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Hart Race Hold 'Em

Introduction

Hart Race Hold 'em is a poker variant by Draft Kings. It is a tournament between you and Kevin Hart, who goes all in every hand. Meanwhile, the player has free will in going all in or folding. To compensate for no free will, Kevin starts with twice as many chips.

 

Rules

The game follows conventional Texas Hold 'Em rules, which I assume the reader is familiar with. However, here is some terminology:

  • Dealer — The dealer is not the one physically dealing cards, but the side to act last.
  • Small Blind — This is a mandated bet. In the case of this game it is one chip and made by the side not dealing.
  • Big Blind — This is another mandated bet. In the case of this game it is two chips and made by the side dealing.
  • All In — This is a bet for the amount of chips held by the side less chips.
  1. The game is based on Texas Hold 'em, which I assume the reader is familiar with.
  2. The game is played in the form of a poker tournament. The player to attain all the chips first, wins.
  3. The tournament is between the player and a video representation of Kevin Hart.
  4. The player starts with 80 chips and Kevin with 160.
  5. The turn to deal alternates. It is randomized who goes first.
  6. The side not dealing bets one chip as the small blind and the dealer bets two as the big blind.
  7. If the player is dealing, Kevin shall always go all in. The player may then call or fold his two-unit big blind bet.
  8. If Kevin is dealing, he shall always go all in. The player may then call or fold his one-unit small blind bet.
  9. If the player loses with a full house, where both sides use both hole cards, then the player shall immediately win the tournament and his wager paying as follows:
    • Four of a kind or better — 1000 to 1
    • Full house with three aces — 100 to 1
    • All other full houses — 10 to 1
  10. For purposes of the bad beat rule, if a card is deprecated, then the hand is counted as an ordinary loss for the player. For example, consider this situation:

    • Player: QQ
    • Kevin: KK
    • Board: AAAQ5

    In this case, the player takes a bad beat, losing AAAQQ vs. AAAKK. However, it isn't clear if the player's two queens were used. Any two of the three queens could be used. In this situation, one of the player's queens is definitely used, but the other is "deprecated," meaning it matches a card on the board and it doesn't matter which is actually used to determine the player's best hand. Since both player queens didn't have to be used to make the best hand, the player does NOT win per the bad beat rule.

  11. Otherwise (outside of winning via a bad beat), if the player wins the tournament, his wager pays even money.

Strategy

As simple as this game seems, calculating the optimal strategy would be very difficult. One would need to consider:

  • Your own cards
  • Whether you're the small or big blind (you have more to lose by folding as the big blind)
  • Stack sizes.

The key to beating this game, or any tournament where you're the stronger player, is to gradually grind down your opponent with stronger starting hands. With 240 chips in the game, it's dangerous when you both have about half, because Kevin can get lucky with the community cards. The stronger player (you) has time on your side and should play a patient slow game. Meanwhile, the weaker player (Kevin) should be aggressive, taking big chances, hoping to win big pots by sheer luck.

That said, the greater the size of the smaller stack, the more conservatively you should play. If either player is short on chips, you don't need to be as picky about what hands to play.

That said, this following table shows the probability of a win, loss and draw of all 169 possible starting hands. The expected value is the probability of winning less the probability of losing. I know this doesn't lead directly to correct strategy in this game, so consider it just a starting point.

