50.473 | 51.532 | -1.059 | 0.97945 |
| T9o, two-tone | 60.334 | 51.532 | +8.802 | 1.17081 |
| T9o, monotone | 59.745 | 51.532 | +8.213 | 1.15938 |
| T9o, paired | 62.226 | 51.532 | +10.694 | 1.20752 |
| 53s, all flops | 38.454 | 39.693 | -1.239 | 0.96879 |
| 53s, rainbow, ten or higher | 33.822 | 39.693 | -5.871 | 0.85209 |
| 53s, rainbow, nine or lower | 49.527 | 39.693 | +9.834 | 1.24775 |
| 53s, two-tone | 39.666 | 39.693 | -0.027 | 0.99932 |
| 53s, monotone | 40.255 | 39.693 | +0.562 | 1.01416 |
| 53s, paired | 37.774 | 39.693 | -1.919 | 0.95165 |
Does a shared suit matter?
Does suit overlap move the numbers? T9o has 62.27% when the hands share a suit and 60.82% when they do not. T9o does better with a shared suit, by 1.45 points.
| Deals | Specific deals | Share of deals | T9o wins | Ties | 53s wins | T9o equity |
|---|---|---|---|---|---|---|
| Share a suit | 24 | 50.00 | 61.363 | 1.822 | 36.815 | 62.274 |
| No shared suit | 24 | 50.00 | 59.951 | 1.735 | 38.314 | 60.819 |
How often this matchup comes up
The class pair covers 48 combinations of specific cards in a fixed seat order, 0.0030% of 1,624,350, and 96 (0.0059%) in either order.
A worked example
Say each player puts $100 in before the flop, making a $200 pot. On average T9o takes back $123.10 of it, which is $23.10 more than it put in, and 53s takes back $76.90, $23.10 less than it put in.
Scaled to 1,000 deals, that is roughly 606 wins for T9o, 376 for 53s and 18 chopped pots.
The same matchup from the other side
One page covers both views. From 53s' side the equity is 38.45%, and from T9o's side it is 61.55%.
Keep exploring
Ts9h against 5d3d is a ready-made deal for the calculator, with no suit in common between the hands. The neighboring matchups below replace one hand with another of similar strength.
How this was computed
All 1,712,304 five-card boards are dealt for every suit pattern among the 48 specific deals of T9o against 53s, and both hands are scored on each. That is a full count, so the percentages are exact. Ties are half a win each, and each board appears once per flop it contains.
Source: our own exact count from the GeorgeLiPoker poker math library. No outside data is used.
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