Probabilities in Texas Hold 'Em

Hand Win Lose Draw EV
2/3 suited 0.330920 0.611231 0.057849 -0.280311
2/4 suited 0.339179 0.602599 0.058221 -0.263420
2/5 suited 0.349295 0.592309 0.058396 -0.243013
2/6 suited 0.348375 0.594996 0.056628 -0.246621
2/7 suited 0.354398 0.591281 0.054321 -0.236882
2/8 suited 0.376792 0.571360 0.051848 -0.194567
2/9 suited 0.399730 0.551426 0.048844 -0.151697
2/T suited 0.425402 0.528612 0.045986 -0.103210
2/J suited 0.452024 0.504461 0.043514 -0.052437
2/Q suited 0.481018 0.477637 0.041344 0.003381
2/K suited 0.512400 0.448165 0.039436 0.064235
2/A suited 0.555063 0.407485 0.037453 0.147578
3/4 suited 0.357274 0.584435 0.058292 -0.227161
3/5 suited 0.367587 0.573728 0.058686 -0.206141
3/6 suited 0.366854 0.576183 0.056963 -0.209329
3/7 suited 0.373036 0.572317 0.054648 -0.199281
3/8 suited 0.382826 0.565356 0.051819 -0.182530
3/9 suited 0.408068 0.542783 0.049149 -0.134715
3/T suited 0.433785 0.519935 0.046281 -0.086150
3/J suited 0.460418 0.495785 0.043797 -0.035368
3/Q suited 0.489384 0.468999 0.041617 0.020385
3/K suited 0.520701 0.439602 0.039697 0.081100
3/A suited 0.563351 0.398944 0.037705 0.164406
4/5 suited 0.385325 0.556257 0.058418 -0.170932
4/6 suited 0.384810 0.558143 0.057047 -0.173334
4/7 suited 0.391089 0.554103 0.054808 -0.163014
4/8 suited 0.401028 0.546995 0.051977 -0.145967
4/9 suited 0.414071 0.536832 0.049097 -0.122761
4/T suited 0.442041 0.511431 0.046528 -0.069390
4/J suited 0.468687 0.487278 0.044036 -0.018591
4/Q suited 0.497630 0.460524 0.041845 0.037106
4/K suited 0.528888 0.431196 0.039916 0.097693
4/A suited 0.571378 0.390705 0.037917 0.180673
5/6 suited 0.403482 0.540814 0.055704 -0.137332
5/7 suited 0.409790 0.536279 0.053931 -0.126489
5/8 suited 0.419905 0.529005 0.051091 -0.109100
5/9 suited 0.433127 0.518690 0.048183 -0.085563
5/T suited 0.449390 0.505065 0.045545 -0.055675
5/J suited 0.478209 0.478472 0.043318 -0.000263
5/Q suited 0.507135 0.451746 0.041119 0.055388
5/K suited 0.538339 0.422480 0.039181 0.115858
5/A suited 0.580641 0.382183 0.037176 0.198459
6/7 suited 0.428295 0.520859 0.050846 -0.092565
6/8 suited 0.438185 0.513320 0.048495 -0.075135
6/9 suited 0.451512 0.502946 0.045542 -0.051434
6/T suited 0.468002 0.489188 0.042810 -0.021186
6/J suited 0.485742 0.473624 0.040633 0.012118
6/Q suited 0.516792 0.444541 0.038666 0.072251
6/K suited 0.548047 0.415232 0.036721 0.132815
6/A suited 0.581789 0.383672 0.034539 0.198117
7/8 suited 0.456841 0.498114 0.045045 -0.041273
7/9 suited 0.469903 0.487548 0.042549 -0.017645
7/T suited 0.486512 0.473732 0.039756 0.012781
7/J suited 0.504545 0.458049 0.037406 0.046496
7/Q suited 0.525235 0.439190 0.035576 0.086045
7/K suited 0.558463 0.407708 0.033828 0.150755
7/A suited 0.593867 0.374188 0.031946 0.219679
8/9 suited 0.488563 0.472548 0.038890 0.016015
8/T suited 0.505091 0.458404 0.036504 0.046687
8/J suited 0.523117 0.442804 0.034080 0.080313
8/Q suited 0.544170 0.423816 0.032014 0.120355
8/K suited 0.567904 0.401657 0.030439 0.166247
8/A suited 0.605078 0.366202 0.028720 0.238876
9/T suited 0.523769 0.443218 0.033013 0.080551
9/J suited 0.541120 0.427870 0.031010 0.113249
9/Q suited 0.562228 0.408942 0.028831 0.153286
9/K suited 0.586381 0.386612 0.027007 0.199770
9/A suited 0.615097 0.359472 0.025431 0.255624
T/J suited 0.561548 0.410991 0.027462 0.150557
T/Q suited 0.581706 0.392355 0.025938 0.189351
T/K suited 0.605871 0.370099 0.024030 0.235771
T/A suited 0.634889 0.342841 0.022269 0.292048
J/Q suited 0.590709 0.385525 0.023767 0.205184
J/K suited 0.614766 0.363419 0.021816 0.251347
J/A suited 0.643976 0.336123 0.019901 0.307854
Q/K suited 0.624084 0.356076 0.019840 0.268008
Q/A suited 0.653137 0.328960 0.017903 0.324177
K/A suited 0.662196 0.321303 0.016500 0.340893
2/3 unsuited 0.292394 0.646330 0.061276 -0.353935
2/4 unsuited 0.301174 0.637179 0.061647 -0.336005
2/5 unsuited 0.311938 0.626245 0.061817 -0.314307
2/6 unsuited 0.310787 0.629284 0.059930 -0.318497
2/7 unsuited 0.317103 0.625430 0.057467 -0.308327
2/8 unsuited 0.340868 0.604315 0.054817 -0.263447
2/9 unsuited 0.365170 0.583211 0.051618 -0.218041
2/T unsuited 0.392391 0.559024 0.048585 -0.166633
2/J unsuited 0.420493 0.533523 0.045984 -0.113031
2/Q unsuited 0.451099 0.505191 0.043710 -0.054091
2/K unsuited 0.484228 0.474053 0.041719 0.010174
2/A unsuited 0.529473 0.430902 0.039625 0.098571
3/4 unsuited 0.320663 0.617745 0.061592 -0.297082
3/5 unsuited 0.331650 0.606354 0.061996 -0.274705
3/6 unsuited 0.330698 0.609145 0.060157 -0.278447
3/7 unsuited 0.337179 0.605134 0.057687 -0.267955
3/8 unsuited 0.347498 0.597822 0.054679 -0.250324
3/9 unsuited 0.374279 0.573889 0.051832 -0.199610
3/T unsuited 0.401552 0.549661 0.048787 -0.148109
3/J unsuited 0.429668 0.524157 0.046176 -0.094489
3/Q unsuited 0.460249 0.495860 0.043891 -0.035611
3/K unsuited 0.493313 0.464799 0.041889 0.028514
3/A unsuited 0.538553 0.421661 0.039786 0.116892
4/5 unsuited 0.350748 0.587642 0.061609 -0.236894
4/6 unsuited 0.350030 0.589820 0.060150 -0.239790
4/7 unsuited 0.356617 0.585621 0.057762 -0.229003
4/8 unsuited 0.367092 0.578156 0.054752 -0.211064
4/9 unsuited 0.380858 0.567437 0.051705 -0.186579
4/T unsuited 0.410554 0.540472 0.048974 -0.129918
4/J unsuited 0.438687 0.514960 0.046353 -0.076272
4/Q unsuited 0.469248 0.486694 0.044058 -0.017446
4/K unsuited 0.502252 0.455702 0.042046 0.046549
4/A unsuited 0.547329 0.412735 0.039936 0.134594
5/6 unsuited 0.370128 0.571242 0.058631 -0.201114
5/7 unsuited 0.376747 0.566507 0.056746 -0.189761
5/8 unsuited 0.387413 0.558862 0.053725 -0.171449
5/9 unsuited 0.401367 0.547984 0.050648 -0.146617
5/T unsuited 0.418575 0.533556 0.047869 -0.114981
5/J unsuited 0.449046 0.505429 0.045525 -0.056382
5/Q unsuited 0.479590 0.477188 0.043222 0.002402
5/K unsuited 0.512539 0.446260 0.041201 0.066279
5/A unsuited 0.557423 0.403492 0.039085 0.153931
6/7 unsuited 0.396538 0.550083 0.053379 -0.153545
6/8 unsuited 0.406966 0.542148 0.050886 -0.135182
6/9 unsuited 0.421034 0.531207 0.047759 -0.110173
6/T unsuited 0.438481 0.516641 0.044878 -0.078160
6/J unsuited 0.457135 0.500250 0.042615 -0.043115
6/Q unsuited 0.489965 0.469484 0.040551 0.020481
6/K unsuited 0.522971 0.438506 0.038523 0.084466
6/A unsuited 0.558703 0.405054 0.036243 0.153649
7/8 unsuited 0.426933 0.525917 0.047150 -0.098984
7/9 unsuited 0.440721 0.514764 0.044515 -0.074044
7/T unsuited 0.458298 0.500135 0.041567 -0.041837
7/J unsuited 0.477261 0.483623 0.039116 -0.006361
7/Q unsuited 0.499044 0.463730 0.037226 0.035313
7/K unsuited 0.534173 0.430426 0.035400 0.103747
7/A unsuited 0.571695 0.394871 0.033434 0.176824
8/9 unsuited 0.460683 0.498743 0.040574 -0.038059
8/T unsuited 0.478181 0.483756 0.038063 -0.005575
8/J unsuited 0.497137 0.467333 0.035530 0.029803
8/Q unsuited 0.519305 0.447309 0.033385 0.071996
8/K unsuited 0.544316 0.423913 0.031771 0.120403
8/A unsuited 0.583742 0.386289 0.029969 0.197452
9/T unsuited 0.498157 0.467524 0.034320 0.030633
9/J unsuited 0.516394 0.451370 0.032236 0.065024
9/Q unsuited 0.538620 0.431411 0.029969 0.107209
9/K unsuited 0.564076 0.407838 0.028086 0.156238
9/A unsuited 0.594497 0.379041 0.026461 0.215456
T/J unsuited 0.538260 0.433306 0.028434 0.104954
T/Q unsuited 0.559474 0.413658 0.026868 0.145816
T/K unsuited 0.584943 0.390165 0.024893 0.194778
T/A unsuited 0.615681 0.361248 0.023071 0.254433
J/Q unsuited 0.569062 0.406369 0.024569 0.162694
J/K unsuited 0.594412 0.383039 0.022549 0.211374
J/A unsuited 0.625352 0.354087 0.020562 0.271265
Q/K unsuited 0.604323 0.375207 0.020471 0.229116
Q/A unsuited 0.635088 0.346451 0.018461 0.288637
K/A unsuited 0.644694 0.338292 0.017014 0.306401
Pair of 2's 0.493852 0.487171 0.018977 0.006680
Pair of 3's 0.528392 0.454531 0.017077 0.073862
Pair of 4's 0.562565 0.422109 0.015326 0.140456
Pair of 5's 0.596400 0.389902 0.013698 0.206498
Pair of 6's 0.627000 0.361305 0.011694 0.265695
Pair of 7's 0.657254 0.332533 0.010213 0.324720
Pair of 8's 0.687174 0.303913 0.008913 0.383261
Pair of 9's 0.716657 0.275511 0.007832 0.441145
Pair of T's 0.746603 0.246367 0.007030 0.500236
Pair of J's 0.771530 0.222140 0.006330 0.549389
Pair of Q's 0.796320 0.197817 0.005863 0.598503
Pair of K's 0.821173 0.173260 0.005567 0.647914
Pair of A's 0.849319 0.145245 0.005436 0.704074

The good news is that DraftKings kindly provides the exact strategy according to your cards, stack sizes, and whether you're the small or big blind. You can find this strategy on the game by clicking settings (the gear) and then "pay table."

Analysis

The following table (kindly provided by DraftKings) shows the probability of all possible outcomes, assuming optimal strategy. The lower right cell shows a house edge of 1.73%.

Probabilities in Texas Hold 'Em

Event Pays Probability Return
Bat beat, quads+ 1000 0.000001 0.001174
Bat beat, aces full 100 0.000050 0.005031
Bad beat, any boat 10 0.000768 0.007678
Normal Win 1 0.483992 0.483992
Loss -1 0.515188 -0.515188
Total   1.000000 -0.017313

Video

Enjoy this video of a tournament I played through.

External Links